Heat Adaptation and Human Performance in aWarming Climate

Steven Sexton, Zhenxuan Wang, and Jamie T. Mullins*

March 2, 2021

Abstract

Labor productivity, human capital formation, and income growth decline amid hotambient temperatures. The implications of such temperature sensitivity for climatechange damages depend upon the capacity for human adaptation to persistent tem-perature changes—as opposed to idiosyncratic temperature variation. Studying mil-lions of collegiate track and field performances from 2005 to 2019, this paper showsthat performance diminution in hot ambient conditions is mitigated by heat adapta-tion, a physiological response to heat stress and associated physical and cognitive im-pairments. Across varied specifications of the temperature-performance relationship,adaptation reduces performance losses from alternative climate change scenarios bymore than 50%.

Keywords: adaptation, climate change, human performanceJEL Codes: Q51, Q54, Q55, J24

*Sexton: Sanford School of Public Policy, Duke University, 201 Science Drive, Durham, NC 27708,USA, steven.sexton@duke.edu. Wang: University Program in Environmental Policy, Duke University, 201Science Drive, Durham, NC 27708, USA, zhenxuan.wang@duke.edu. Mullins: Department of ResourceEconomics, University of Massachusetts Amherst, 80 Campus Center Way, Amherst, MA 01035, USA,jmullins@umass.edu.

1 Introduction

As high ambient temperatures are expected to become more common due to global cli-

mate warming, evidence is accumulating that exposures to such conditions impair human

performance across many domains. Scholastic test scores fall, learning is diminished, and

labor supply and productivity decline (Graff Zivin and Neidell 2014; Garg, Jagnani and

Taraz 2020; Graff Zivin, Hsiang and Neidell 2018; Park 2020; Park et al. 2020). In labora-

tory settings, decision-making and cognition are impaired at even moderately high am-

bient temperatures (Seppanen, Fisk and Faulkner 2003). Such impacts result from physi-

ological responses to hot environments that favor heat dissipation, including increases in

cutaneous blood flow, at the expense of blood flow to muscles and other organs, including

the brain (Robinson et al. 1943; Yoshimura 1960; Wyndham 1967; Brinnel, Cabanac and

Hales 1987). They imply losses in human capital formation and labor productivity from a

warming climate that are evidenced by the temperature sensitivity of aggregate economic

production (Hsiang 2010; Dell, Jones and Olken 2012; Burke, Hsiang and Miguel 2015b).

These temperature impacts are typically estimated from idiosyncratic changes in tem-

perature, and, thus, they predict losses from a mean-shift in the temperature distribu-

tion due to climate change in the absence of human adaptation to persistent temperature

changes (Auffhammer et al. 2013; Burke and Emerick 2015; Hsiang 2016; Graff Zivin,

Hsiang and Neidell 2018; Dell, Jones and Olken 2014; Deschenes and Greenstone 2007,

2011). Though mortality impacts of weather and efforts to mitigate the harm from tem-

perature extremes vary by climate, evidence of human adaptation to climate change is

sparse, even in the climate-exposed agriculture sector (Schlenker and Roberts 2009; De-

schenes and Greenstone 2011; Burke and Emerick 2015; Heutel, Miller and Molitor 2020).

The lack of evidence of climate change adaptation may reflect incorrect perceptions of

harms or high costs of behavior changes that moderate the ill-effects of heat exposure

(David et al. 1975; Mendelsohn 2000; Heutel, Miller and Molitor 2020; Moore et al. 2019).

This paper estimates the human performance effect of heat adaptation, or acclimatiza-

1

tion, and its implications for estimates of human performance losses from climate change.

Acclimatization is defined by the U.S. Centers for Disease Control and Prevention (CDC)

as “the beneficial physiological adaptations that occur during repeated exposure to a hot

environment.” Such adaptations occur within one week and persist amid heat exposure,

yielding reduced body temperature, improved skin blood flow, improved thermal toler-

ance, increased sweat rate, and other physiologic responses that improve thermal comfort

in hot environments and mitigate the consequences of heat stress, including diminished

performance (Periard, Racinais and Sawka 2015). The universal human capacity for ac-

climatization has been investigated, predominantly in occupational and military settings,

since at least 1768, when it was documented in Europeans exposed to East and West

Indian climates (Lind 1768; Horvath and Shelley 1946; Hellon et al. 1956; Strydom et al.

1966; Wyndham 1967; Pandolf, Burse and Goldman 1977; Henschel, Taylor and Keys 1943;

Robinson et al. 1943; Lind 1963; Shvartz et al. 1973). European colonists were observed to

“enjoy a pretty good state of health” upon acclimatization (Lind 1768).

We employ data on millions of outdoor, collegiate track and field performances by

hundreds of thousands of athletes and exploit idiosyncratic variation in competition tem-

peratures and preceding 7-day temperature exposures to identify their causal effects on

performance. Performance losses from projected end-of-century climate change are sim-

ulated, as are the losses avoided by acclimatization.

We estimate statistically significant effects of acclimatization: performance in hot tem-

peratures is diminished for some events, but previous exposures to hot temperatures

mitigate these performance losses. Such human adaptation is projected to reduce per-

formance losses from climate change by at least 50% relative to projections that ignore

acclimatization. Thus, we show existing studies that ignore acclimatization or exclude

sufficient temperature lags are confounded by lagged temperature effects that attenuate

estimates of performance sensitivity to contemporaneous temperatures.1 At the same

1See for instance Park (2020); Baylis (2020); Dundas and von Haefen (2020); Heyes and Saberian (2019);Heilmann and Kahn (2019). Adhvaryu, Kala and Nyshadham (2020); Somanathan et al. (Forthcoming) are

2

time, these temperature parameters overstate performance losses from climate change by

ignoring capacity to adapt to a mean temperature shift. The magnitude of these biases in-

creases in the variance of contemporaneous and lagged temperatures because contempo-

raneous temperature less effectively proxies for the omitted lagged temperature effects.2

Even where lagged temperature effects are modelled in the previous literature in order

to deconfound contemporaneous temperature effects, their implications for adaptation to

climate change are ignored.3

Though we exploit idiosyncratic temperature variation to identify the human capacity

for acclimatization, we use the identified parameters to estimate the performance conse-

quences of acclimatization amid alternative projections of future temperatures defined by

increased mean temperatures relative to today. On average, the additional acclimatization

attributable to a long-term shift in mean temperature will persist amid a persistent mean

shift. Hence, a relatively short 1-2 week spell of performance diminution during adapta-

tion is rewarded by long-term adaptation to climate warming, the benefits of which dwarf

short-lived adaptation costs. Beyond adaptation to the mean temperature shift, our sim-

ulations also admit adaptation to intra-annual and intra-seasonal temperature variation,

though this does not change markedly in our temperature projections.

The study of acclimatization in this setting is advantageous for several reasons. First,

performance in track and field events is precisely, consistently, and objectively measured

by distance, height, or speed, and directly comparable across venues, particularly when

conditioned on event and venue-specific factors. Second, our reliance upon student ath-

lete performances allows credible measurement of pre-competition “training” tempera-

ture exposures so long as collegiate athletes reside at or near their home institutions be-

prominent examples of models that include temperature lags and avoid such bias.2The Pearson correlation of contemporaneous daily average temperature and the preceding one-week

average of daily average temperature is 0.532 in our data. Hence, we show failure to model lagged temper-ature effects introduces considerable bias in projections of future climate change harms.

3Though they do not include temperature lags in their models of temperature effects on time allocationbetween labor and leisure, Graff Zivin and Neidell (2014) explore the possibility for adaptations inclusiveof acclimatization to mute temperature induced reallocations. They do not find robust evidence of acclima-tization.

3

tween collegiate competitions. Third, by exploiting random variation in one-week spells

of weather, this study identifies the causal performance effects of a rapid adaptive re-

sponse while flexibly controlling for individual athlete characteristics. Studies of other

forms of climate change adaptation are hindered by the temporal invariance of climate

over relevant time frames, and, therefore, are subject to omitted variables bias, including

that induced by endogenous location choices. Because the beneficial effects of human ac-

climatization emerge quickly and persist with continued exposure to high temperatures,

this setting provides the unique opportunity to leverage plausibly random temperature

variation to identify an adaptive response that is relevant to a long-term mean shift in the

temperature distribution.

The physiological consequences of heat stress and the responses afforded by acclima-

tization both indicate that the performance effects we estimate likely generalize to other

populations and to other performance settings, including those that are relatively more

cognitively demanding. In particular, heat stress diminishes cerebral blood flow, leading

to the accumulation of heat in the brain, which has been shown to acutely impact brain

function. In fact, the brain is particularly sensitive to heat, and acclimatization is shown

to mitigate heat-induced decline in cognitive function (Nielsen and Nybo 2003; Nybo

and Nielsen 2001; Brinnel, Cabanac and Hales 1987; Hales, Hubbard and Gaffin 2010; Wi-

jayanto et al. 2017; Radakovic et al. 2007; Racinais et al. 2017). Moreover, acclimatization

is induced by exposure to elevated temperature, not by physical activity per se, and it is

observed in experimental settings among young and old, and trained and untrained in-

dividuals. It is evidenced by performance of physical, cognitive, and occupational tasks

(Hanna and Brown 1983; Periard, Racinais and Sawka 2015; Dresoti 1935; Horvath and

Shelley 1946; Hellon et al. 1956; Strydom et al. 1966; Wyndham 1967; Robinson et al. 1943;

Pandolf, Burse and Goldman 1977; Pandolf et al. 1988; Shvartz et al. 1973; Wagner et al.

1972; Armstrong and Maresh 1991). There are no known demographic limitations to ac-

climatization (Hanna and Brown 1983; Edholm and Weiner 1981). Consequently, the U.S.

4

Occupational Safety and Health Administration (OSHA) and the CDC recommend ac-

climatization protocols for all heat-exposed workers across occupations.

This paper proceeds by introducing data and methods in section 2. Section 3 presents

results. Section 4 discusses the implications of these results.

2 Data and Methods

2.1 Identification of Heat and Acclimatization Effects

The extent to which performance is diminished amid hot temperatures is assessed sepa-

rately for sprint, strength and endurance events contested at collegiate competitions from

2005-2019. Standardized measures of 3.8 million performances are related to a function

of contemporaneous daily average temperature, g(T), that is flexibly modeled as either a

step function admitting a unique temperature response for each 5◦F temperature interval,

a quadratic or cubic function of temperature, or a linear or cubic temperature spline. Stan-

dardized performance for athlete i in year j ∈ {1, 2, 3, 4} of athletic eligibility competing

in event e during meet m at venue z in week-of-season w is estimated as:

yijemzw = g(Tm) + δ′Xem + κdiz + αi + σj + ρiez + τw + εijemzw (1)

where Xem is a vector of control variables that includes precipitation, dew point, ozone,

and “wind assist”, an event-and-competition-specific measure of wind speed and direc-

tion; diz is the distance between the home institution of athlete i and venue z. We control

for fixed effects by athlete (αi), athlete year of eligibility, i.e., freshman, sophomore, etc.,

(σj), a triple interaction of indicators for event, venue, and home-field advantage (ρiez),

and week of competitive season (τw). εijemzw is an idiosyncratic error. Standard errors are

two-way clustered by athlete and competition.4

4Collegiate competition schedules are typically determined months in advance of competition in coor-dination among teams and athletic conferences. That is, venues are selected long before accurate weather

5

The performance response to pre-competition temperature exposures is investigated

by interacting the competition temperature function with f (H), a function of 7-day (or

14-day) average daily temperature at the athlete’s home institution immediately preced-

ing competition. This function is alternatively modeled as (1) the difference in the pre-

competition average temperature exposure and competition temperature, (2) an indicator

for whether the pre-competition average temperature exposure exceeds 60◦F, (3) the mean

daily average temperature during the pre-competition exposure period, and (4) the count

of days during the pre-competition exposure period for which average temperature ex-

ceeded 60◦F.5

The response to f (H) is allowed to vary across g(T) by interacting the two functions.

For identification of acclimatization effects, we specify g(·) as the competition tempera-

ture step function previously defined. Thus, we estimate:

yijemzw = ∑b∈B\{55−60}

βbtempbinbm + ∑

b∈Bγb

(tempbinb

m × f (Him))

+ δ′Xem + κdiz + αi + σj + ρiez + τw + εijemzw (2)

where tempbinbm are indicators for the temperature bin that includes Tm for b ∈ B = {<

40, 40− 45, . . . , 70− 75,> 75}. For performances impeded by hot competition temper-

forecasts are available. Hence, it is extremely unlikely venues are selected according to weather, thoughthey may be determined as a function of climate, i.e., mean weather. Variation in outcomes due to selectionalong mean venue characteristics is absorbed by venue fixed effects. To test for selection on weather, werelated venue adoption probability for each observed competition to a step function of daily average tem-perature on event date, meet fixed effects, and venue-by-month-of-year fixed effects. We find no evidenceof selection away from venues that experience hot temperatures on competition day. However, we estimatestatistically significant negative effects of cold weather on venue selection probability. We attribute thiseffect to the cancellation of scheduled events due to winter storms or cold shocks. Results are availablefrom the authors upon request. These results notwithstanding, we conclude that were venues selected toavoid hot temperatures, and were such selection of relatively cool venues to advantage proximal teams alsoexposed to relatively cool weather to an extent beyond that captured by their proximity and any home-fieldadvantage, for which we control, then we would attribute the relatively strong performances of such teamsto relatively cool pre-competition temperatures. This would induce a downward bias in our estimates ofacclimatization.

5Results reported in the manuscript are for f (H) defined by a 7-day pre-competition exposure period.Results are similar if f (H) is a function of a 14-day exposure period, as shown in the appendix.

6

atures, i.e., βb < 0, acclimatization is identified as statistically significant and positive

marginal effects of pre-competition heat exposures, i.e. γb > 0.

2.2 Simulating Performances in Warmer Climates

With sufficient density of performance observations in each competition temperature bin

for each bin of pre-competition temperature exposures, we could estimate the temperature-

performance relationship non-parametrically with sufficient temperature granularity to

inform projections of performance in alternative climate warming scenarios. Absent data

with such density of observations, we estimate continuous, semi-parametric temperature

functions in the spirit of (2). In our baseline specification, the competition temperature

function, g(T), is flexibly modeled as a linear spline with knots at 50, 60, and 70◦F, and

f (H) is modeled as a linear spline with knots at 50◦F and 60◦F, representing approx-

imately the 33rd and 66th percentiles of the pre-competition temperature distribution.

Specifically, g( f (H), T) is defined as:

g( f (H), T)) = β0T +7

∑k=5

βk1[T > 10k](T − 10k)

+2

∑p=0

max(H − Cp, 0)×[

βp0T +

7

∑k=5

βpk1[T > 10k](T − 10k)

](3)

where Cp (p = 0, 1, 2) is the 0, 33rd, and 66th percentiles of the historic training tempera-

ture distribution.

We use parameter estimates from these models to generate conditional predictions of

future performances pursuant to future temperature scenarios described in the next sec-

tion. We project future performances based on four distinct assumptions about acclima-

tization. In the first simulation, pre-competition temperatures are completely omitted

from the estimation of the temperature-performance relationship. This is consistent with

treatment in some of the literature that precedes us. The resulting competition temper-

7

ature parameters are used to predict future performances as a function of future com-

petition temperature projections. In the second simulation, we estimate (3) inclusive of

pre-competition temperature exposures and use the full set of temperature parameters to

predict future performances as a function of projected competition and pre-competition

temperatures. In this way, we expressly model acclimatization due to hotter competition

and pre-competition temperatures.

A third simulation estimates parameters as in (3) but assumes only competition tem-

peratures are hotter than the historic record used in estimation. This scenario is deemed

highly unlikely because there is no reason to expect only competition days become hot-

ter due to climate change. However, this simulation mirrors others studying adaptation

that conservatively assume agents do not adapt beyond actions observed in the historical

record. In the present setting, however, the adaptation is a consequence of an autonomous

response that exhibits increasing returns to performance at higher temperatures over the

study period.

A final simulation estimates (3) to identify competition temperature effects uncon-

founded by pre-competition temperature exposures, but projects future performances as

a function only of competition temperature. This simulation effectively “turns off” the

human capacity for heat adaptation. It is distinguished from the first simulation by de-

confounding competition temperature responses from adventitious, or random, acclima-

tization due to idiosyncratic weather variation in the historical data. It, thus, excludes

both the systematic acclimatization in response to a mean shift in temperature that is

modeled in our second simulation, as well as the adventitious acclimatization due to ran-

dom weather fluctuations that confounds the first simulation.

8

2.3 Data

2.3.1 Dependent Variable

Track and field performance outcomes are reported by Direct Athletics, Inc., which oper-

ates the official track and field results reporting system of the National Collegiate Athletic

Association. All outdoor results from 2005-2019 were scraped from a website operated by

Direct Athletics, as were competition date, event type, venue, athlete gender, year of eli-

gibility, home institution, and “wind assist.” These data include 3.8 million results across

8,486 competitions for 3,166 teams and 281,328 athletes. Venue and home institution zip

codes were obtained from Google Maps.

In order to compare performances across events, and following Mullins (2018), a result

i in event e, Resultie, is standardized as:

yie =−|WorldRecorde − Resultie|

SD(Resulte),

where WorldRecorde is the 2019 World Record in event e and SD(Resulte) is the standard

deviation of event e results reported in the data. The negative sign ensures that an increase

in this standardized measure is associated with a move toward the world record, which is

always an improvement in performance.6 Men’s and women’s competitions are treated as

separate events. Events are classified as “Sprint”, “Strength”, or “Endurance” as indicated

in Appendix Table A1.7 Summary statistics for standardized results and independent

variables are reported in Appendix Table A2.

6World records are reported by World Athletics: https://www.worldathletics.org/records/by-category/world-records.

7Following convention, endurance events include all running races of 800-meter distance or greater.Strength events include all jumping and throwing events.

9

2.3.2 Temperature

Pre-competition and competition temperature observations are the daily average temper-

atures recorded by the Global Historical Climatological Network (GHCN) and reported

by the National Centers for Environmental Information. For each training and competi-

tion zip code, daily average temperatures are computed as the inverse-distance-weighted

average of the observations of all weather stations within 50-kilometers of the respective

zip code centroids. For missing observations from these weather stations, we interpo-

late temperatures by taking the weighted average of the temperatures within 5 days of

the missing observation with higher weights assigned to observations in greater proxim-

ity to the missing observation. Competition weather characteristics, including tempera-

ture, are computed as averages across days of the competition because dates on which

specific events are contested at competitions are unreported in the data. Because we

do not precisely measure event-specific competition temperatures or athlete-specific pre-

competition temperature exposures, our estimates of temperature responses are attenu-

ated by measurement error.

2.3.3 Control Variables

Our main analyses control for inverse-distance-weighted average precipitation and dew

point as observed at weather stations within 50 kilometers of zip code centroids, and wind

assist as observed at the time and venue of competition. Precipitation is measured in

inches per day. Dew point is specified as a step function with intervals of 5◦F. Wind assis-

tance is measured in meters per second. We also control for daily average ozone measured

in parts per million by air quality monitoring stations of the Environmental Protection

Agency (EPA) Air Quality System. Zip-code measures are the inverse-distance-weighted

average of observations within 50 kilometers. Results are robust to the exclusion of these

control variables, as reported in Appendix A1.5.

10

2.3.4 Future Temperatures

Simulations of the performance impacts of climate change rely upon assumptions about

future temperature distributions. In our baseline future temperature scenario, we assume

the same athletes compete in the same competitions amid the temperatures projected for

80 years in the future. Temperatures for these days are projected by the NASA Earth

Exchange Global Daily Downscaled Projections (NEX-GDDP) dataset. These data report

daily temperatures for each of 21 climate models of the Coupled Model Intercompari-

son Project 5 (CMIP5) model set that projects daily temperatures. Our baseline model re-

lies upon temperature projections pursuant to the Representative Concentration Pathway

(RCP) 8.5 “business as usual” scenario, wherein emissions continue to rise throughout the

21st century (van Vuuren et al. 2011). Daily maximum and minimum temperatures are

projected for each climate model at a spatial resolution of 25 square-kilometers. We aver-

age these daily maximum and minimum temperatures to generate a daily average tem-

perature, and we further average these daily averages across all 21 climate models. Zip

code projections are the daily average temperatures projected for the 25 square kilome-

ters nearest the zip code centroid. Relative to observations in the historical record of this

analysis, these projections result in an average 7.4◦F increase in competition temperature

and an average 7.0◦F increase in one-week pre-competition temperature.

We also report results in Appendix A1.3 for three alternative future temperature sce-

narios, including one that employs climate model projections of warming from stabilized

carbon emissions over the century, i.e., RCP4.5. Additionally, we consider mean shifts in

daily average temperatures of 1, 2, and 4◦F. The distributions of historical temperatures

and temperature projections by the climate models are shown in Appendix Figure A1.

These distributions are also summarized in Appendix Table A2.

11

3 Results

3.1 Temperature Effects

For strength, sprint, and endurance events, performance is estimated to generally increase

at a decreasing rate in temperature, yielding concave performance-temperature relation-

ships. This is shown in Figure 1, which depicts the estimated temperature step func-

tions in blue, and 95% confidence intervals defined by the gray-dashed lines. The vertical

axis in each figure marks the change in performances relative to 55-60◦F. The horizon-

tal axis indicates contemporaneous (competition) temperature intervals. The histogram

in each panel of Figure 1 shows the distribution of daily average competition tempera-

ture in the analyzed data for each event category. This concave temperature relationship

exhibited across event categories in the figure is common to many outcomes of interest

to economists, including economic growth, labor supply, and crop yields, and it implies

an optimal temperature for performance beyond which performances suffer (e.g., Burke,

Hsiang and Miguel 2015a; Graff Zivin and Neidell 2014; Schlenker and Roberts 2009).

Sprint and strength event performances improve on average amid warmer competi-

tion temperatures up to 75◦F, beyond which performance declines modestly and insignif-

icantly. In contrast, performances in endurance events decline significantly when tem-

peratures are above 60◦F. An absence of significant performance decline for sprint and

strength events is unsurprising: we do not observe extremely hot average temperatures

in the data because collegiate competition occurs in spring in North America; and the

short-duration efforts that characterize sprint and strength events are unlikely to generate

sufficient metabolic heat to induce heat stress amid mild temperatures. Absent heat stress,

acclimatization is not expected to provide discernible performance gains (Periard, Raci-

nais and Sawka 2015). Therefore, our subsequent analysis focuses on endurance events.

Further results for strength and sprint events are reported in Appendix A1.11 and are

appropriately interpreted as placebo, or falsification, tests.

12

Heterogeneity in the competition-temperature response function by pre-competition

temperature exposure is demonstrated in Figure 2. It depicts the performance effects of

competition temperature separately for the one-third of performances preceded by the

coolest training temperatures (in blue) and for the one third of performances preceded

by the warmest training temperatures (in red). Dashed lines indicate +/- two standard

errors. Panel A displays an estimated quadratic function of competition temperature.

An estimated cubic function of temperature is shown in panel B. Panel C depicts an es-

timated linear spline with two knots at 50◦F and 60◦F, and a cubic spline with knots at

50◦F, 56◦F, and 63◦F, respectively the 25th, 50th, and 75th percentiles of average training

temperatures, is shown in panel D. With each of these specifications, both the level and

temperature of peak performance are estimated to be greater for performances preceded

by hot temperature exposure than for those preceded by relatively cool temperature ex-

posure. The differences in performance levels are statistically significant at the 5% level

or greater across a range of hot temperatures for each specification. At cool competition

temperatures, performances are similar whether preceded by relatively hot or cold expo-

sures, indicative of pre-competition exposure to high temperatures mitigating heat stress,

as opposed to providing a generalized performance advantage.

Estimates of the marginal effect of the difference in pre-competition and competition

temperature exposures at each 5◦F interval of competition temperature, i.e., γb in (2), are

reported in Table 1. As reported in column (1) of the table, the hotter is pre-competition

exposure relative to competition temperature, the better is performance at warm com-

petitions, ceteris paribus. The same is true for pre-competition exposures defined by the

fourteen days preceding competition, as we show in the appendix. Below daily aver-

age competition temperatures of 55◦F, temperature differences have no statistically sig-

nificant performance effect. Above daily average competition temperatures of 60◦F, the

performance effects of temperature differences are statistically significant at the 1% level

for each temperature interval. The magnitudes of the effect increase monotonically up

13

to daily average temperatures of 75◦F. Across hot competitions with daily average tem-

peratures greater than 70◦F, each 1-degree increase in temperature difference reduces the

performance loss from high competition temperature by 1.6 – 3.5%.

Similar results are obtained if the competition temperature step function is interacted

with counts of days in the week prior to competition for which daily average tempera-

ture exceeded 60◦F. These are reported in column (2). Column (3) reports results relating

performance to the interaction of the competition temperature step function and average

temperature during the pre-competition exposure period. Results reported in column (4)

demonstrate that training in the warmest one-third of temperatures in the data offsets

hot competition temperature losses by 44—72% relative to training in the coolest third of

temperatures for those competitions contested between 65− 75◦F. These marginal effects

are statistically significant at the 1% level.8

To explore whether longer exposures to hot temperatures also mediate the effect of hot

competitions, we interact the contemporaneous temperature step function with a count

of the number of days for which average daily temperature exceeds 60◦F in the one year

preceding competition. Hot average temperatures at home institutions statistically sig-

nificantly improve performances at all but the coldest competition temperatures, as re-

ported in column (5) of Table 1. The magnitude of performance improvements is greatest

for competition temperatures above 70◦F. The marginal effect of an additional hot day is

approximately an order of magnitude greater if it occurs within seven days of competi-

tion than if it occurs within one year as evident by comparing point estimates of column

(5) to those of column (2).

Consistent with physiological theories of seasonal acclimatization, we also find that

8The fact that exposure to hot temperatures during pre-competition periods boosts performance at hotcompetitions and not across all competition temperatures is consistent with theory of acclimatization andinconsistent with a theory that posits athletes seek to avoid heat ahead of competitions and consequentlyforego training to arrive rested at competitions preceded by hot temperatures. This phenomenon shouldmanifest in improved performances across competition temperatures, contrary to what we report. Such aphenomenon would also imply a suboptimal training response whereby training stress before competitionis reduced rather than held constant by compensating for heat stress via marginal reductions to trainingvolume or intensity.

14

acclimatization benefits are greatest for performances occurring within the first half of

the competitive season, which typically runs from spring to summer amid progressively

warming temperatures across the U.S. Intuitively, the first exposure to warm training

temperatures confers adaptation benefits to all future warm competitions unless an ab-

sence of heat exposure causes acclimatization to degrade. These results are reported in

Appendix A1.2. As also reported in the appendix (see A1.1), we find no evidence of

systematic differences across athlete abilities in the magnitudes of acclimatization effects

relative to competition temperature responses, indicating common acclimatization across

abilities.

3.2 Performance Losses from Climate Change

The performance effects of temperature form a performance surface defined by compe-

tition and training temperatures. This estimated surface is depicted in Appendix Figure

A2a for our baseline model given by (3), and in Appendix Figure A2b for the competi-

tion temperature function specified as a quadratic, a cubic, a two-knot linear spline, and

a three-knot cubic spline.9 These figures depict three-dimensional, concave functions.

The competition-temperature-performance plane defines the concavity, which becomes

flatter with movement toward higher temperatures along the training temperature axis.

Estimated coefficients for competition and training temperature splines of our baseline

model are reported in Appendix Table A3.10

For each of these temperature functions, Table 2 reports predicted performance changes

by end of century for simulations that (1) ignore acclimatization in estimation of contem-

poraneous temperature effects and in projecting future performances (scenario 1), and (2)

explicitly model acclimatization in estimation and prediction (scenario 2). We report both

the level change measured in standardized performance result and the corresponding

9The linear spline is defined by knots at 50 and 60◦F; the cubic spline is defined by knots at 49, 56, and63◦F.

10Temperature parameter estimates of the alternative models are available from the authors upon request.

15

percentage change relative to the current performance. Across alternative specifications

of temperature functions, future performances are predicted to decline amid a warmer

climate. When explicitly modeled, however, acclimatization reduces these performance

losses by 50-58%. Hence, models that ignore the ameliorative effects of acclimatization

may overstate future performance losses by 100% or more. These differences in perfor-

mance changes are statistically significant as determined by 1,000 bootstrap samples of

athletes in the data. The distribution of these bootstrapped estimates of mean perfor-

mance losses for each simulation are shown in Figure 3 for our baseline model.

Table 2 also reports results for two additional simulations. The first of these sup-

poses that competition temperatures are warmer in the future, but pre-competition tem-

peratures are those observed in the historical record of this study (scenario 3). As such,

the scope for acclimatization, i.e., the extent of adaptation, is limited to that which is

observed in the historical record. This simulation admits no systematic acclimatization

to the warmer climate reflected in competition temperatures and no greater idiosyn-

cratic adaptation to warmer temperatures during pre-competition exposures. Perfor-

mance changes reported in scenario 3 are strikingly similar to those reported in scenario

1, indicating that the acclimatization effects on performance changes estimated in sce-

nario 2 are not predominantly attributable to relatively greater benefits of adventitious

acclimatization. A comparison of the first three scenarios of the table suggests that con-

siderable mitigation of performance losses is afforded by systematic acclimatization to a

mean temperature shift, not to adventitious acclimatization.

The final simulation we consider assumes future humans do not adapt to temperature.

We purge contemporaneous temperature effect estimates of bias from adventitious ac-

climatization (by controlling for acclimatization in the historical data) and project perfor-

mances amid warmer competition temperatures without consideration of pre-competition

temperatures. These results are reported in the last two rows of Table 2. The perfor-

mance change under this scenario is appropriately compared to the performance change

16

reported in scenario 2 wherein temperature parameters are estimated from the same em-

pirical specification. Performance losses under this scenario are an order of magnitude

greater than those under the model that explicitly accounts for acclimatization, highlight-

ing both the bias in conventional estimates of contemporaneous temperature response

that ignore heat adaptations or lagged temperature effects and the considerable capacity

for heat adaptation to ameliorate harms from climate change.

3.3 Robustness and Limitations

The foregoing results are robust to various permutations of the modeling choices pre-

viously described, including definition of two-week pre-competition exposure periods,

measurement of temperatures by daily maximums rather than daily averages, omission

of control variables in estimation of temperature effects, and alternative specifications of

fixed effects and assumptions about error correlation structures. We also demonstrate

that the performance losses avoided by systematic acclimatization to mean temperature

shifts are similar for alternative future temperature scenarios. These results are reported

in the appendix.

Despite the robustness of our main results, and the advantages afforded by the quasi-

experimental setting of this study, it is not without limitations. First, we imprecisely mea-

sure the temperatures at which performances occur and the temperatures to which indi-

viduals are exposed prior to performances. Imprecision in our measures of temperature

exposures likely results in classical measurement error that attenuates our estimates of

competition temperature response and heterogeneity by training temperature exposure.

Strategic behavior that we deem unlikely may cause dependence between measurement

errors and the true, underlying temperature exposures. However, such dependence is

likely still to attenuate estimates of the acclimatization effect. If colleges and universities

in extreme climates are equipped with facilities to minimize exposure to extreme temper-

atures, such as indoor tracks, treadmills, etc., then our analysis overstates the variation

17

in pre-competition temperature exposure across collegiate teams. We would attribute

marginal changes in performance to differences in pre-competition exposures that are too

large, biasing toward zero our estimates of the acclimatization effect. Similarly, if ath-

letes affirmatively seek to acclimatize in advance of events expected to be contested in

hot conditions, e.g., by training away from campus or in climate-controlled settings, then

we attribute the relatively strong performances of such actively acclimatized athletes to

relatively cool ambient conditions at their home institutions. This raises the average per-

formances among those preceded by relatively cool observed temperatures and lowers

the estimated average gain from hot pre-competition temperature exposure.

Second, this analysis identifies acclimatization to warm temperatures in the current

climate. There may exist limits to adaptation such that acclimatization is ineffective in

mitigating performance losses at extreme competition temperatures not observed in the

temperature record of our analysis. Likewise, training in extreme temperatures may

less effectively moderate performance losses in hot competition environments. Our re-

sults, however, suggest acclimatization benefits are increasing over the support of com-

petition and training temperatures in our data. This is evident in Appendix Figures

A3a and A3b, which show the mean temperature response for each of several distinct

ranges of pre-competition temperature, i.e., 35-44◦F, 45-54◦F, etc. Temperature sensitiv-

ity is lower on average for performances preceded by warmer pre-competition tempera-

tures, performances are generally better at hot competitions when preceded by warmer

pre-competition temperature exposures, and the performance difference between those

results preceded by hot or cold temperature exposures generally increases in competi-

tion temperature. Thus, the scope for future acclimatization is likely to be greater than

that which is exhibited in the historical record of any analysis. This evidence not with-

standing, assessment of any such limitations to thermo-regulatory adaptation comprises

interesting ground for future research.

Finally, the setting of this study is admittedly specific. Yet the robust findings of the

18

physiological literature on the universality of acclimatization implies the scope for such

adaptation and its capacity to mitigate cognitive and physical harms of heat stress across

settings should be in proportion to the heat stress to which individuals are exposed. Our

findings are relevant, therefore, to any setting in which heat stress affects outcomes of

interest. As there is growing interest in the research community and among policymakers

about the performance and health consequences of cumulative heat stress, e.g., during

heatwaves, it is important to highlight that performance in our setting is unlikely to be

encumbered by cumulative heat stress given opportunities for individuals to retire from

the heat to climate-controlled conditions outside of training periods. However, because

acclimatization also likely diminishes heat stress in response to heat exposure, it slows the

accumulation of heat stress, and may thereby confer additional performance and health

benefits during heatwaves. If acclimatization reduces the harms from cumulative heat

stress in this way, then the benefits of acclimatization may be even greater than those we

estimate here.

4 Discussion

Evidence of climate change adaptation is difficult to obtain because of the relative tem-

poral invariance of climate and because, in most settings, short-run temperature shocks

are unlikely to induce adaptations that may be undertaken in response to expected long-

term temperature changes. Studies that exploit temperature shocks can identify low-cost,

and short-run adaptations, like changes to the timing of recreation, but they cannot iden-

tify costlier adaptations to climate warming that may only be undertaken in response

to expected long-run temperature changes (Dundas and von Haefen 2020). Studies that

instead rely upon cross-sectional climate variation are subject to selection bias, and po-

tentially other omitted variables bias (Heutel, Miller and Molitor 2020; Deschenes and

Greenstone 2011). Finally, those studies that exploit slight temperature variation in long-

19

run mean temperatures since the mid- to late-twentieth century seek to identify adap-

tation to temperature differences that may reflect idiosyncratic weather variations and

that may have been unanticipated by agents when decisions were made about long-term

adaptation investments (Burke and Emerick 2015).

This paper’s focus on acclimatization overcomes many of these challenges to identify

one mechanism of adaptation to persistent temperature change. Because acclimatization

benefits accrue from as little as one-week exposure to hot temperatures, the research de-

sign of this paper exploits random, short-run temperature variation in combination with

fixed competition schedules to identify a response to persistent temperature change that

is unconfounded by the omitted variables that impede cross-sectional studies. The statis-

tical evidence documented in this paper of acclimatization and its impacts on human per-

formance amid climate warming, though novel, is consistent with numerous case studies

in the physiology literature on thermoregulation and hyperthermia (Nielsen and Nybo

2003; Nybo and Nielsen 2001; Brinnel, Cabanac and Hales 1987; Hales, Hubbard and Gaf-

fin 2010; Hanna and Brown 1983; Periard, Racinais and Sawka 2015; Dresoti 1935; Horvath

and Shelley 1946; Hellon et al. 1956; Strydom et al. 1966; Wyndham 1967; Robinson et al.

1943; Pandolf, Burse and Goldman 1977; Pandolf et al. 1988; Shvartz et al. 1973; Eichna

et al. 1950; Wyndham et al. 1968; Fox et al. 1967; Lind 1963; Edholm and Weiner 1981).

This literature documents heat adaptation among all test subjects, including young and

old, athletic and nonathletic. It also documents both the particular sensitivity of the brain

to heat stress and the moderating effects of acclimatization on such sensitivity (e.g., Raci-

nais et al. 2017; Radakovic et al. 2007; Wijayanto et al. 2017. Acclimatization occurs with

remarkable ease (Hanna and Brown 1983), leading to lower heart rates, internal body tem-

peratures, skin temperatures, and perceived effort in hot environments, as well as higher

blood flow and perceived comfort.

This fairly rapid and autonomous response to hot temperatures may, therefore, consti-

tute a low-cost human adaptation to climate warming that significantly mitigates future

20

human performance declines and improves human comfort. Such physiological adapta-

tions may explain, for instance, why youth cognitive performance in the U.S. is impaired

by hot temperatures, and, yet, long-run cognitive attainment is not (Graff Zivin, Hsiang

and Neidell 2018). Likewise, heterogeneity in the sensitivity of mortality to extreme tem-

peratures across climate zones may reflect acclimatization, in addition to other long-run

adaptations, like infrastructure and durable goods investments (Heutel, Miller and Moli-

tor 2020).

The acclimatization identified in this paper constitutes passive adaptation because it

is identified from ambient temperature exposures where individuals reside. Such passive

acclimatization is expected to occur in a warmer climate in any setting in which individu-

als are customarily exposed to elevated temperatures, whether in a classroom, a factory, or

on an athletic field (Fox et al. 1967; Hanna and Brown 1983; Periard, Racinais and Sawka

2015). Just as acclimatization occurs rapidly amid repeated exposure to hot temperatures,

the adaptation also dissipates quickly upon the cessation of hot temperature exposures.

In the context of climate change, however, this does not imply a short-run adaptation, as

predicted changes in temperature are generally approximated by a mean shift in the tem-

perature distribution. Acclimatization can be expected to afford a long-run adaptation to

such a mean shift in temperatures unless and until it is reversed.

Models that relate human performance or other economic outcomes only to contem-

poraneous temperature generate biased estimates of contemporaneous temperature sen-

sitivity amid the autonomous heat adaptation identified in this study. Just as this study

identifies acclimatization parameters from idiosyncratic variation in one-week tempera-

ture distributions, studies that ignore acclimatization are likely to estimate contempora-

neous temperature responses that are biased down by such adventitious acclimatization.

Despite this downward bias in the estimated contemporaneous temperature responses,

projections of climate change damages based upon such parameter estimates are biased

up, implying greater losses in human performance, for instance, than are expected if hu-

21

mans acclimatize. They fail to account for the greater adventitious and systematic ac-

climatization induced by a warmer climate.

22

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Tables

Table 1: Adaptation from One-Week Exposure to Warm Temperatures

Variables (1) (2) (3) (4) (5)Interact With: Temperature # Days > 60 F Mean Training Hottest 3rd of # Days > 60 F

Difference in One Week Temperature Pre Exposure in One Year

≤40 F 0.00065 0.00400 0.00185* 0.12275*** -0.00013(0.00093) (0.00507) (0.00096) (0.03112) (0.00020)

40-45 F 0.00010 0.00241 0.00079 -0.00533 0.00033**(0.00065) (0.00260) (0.00063) (0.01617) (0.00016)

45-50 F 0.00048 0.00147 0.00040 0.00496 0.00027**(0.00037) (0.00137) (0.00037) (0.00776) (0.00012)

50-55 F 0.00052 0.00028 0.00066** 0.00859 0.00030***(0.00032) (0.00105) (0.00032) (0.00645) (0.00010)

55-60 F 0.00062** -0.00048 0.00049 0.00493 0.00027***(0.00031) (0.00096) (0.00031) (0.00612) (0.00010)

60-65 F 0.00107*** 0.00079 0.00089*** 0.02398*** 0.00034***(0.00030) (0.00086) (0.00030) (0.00603) (0.00010)

65-70 F 0.00145*** 0.00284*** 0.00123*** 0.03660*** 0.00038***(0.00035) (0.00107) (0.00035) (0.00726) (0.00010)

70-75 F 0.00176*** 0.00385** 0.00163*** 0.03911*** 0.00047***(0.00046) (0.00157) (0.00047) (0.01204) (0.00011)

≥75 F 0.00165*** 0.00371* 0.00118** 0.02937 0.00052***(0.00061) (0.00200) (0.00059) (0.01861) (0.00012)

Observations 929,470 929,470 929,470 541,665 929,470# Athletes 101,798 101,798 101798 85,280 101,798Adjusted R2 0.886 0.886 0.886 0.886 0.900

Notes: This table presents the coefficient estimates for the interaction terms between the competitiontemperature step function and a function of one-week average temperature at athlete’s home institu-tions immediately preceding the competitions, including the difference in the pre-competition averagetemperature exposure and competition temperature (Column 1), the count of days within one weekprior to the competition for which average temperature exceeded 60◦F (Column 2), the average tem-perature during the pre-competition exposure period (Column 3), and an indicator for whether the pre-competition average temperature exceeds 60◦F (Column 4). In Column 4, we compare the performanceof the athletes who experienced the coolest and the warmest third of pre-competition temperature ex-posure. Column 5 interacts the competition temperature step function with the count of days withinone year prior to the competition for which average temperature exceeded 60◦F. The standard errorsin parentheses are two-way clustered at the athlete and competition level. *** p < 0.01, ** p < 0.05, *p < 0.1.

27

Table 2: Estimated Performance Change by 2100 from RCP8.5 Climate Warming

Scenarios Baseline Quadratic CubicLinear Spline Cubic Spline

2 Knots 3 Knots

Scenario 1: Absent Explicit Accounting for AdaptationLevel Change -0.0102 -0.0112 -0.0110 -0.0097 -0.0096

(0.0000) (0.0000) (0.0000) (0.0000) (0.0000)Percentage Change (%) -0.6488 -0.7136 -0.7005 -0.6108 -0.5973

(0.0103) (0.0066) (0.0079) (0.0113) (0.0131)

Scenario 2: Accounting for Future AdaptationLevel Change -0.0026 -0.0047 -0.0037 -0.0031 -0.0038

(0.0000) (0.0000) (0.0000) (0.0000) (0.0000)Percentage Change (%) -0.2369 -0.3547 -0.3010 -0.2593 -0.2916

(0.0116) (0.0077) (0.0095) (0.0130) (0.0135)

Scenario 3: Accounting for Historical AdaptationLevel Change -0.0107 -0.0120 -0.0114 -0.0104 -0.0102

(0.0000) (0.0000) (0.0000) (0.0000) (0.0000)Percentage Change (%) -0.6725 -0.7514 -0.7198 -0.6465 -0.6280

(0.0118) (0.0071) (0.0092) (0.0125) (0.0131)

Scenario 4: “Turn Off” Adaptation EffectLevel Change -0.0346 -0.0343 -0.0251 -0.0216 -0.0183

(0.0001) (0.0001) (0.0000) (0.0000) (0.0000)Percentage Change (%) -2.0602 -2.0123 -1.4440 -1.2086 -1.0641

(0.0367) (0.0142) (0.0156) (0.0270) (0.0038)

Notes: In scenario 1, we estimate the semi-parametric function specified in Equation (3) of the manuscript without explicitly account-ing for adaptation effect, i.e., not including the terms with pre-competition temperatures. In row scenario, we account for adaptationeffect by including the pre-competition temperatures in the semi-parametric estimation, and assume that both competition and pre-competition temperature are warmer in the future. In scenario 3, we assume that competition temperatures are warmer in the future,but pre-competition temperatures are those observed in the historical record. In scenario 4, the scenario is modeled by including a func-tion of pre-competition temperature in the estimation of competition temperature responses, but setting equal to zero those parametersrelated to pre-competition temperature. For each scenario, we calculate the level change measured in standardized performance resultand the percentage change measured in percent.

28

Figures-.2

-.15

-.1-.0

50

.05

Perfo

rman

ce C

hang

e R

elat

ive

to 5

5-60

F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 >75

Estimate 95% CI

Endurance

-.2-.1

5-.1

-.05

0.0

5Pe

rform

ance

Cha

nge

Rel

ativ

e to

55-

60F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 >75

Estimate 95% CI

Sprint

-.2-.1

5-.1

-.05

0.0

5Pe

rform

ance

Cha

nge

Rel

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e to

55-

60F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 >75

Estimate 95% CI

Strength

0.0

1.02

.03.

04.0

5D

ensi

ty

40 45 50 55 60 65 70 75Mean Daily Temperature (F)

0.0

1.02

.03.

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5D

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40 45 50 55 60 65 70 75Mean Daily Temperature (F)

0.0

1.02

.03.

04.0

5D

ensi

ty

40 45 50 55 60 65 70 75Mean Daily Temperature (F)

Figure 1: Nonlinear Relation between Temperature and Performance by Event Type

Notes: Event types are defined in the Supplementary Materials. Graphs at the top of each frame displaychanges in performance by 5◦F competition temperature interval relative to performance at 55-60◦F . The95% confidence band, after adjusting for competition and athlete error correlation, is depicted betweenthe gray, dashed curves. Histograms at the bottom of each frame display the distribution of competitiontemperature exposure among all competitions in the event category.

29

-2.6

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-2.4

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Per

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ance

Rel

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40 45 50 55 60 65 70 75 80Temperature (F)

Quadratic

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Stan

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Per

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ance

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d40 45 50 55 60 65 70 75 80

Temperature (F)

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40 45 50 55 60 65 70 75 80Temperature (F)

Linear Spline

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40 45 50 55 60 65 70 75 80Temperature (F)

Cubic Spline

+/- 2SE Warmest Pre-Exposure

+/- 2SE Coolest Pre-Exposure

Figure 2: Nonlinear Relation between Temperature and Performance by Pre-competitionTemperature Exposure.

Notes: Each frame depicts a non-linear temperature relation for one-third of competitions preceded bywarmest one-week temperature averages (in red) and coolest one-week temperature averages (in blue).The horizontal axis is standardized performance relative to world record. Less negative values indicateperformances closer to the world record. Dashed lines define +/- two standard errors corrected for possibleathlete and competition error correlation. From right to left, panels depict quadratic, cubic, linear spline,and cubic spline functions of competition temperature.

30

02

46

810

Den

sity

-.8 -.6 -.4 -.2 0Percentage Change in Performance (%)

Absent Explicit Accounting for Adaptation

Accounting for Future Adaptation

Figure 3: Distribution of Bootstrap Estimates of Mean Performance Losses

Notes: This figure plots the distribution of block-bootstrap estimates of mean performance losses at theend of the century for the baseline performance model in Equation 3 that respectively models or ignoresadaptation to pre-competition temperature exposures. To account for sampling uncertainty, the perfor-mance model is estimated 1,000 times by randomly sampling with replacement the athletes in the data. Foreach bootstrap sample, estimated competition and training temperature effects are used to project end-of-century performance changes.

31

Online Appendix

A1 Robustness and Generalizability

A1.1 Acclimatization by Ability

While the physiology literature documents acclimatization by trained athletes and un-trained individuals, we demonstrate the phenomenon is common across terciles of athleteability. Athletes are divided into terciles by athlete-mean standardized performance. Weestimate (2) for each tercile (or tier) of athlete and for each of three training temperaturefunctions. These results are reported in Table A4. They show evidence of acclimatizationin each athlete tier and reveal no systematic differences in magnitudes of acclimatizationeffects relative to competition temperature effects across abilities. Evidence of acclimati-zation is weakest when (2) is estimated by interacting a count of hot days one week beforecompetition with the competition temperature step function, but uniformly so across ath-lete abilities. Because data are stratified by athlete and not performance, and becausecompetition frequency varies by ability, observations are not equal across athlete tiers.

A1.2 Acclimatization by Part of Season

We test for evidence of seasonal acclimatization by separately estimating performance re-sponses to pre-competition temperature exposures that occur in the first and second halfof the competition season, which occurs during a period of warming temperatures duringthe spring season. Specifically, we separately estimate equation (3) for performances oc-curring within the first 23 weeks of the season and for performances occurring beyond 23weeks. These results are reported in Table A5. For each function of pre-competition tem-perature, the pre-competition temperature response is greatest for those performancesthat occur early in the season. These effects are consistently statistically significant atthe 5% level or higher for hot competition environments. This result is consistent withseasonal acclimatization diminishing the benefit of hot pre-competition exposure imme-diately before late season competitions because some acclimatization, at least, is likely tohave already occurred in response to warm spells earlier in the season.

A1.3 Alternative Future Temperature Scenarios

Our main analysis projects daily temperatures from 2089-2099 using climate model sim-ulations of RCP8.5 emissions. We demonstrate the robustness of acclimatization effectson performance changes across alternative future temperature projections. As describedabove, we draw upon climate model temperature projections for RCP 4.5, which yieldsa 3.2-degree average increase in temperatures in our data. Despite the mean increase intemperatures, variability implies that projected daily temperatures may decline relativeto corresponding daily temperatures observed in our historical data. Hence, we also con-sider future temperature scenarios defined by mean temperature increases of 1, 1.6, 2, 3.2,and 4◦F. Results of these simulations for each of the estimated temperature functions are

32

reported in Table A6. The RCP4.5 scenario yields a mean performance increase relativeto the historic performances observed in our data. As shown in Figure A1, the varianceof temperatures projected by the climate models for RCP4.5 and RCP8.5 is smaller thanthe variance we observe in the historical record for either competition or training tem-peratures. The distribution of the RCP4.5 scenario temperature projections, in particular,includes more mass in the range of ideal competition temperatures and less mass in thetails of the distribution. Because temperature extremes are estimated to impede perfor-mance in our models, the reduced frequency of extremes implies performance gains. ForRCP8.5 temperature projections, the performance gains implied by reduced frequencyof extreme temperatures is offset by a mean shift to warmer temperatures that impedeperformance on average. In all but the modeled temperature projections for RCP4.5, per-formance declines.

In our baseline model, performance projections that ignore acclimatization effectsoverstate estimated future losses or understate potential gains by at least 80%. Acrossmodeled temperature scenarios, baseline model performance projections are on average149% greater if they do not explicitly model acclimatization effects. Results are similar foralternative specifications of the temperature function.

A1.4 Symmetry of Historic and Projected Temperature Measures

Climate model temperature projections report daily maximum and minimum temper-atures and not a daily average temperature. As described above, we compute a dailyaverage as the arithmetic mean of the reported daily maximum and minimum tempera-tures. In the historical temperature record, however, daily average temperatures reflectthe average temperature across hourly daily records. If the diurnal temperature trendsare not linear, the daily average temperatures we observe in the historical data are distinctfunctions relative to the average daily future temperatures we compute from the climatemodel output. Our baseline future performance simulations admit these non-symmetrictemperature measurements because this approach preserves the richness of the data inthe historical record without requiring the imputation of hourly projected temperaturesfor future periods.

Our results are robust to the two alternative ways of treating historical and futuretemperatures symmetrically. The first approach estimates equation 3 in the manuscriptusing the simple average of daily maximum and minimum temperatures observed in thehistorical record, consistent with how future daily average temperatures are projected.The estimates of these performance changes for alternative temperature scenarios andtemperature functions are consistent with performance changes estimated in our mainresults. These are reported in Table A7.

The second approach imputes hourly temperatures from the future maximum andminimum temperature projections reported by the climate models. This imputation isdone pursuant to equations defining the daily temperature cycle as a function of maxi-mum and minimum temperatures and day length. Specifically, we implement the equa-tions provided by Linvill (1990), which are based upon a sine curve for daytime temper-ature with a logarithmic nighttime decay. Day length is obtained by computing sunriseand sunset times according to geographic latitude and equations of Spencer (1971) and

33

Almorox, Hontoria and Benito (2005). Daily temperature averages are then computedfrom these imputed hourly temperatures. Projected performance changes pursuant tothis calculation of daily average temperature projections are similar to our main results,demonstrating that projected performance changes are not sensitive to the manner inwhich temperature averages are computed across the historical record and projections.These results are reported in Table A8.

A1.5 Omit Control Variables

Our main results are robust to various alternative specifications. First, we exclude allcovariates except the fixed effects. The non-linear competition temperature relations arelargely unchanged for endurance, sprint, and strength categories, as shown in FigureA4a. The acclimatization effect from temperatures one week prior to competition is alsosimilar, as shown in Table A9. Heterogeneity in competition temperature effects acrossthe coolest and warmest terciles of pre-competition exposures is also similar, as shown inFigure A6a.

A1.6 Define Two-Week Pre-Competition Exposure Period

Our main analysis determines pre-competition temperature exposure to be a summaryfunction of daily average temperatures one week prior to competition. This reflects theconsiderable evidence in the physiology literature that acclimatization benefits accrue inapproximately one week. We demonstrate that a common pattern of acclimatization isestimated if pre-competition exposure is determined by temperatures two weeks prior tocompetition. These results are reported in Table A11 and Figure A7b. We prefer estimatesfrom one week exposures because of the evidence from the physiological literature andbecause of the greater measurement error that attends efforts to summarize temperaturedistributions over two weeks relative to one week. For instance, a moderately hot two-week period could be characterized by a hot period 8-14 days prior to competition and arelatively cool period 1-7 days before competition. This pattern of exposure is expected tobe associated with less acclimatization than a two-week period of common average tem-perature during which the relatively cool temperatures preceded the hot temperatures.The former could be associated with acclimatization and, subsequently, diminution inacclimatization prior to competition. The latter temperature phenomenon is expectedto induce relatively more acclimatization at competition. Thus, summary measures oftwo-week temperature exposures are associated with greater measurement error that at-tenuates estimates of acclimatization effects.

A1.7 Introduce Additional Fixed Effects

Acclimatization marginal effects are similar if we saturate the models with additionalfixed effects. In particular, we introduce interactions of team and venue indicators to flex-ibly control for performance affects that might attend common training and competitionclimates or other factors associated with proximity or distance between home institutionsand venues. These results are reported in Table A12 and Figures A4c and A6c.

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A1.8 Alternative Error Structures

Our main results report standard errors robust to error correlation within performancesby the same athlete and across athletes within common competitions. We also reportresults that admit error correlation within teams and within weeks of the competitionseason. Admitting the possibility for such correlation does not appreciably affect thestandard errors of the non-linear competition temperature relation, as shown in FigureA5a. Larger standard errors, however, moderately increase p-values in specifications thatadmit heterogeneous temperature effects by pre-competition temperature exposures, par-ticularly in the tails of the competition temperature distribution. Consequently, trainingtemperature is estimated to have a statistically insignificant effect on performances in thehottest temperature category of competitions in two of four specifications. The statisti-cal significance of other coefficients are unaffected. These standard errors are availablefrom the authors upon request. Similarly, the differences between competition temper-ature relations across hot and cold training temperature terciles are diminished, thoughthe marginal competition temperature effects remain statistically distinct across a rangeof hot competition temperatures, as shown in Figure A6d.

A1.9 Define Exposures by Daily Maximum Temperatures

We also evaluate the robustness of our main results to specifying competition and train-ing temperatures according to daily maximum temperatures. We remain agnostic as towhen individuals are exposed to ambient temperatures during the day. Nevertheless, wedemonstrate results are robust to estimating performance responses to daily maximumcompetition temperature and pre-competition-period averages of daily maximum tem-peratures at training locations. Results are reported in Figures A5b and A7a and TableA13. As noted in Table A13, training temperature effects are statistically significant for allhot competition temperatures except above 90◦F.

A1.10 Omit Temperature Interpolation

As described in Section 2.3.2, we interpolate missing weather observations of any sta-tion within 50-kilometers of a team or competition venue. These interpolations are madeacross time, potentially increasing the correlation between pre-competition temperatureexposures and competition temperatures. We repeat the analysis omitting any temper-ature interpolation. Hence, some temperature measures may reflect observations fromonly a subset of weather stations within the 50-kilometer radius. Absent interpolation,we are missing temperature readings for 0.004% of observations; these are consequentlyomitted. Without interpolation, the correlation of pre-competition and competition tem-peratures is reduced 0.001 from 0.532. Our main results for this sample are reported inTable A14. They are consistent with the main results reported in the manuscript.

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A1.11 Strength and Sprint Event Placebos

Finally, we report our main results for strength and sprint events. As indicated in themanuscript, in the absence of evidence of performance diminution at hot temperatures inthese event categories, we do not expect to identify evidence of acclimatization benefitsto performance. Hence, we interpret these results as placebo or falsification tests. Asshown in Table A15 and Figure A8, we find little evidence of statistically significant effectsassociated with pre-competition temperature exposures for sprint or strength events.

References

Almorox, J, C Hontoria, and M Benito. 2005. “Statistical validation of daylength defini-tions for estimation of global solar radiation in Toledo, Spain.” Energy Conversion andManagement, 46(9-10): 1465–1471.

Linvill, Dale E. 1990. “Calculating chilling hours and chill units from daily maximumand minimum temperature observations.” HortScience, 25(1): 14–16.

Spencer, JW. 1971. “Fourier series reprensentation of the position of the sun.” Search,2(5): 172.

36

A2 Appendix Tables

Table A1: Classification of Track and Field Events

Event Type Event Name # Obs. Percent

Sprint Events

60m Dash 335 0.01100m Dash 278,851 8.13200m Dash 296,241 8.64300m Dash 285 0.01400m Dash 227,657 6.64500m Dash 6 0.00600m Run 349 0.0160m Hurdles 192 0.01100m Hurdles 107,916 3.15110m Hurdles 85,519 2.49400m Hurdles 156,633 4.57

Endurance Events

1 Mile Run 6,368 0.192 Mile Run 765 0.02800m Run 291,095 8.491,000m Run 477 0.011,500m Run 296,568 8.653,000m Run 37,570 1.105,000m Run 177,163 5.1710,000m Run 53,539 1.562,000m Steeplechase 1,209 0.043,000m Steeplechase 88,637 2.58

Strength Events

Discus Throw 207,801 6.06Hammer Throw 175,886 5.13Weight Throw 44 0High Jump 122,813 3.58Long Jump 194,541 5.67Triple Jump 114,342 3.33Javelin 176,331 5.14Pole Vault 113,758 3.32Shot Put 204,884 5.97

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Table A2: Summary Statistics

Variable N Mean SD Min Max

Whole SampleAthlete Performance

All Events 3,429,234 -3.305 1.449 -9.939 0.000Endurance Events 953,391 -2.413 1.038 -9.939 0.000Sprint Events 1,153,984 -2.646 1.021 -9.200 -0.025Strength Events 1,310,400 -4.530 1.149 -8.022 -0.021

Meet Weather Conditions

Temperature (F) 3,429,234 57.019 9.879 20.100 90.174Dew Point (F) 3,419,139 42.275 11.871 -10.265 76.557Wind (mph) 3,423,086 7.673 3.533 0.575 25.437Preciptation (in) 3,429,234 0.080 0.203 0.000 3.529Ozone (ppm) 3,429,234 0.037 0.008 0.004 0.077

Team Pre-Exposure

Temperature (F) 3,429,234 55.076 8.671 40.000 93.320

Team Characteristics

Travel Distance (km) 3,429,234 270.938 474.304 0.000 7666.728

Endurance EventsMeet Weather Conditions

Dew Point (F) 950,862 42.152 11.740 -10.265 75.269Wind (mph) 951,984 7.646 3.512 0.575 25.437Preciptation (in) 953,391 0.082 0.204 0.000 3.529Ozone (ppm) 953,391 0.037 0.008 0.004 0.077

Meet Temperature (F)

Historical 953,391 56.832 9.788 20.100 87.000RCP4.5 953,391 60.073 7.412 35.542 85.732RCP8.5 953,391 64.189 7.562 38.468 90.924

Team Pre-Exposure Temperature (F)

Historical 953,391 54.930 8.492 40.000 93.320RCP4.5 953,391 57.923 7.731 30.654 89.071RCP8.5 953,391 61.949 7.918 35.548 95.568

Team Characteristics

Travel Distance (km) 953,391 277.234 497.490 0.000 7666.728

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Table A3: Semi-parametric Estimation

VARIABLES (1) (2)

T 0.00412*** 0.00201**(0.000484) (0.000816)

(T − 50) × 1[T > 50] -0.000161 -0.0101*(0.000437) (0.00594)

(T − 60) × 1[T > 60] -0.00511*** 0.00913(0.000547) (0.0103)

(T − 70) × 1[T > 70] -0.00947*** -0.0393(0.00116) (0.0301)

H × T 4.45e-05***(1.29e-05)

H × (T − 50) × 1[T > 50] 0.000204(0.000125)

H × (T − 60) × 1[T > 60] -0.000340(0.000218)

H × (T − 70) × 1[T > 70] 0.000606(0.000624)

(H − 50) × 1[H > 50] × T -5.99e-06(1.17e-05)

(H − 50) × 1[H > 50] × (T − 50) × 1[T > 50] 2.30e-05(9.25e-05)

(H − 50) × 1[H > 50] × (T − 60) × 1[T > 60] 0.000402***(0.000138)

(H − 50) × 1[H > 50] × (T − 70) × 1[T > 70] -0.000223(0.000271)

(H − 60) × 1[H > 60] × T -2.18e-05(1.79e-05)

(H − 60) × 1[H > 60] × (T − 50) × 1[T > 50] 9.78e-05(0.000120)

(H − 60) × 1[H > 60] × (T − 60) × 1[T > 60] -7.04e-05(0.000100)

(H − 60) × 1[H > 60] × (T − 70) × 1[T > 70] 0.000217*(0.000123)

Observations 929,470 929,470# Athletes 101,798 101,798Adjusted R2 0.886 0.886

Notes: This table presents the results of the semi-parametric temperature functions as de-fined by Equation (3) in the manuscript. Column (1) reports the coefficient estimates forhomogeneous effect without adaptation. Column (3) reports the coefficient estimates forheterogeneous effect that account for adaptation. *** p < 0.01, ** p < 0.05, * p < 0.1.

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Table A4: Adaptation from One-Week Exposure to Warm Temperatures by Athlete Tiers

Temperature Difference Number of Days > 60 F Mean Training Temperature Hottest 3rd of Pre Exposure

VARIABLES Tier 1 Tier2 Tier3 Tier1 Tier2 Tier3 Tier1 Tier2 Tier3 Tier1 Tier2 Tier3

≤ 40 F 0.00139 -0.00003 0.00058 0.00456 0.00042 0.00864 0.00332*** 0.00122 0.00157 0.15391*** 0.09377** 0.12848**(0.00106) (0.00100) (0.00142) (0.00641) (0.00558) (0.00745) (0.00115) (0.00105) (0.00148) (0.03572) (0.04557) (0.06270)

40-45 F 0.00025 0.00013 -0.00016 0.00383 0.00177 0.00136 0.00099 0.00090 0.00025 0.01234 -0.00282 -0.00658(0.00070) (0.00073) (0.00101) (0.00310) (0.00310) (0.00410) (0.00069) (0.00072) (0.00101) (0.01971) (0.01958) (0.02796)

45-50 F 0.00034 0.00003 0.00079 0.00241* -0.00167 0.00301 0.00034 -0.00008 0.00054 0.01621* -0.01336 0.00249(0.00039) (0.00046) (0.00067) (0.00140) (0.00180) (0.00266) (0.00039) (0.00046) (0.00067) (0.00831) (0.01059) (0.01611)

50-55 F -0.00013 0.00057 0.00164*** -0.00107 0.00117 0.00232 0.00002 0.00065 0.00169*** 0.00317 0.00926 0.02501*(0.00034) (0.00041) (0.00060) (0.00108) (0.00139) (0.00210) (0.00035) (0.00041) (0.00060) (0.00718) (0.00818) (0.01334)

55-60 F 0.00056* 0.00047 0.00057 -0.00011 -0.00110 -0.00084 0.00047 0.00027 0.00027 0.01144* -0.00370 0.00331(0.00031) (0.00040) (0.00064) (0.00096) (0.00123) (0.00204) (0.00032) (0.00040) (0.00063) (0.00635) (0.00815) (0.01288)

60-65 F 0.00058** 0.00107*** 0.00207*** -0.00013 0.00139 0.00269 0.00044 0.00082** 0.00180*** 0.01654*** 0.01489* 0.05174***(0.00028) (0.00041) (0.00067) (0.00081) (0.00119) (0.00204) (0.00028) (0.00041) (0.00068) (0.00579) (0.00868) (0.01466)

65-70 F 0.00100*** 0.00174*** 0.00157** 0.00180* 0.00390*** 0.00202 0.00089** 0.00142*** 0.00081 0.02818*** 0.03939*** 0.04926***(0.00036) (0.00046) (0.00078) (0.00105) (0.00145) (0.00245) (0.00035) (0.00046) (0.00081) (0.00708) (0.01006) (0.01784)

70-75 F 0.00129*** 0.00200*** 0.00206* 0.00271* 0.00536*** 0.00129 0.00112*** 0.00177*** 0.00177 0.03002*** 0.03332* 0.07282**(0.00040) (0.00058) (0.00117) (0.00138) (0.00206) (0.00405) (0.00041) (0.00059) (0.00117) (0.01053) (0.01803) (0.03243)

≥ 75 F 0.00079 0.00038 0.00497*** 0.00073 0.00194 0.01344* 0.00028 0.00013 0.00401** 0.02861 -0.03448 0.03532(0.00059) (0.00096) (0.00166) (0.00159) (0.00360) (0.00757) (0.00052) (0.00096) (0.00171) (0.01757) (0.04356) (0.05520)

Observations 397,011 321,320 207,613 397,011 321,320 207,613 397,011 321,320 207,613 236,010 184,808 116,797# Athletes 35,622 35,004 30,963 35,622 35,004 30,963 35,622 35,004 30,963 31,092 29,735 24,053Adjusted R2 0.772 0.718 0.805 0.772 0.718 0.805 0.772 0.718 0.805 0.769 0.719 0.805

Notes: This table presents the coefficient estimates for the interaction terms between the competition temperature step function and a function of one-week average temperature at athlete’s homeinstitutions immediately preceding the competitions, including the difference in the pre-competition average temperature exposure and competition temperature (Columns 1 – 3), the count ofdays within one week prior to the competition for which average temperature exceeded 60◦F (Columns 4 – 6), the average temperature during the pre-competition exposure period (Columns 7 –9), and an indicator for whether the pre-competition average temperature exceeds 60◦F (Columns 10 – 12). In Columns 10 – 12, we compare the performance of the athletes who experienced thecoolest and the warmest third of pre-competition temperature exposure. Athletes are divided into three terciles by athlete-mean standardized performance in endurance events. Tiers 1, 2 and 3represent the first, second, and third terciles of athletes, respectively. In each column, we include the competition temperature step function, precipitation, dew point, wind assist, ozone, and theshortest distance between athlete’s home institution and competition venue. We also control for fixed effects by athlete, year-of-eligibility, event-venue-home, and week of competitive season.The standard errors in parentheses are two-way clustered at the athlete and competition level. *** p < 0.01, ** p < 0.05, * p < 0.1.

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Table A5: Acclimatization by Week of Competition Season

Variables Temperature # Days > 60 F Mean Training Hottest 3rd ofInteract With: Difference in One Week Temperature Pre Exposure

Week of Season: ≤23 >23 ≤23 >23 ≤23 >23 ≤23 >23

(1) (2) (3) (4) (5) (6) (7) (8)

≤40 F 0.00086 -0.00552*** 0.00433 -0.01600 0.00151 -0.00514*** 0.05555 0.00413(0.00103) (0.00175) (0.00593) (0.01035) (0.00107) (0.00183) (0.03713) (0.10383)

40-45 F 0.00031 -0.00227** 0.00317 -0.00231 0.00091 -0.00181* 0.00402 -0.01814(0.00087) (0.00101) (0.00355) (0.00377) (0.00085) (0.00094) (0.02572) (0.02317)

45-50 F 0.00017 0.00076 0.00284 0.00160 -0.00005 0.00036 0.00354 -0.00962(0.00052) (0.00052) (0.00207) (0.00173) (0.00051) (0.00050) (0.01276) (0.00993)

50-55 F 0.00135*** -0.00122*** 0.00431*** -0.00298** 0.00150*** -0.00149*** 0.01700* -0.02219**(0.00043) (0.00045) (0.00154) (0.00137) (0.00044) (0.00045) (0.00958) (0.00916)

55-60 F 0.00197*** -0.00016 0.00443*** -0.00169 0.00178*** -0.00049 0.02015** -0.01510*(0.00041) (0.00040) (0.00131) (0.00121) (0.00041) (0.00041) (0.00908) (0.00836)

60-65 F 0.00247*** -0.00007 0.00525*** -0.00096 0.00221*** -0.00056 0.03259*** -0.00827(0.00040) (0.00041) (0.00120) (0.00115) (0.00040) (0.00042) (0.00866) (0.00854)

65-70 F 0.00251*** 0.00119*** 0.00587*** 0.00316** 0.00237*** 0.00081* 0.04017*** 0.02497**(0.00047) (0.00046) (0.00150) (0.00134) (0.00048) (0.00046) (0.01080) (0.00989)

70-75 F 0.00270*** 0.00139** 0.00535** 0.00359* 0.00274*** 0.00143** 0.02790* 0.03510**(0.00068) (0.00056) (0.00259) (0.00192) (0.00070) (0.00057) (0.01692) (0.01715)

≥75 F 0.00256** 0.00146** 0.01380*** 0.00252 0.00318*** 0.00108* 0.05912* 0.01640(0.00111) (0.00057) (0.00414) (0.00180) (0.00108) (0.00061) (0.03118) (0.02539)

Observations 414,945 484,823 414,945 484,823 414,945 484,823 255,185 252,033# Athletes 77,713 80,276 77,713 80,276 77713 80276 61,992 56,314Adjusted R2 0.886 0.888 0.886 0.888 0.886 0.888 0.886 0.887

Notes: We divide our sample into two parts by week of competition season – before the 23rd week and after the 23rd week. We then conductthe analysis using the subsamples separately. The table presents the coefficient estimates for the interaction terms between the competitiontemperature step function and a function of one-week average temperature at athlete’s home institutions immediately preceding the competi-tions, including the difference in the pre-competition average temperature exposure and competition temperature (Columns 1 – 2), the countof days within one week prior to the competition for which average temperature exceeded 60◦F (Columns 3 – 4), the average temperatureduring the pre-competition exposure period (Columns 5 – 6), and an indicator for whether the pre-competition average temperature exceeds60◦F (Columns 7 – 8). In Columns 7 – 8, we compare the performance of the athletes who experienced the coolest and the warmest third ofpre-competition temperature exposure. *** p < 0.01, ** p < 0.05, * p < 0.1.

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Table A6: Estimated Performance Change under Different Temperature Scenarios

Scenarios Baseline Quadratic CubicLinear Spline Cubic Spline

2 Knots 3 Knots

RCP4.5

Absent Explicit Accounting for Adaptation (%) 0.1658 0.1122 0.1304 0.1892 0.1983(0.0103) (0.0081) (0.0089) (0.0108) (0.0141)

Accounting for Future Adaptation (%) 0.4103 0.3353 0.3763 0.4254 0.4015(0.0112) (0.0089) (0.0102) (0.0116) (0.0145)

Temperature + 1F

Absent Explicit Accounting for Adaptation (%) -0.0804 -0.0865 -0.0874 -0.0764 -0.0796(0.0021) (0.0018) (0.0017) (0.0021) (0.0017)

Accounting for Future Adaptation (%) -0.0296 -0.0384 -0.0387 -0.0268 -0.0307(0.0019) (0.0016) (0.0017) (0.0019) (0.0017)

Temperature + 2F

Absent Explicit Accounting for Adaptation (%) -0.1849 -0.1968 -0.1993 -0.1753 -0.1784(0.0042) (0.0033) (0.0033) (0.0041) (0.0034)

Accounting for Future Adaptation (%) -0.0850 -0.1029 -0.1039 -0.0794 -0.0841(0.0039) (0.0031) (0.0032) (0.0037) (0.0034)

Temperature + 4F

Absent Explicit Accounting for Adaptation (%) -0.4671 -0.4885 -0.4985 -0.4380 -0.4314(0.0084) (0.0058) (0.0059) (0.0082) (0.0069)

Accounting for Future Adaptation (%) -0.2765 -0.3100 -0.3160 -0.2609 -0.2583(0.0077) (0.0055) (0.0058) (0.0074) (0.0068)

Notes: This table presents the simulated performance change under alternative future temperature scenarios. In row 1, we estimate thesemi-parametric function specified in Equation (3) of the manuscript without explicitly accounting for adaptation effect, i.e., not includ-ing the terms with pre-competition temperatures. In row 2, we account for adaptation effect by including the pre-competition tempera-tures in the semi-parametric estimation, and assume that both competition and pre-competition temperature are warmer in the future.

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Table A7: Estimated Performance Change using Average of Minimum and Maximum of Historical Temperature

ScenariosBaseline Quadratic Cubic

Linear Spline Cubic Spline2 Knots 3 Knots

RCP8.5

Absent Explicit Accounting for Adaptation (%) -0.7610 -0.8009 -0.7935 -0.7042 -0.6732(0.0075) (0.0053) (0.0065) (0.0087) (0.0112)

Accounting for Future Adaptation (%) -0.3639 -0.4607 -0.4239 -0.3848 -0.3830(0.0087) (0.0062) (0.0077) (0.0103) (0.0117)

RCP4.5

Absent Explicit Accounting for Adaptation (%) 0.1210 0.0942 0.1086 0.1527 0.1752(0.0083) (0.0068) (0.0075) (0.0089) (0.0125)

Accounting for Future Adaptation (%) 0.3539 0.3062 0.3356 0.3688 0.3692(0.0093) (0.0074) (0.0085) (0.0098) (0.0130)

Temperature + 1F

Absent Explicit Accounting for Adaptation (%) -0.0986 -0.1030 -0.1044 -0.0934 -0.0956(0.0022) (0.0016) (0.0016) (0.0021) (0.0017)

Accounting for Future Adaptation (%) -0.0512 -0.0568 -0.0582 -0.0475 -0.0490(0.0021) (0.0015) (0.0016) (0.0020) (0.0017)

Temperature + 1.6F

Absent Explicit Accounting for Adaptation (%) -0.1696 -0.1768 -0.1795 -0.1605 -0.1622(0.0035) (0.0025) (0.0025) (0.0034) (0.0027)

Accounting for Future Adaptation (%) -0.0945 -0.1042 -0.1068 -0.0887 -0.0897(0.0034) (0.0023) (0.0024) (0.0032) (0.0026)

Temperature + 2F

Absent Explicit Accounting for Adaptation (%) -0.2220 -0.2310 -0.2347 -0.2096 -0.2105(0.0044) (0.0031) (0.0030) (0.0043) (0.0033)

Accounting for Future Adaptation (%) -0.1290 -0.1414 -0.1449 -0.1213 -0.1213(0.0042) (0.0028) (0.0030) (0.0040) (0.0033)

Temperature + 3.2F

Absent Explicit Accounting for Adaptation (%) -0.4054 -0.4177 -0.4258 -0.3788 -0.3732(0.0070) (0.0045) (0.0046) (0.0068) (0.0053)

Accounting for Future Adaptation (%) -0.2601 -0.2792 -0.2867 -0.2444 -0.2380(0.0067) (0.0042) (0.0045) (0.0064) (0.0053)

Temperature + 4F

Absent Explicit Accounting for Adaptation (%) -0.5471 -0.5621 -0.5747 -0.5073 -0.4964(0.0087) (0.0053) (0.0055) (0.0086) (0.0067)

Accounting for Future Adaptation (%) -0.3686 -0.3926 -0.4039 -0.3450 -0.3333(0.0084) (0.0050) (0.0053) (0.0080) (0.0066)

Notes: We use the average of minimum and maximum of historical temperature to estimate the semiparametric function and conductthe simulations.

43

Table A8: Estimated Performance Change using Interpolated Daily Average Temperature Projection

Scenarios Baseline Quadratic CubicLinear Spline Cubic Spline

2 Knots 3 Knots

RCP4.5

Absent Explicit Accounting for Adaptation (%) 0.1421 0.0895 0.1064 0.1647 0.1740(0.0104) (0.0082) (0.0088) (0.0107) (0.0135)

Accounting for Future Adaptation (%) 0.3875 0.3119 0.3527 0.3987 0.3757(0.0112) (0.0089) (0.0101) (0.0115) (0.0139)

RCP8.5

Absent Explicit Accounting for Adaptation (%) -0.6806 -0.7452 -0.7360 -0.6384 -0.6208(0.0104) (0.0070) (0.0083) (0.0113) (0.0138)

Accounting for Future Adaptation (%) -0.2646 -0.3853 -0.3323 -0.2898 -0.3167(0.0116) (0.0081) (0.0098) (0.0128) (0.0141)

Notes: We interpolate hourly temperature based on temperature extremes for the future period using the R package chillR. For details,please see http://mirror.fcaglp.unlp.edu.ar/CRAN/web/packages/chillR/vignettes/hourly temperatures.html.

44

Table A9: Adaptation from One-Week Exposure to Warm Temperatures–Exclude Covariates

Variables (1) (2) (3) (4)Interact With: Temperature # Days > 60 F Mean Training Hottest 3rd of

Difference in One Week Temperature Pre Exposure

≤40 F 0.00061 0.00539 0.00195** 0.12939***(0.00093) (0.00514) (0.00097) (0.03165)

40-45 F 0.00014 0.00275 0.00088 -0.00082(0.00066) (0.00265) (0.00064) (0.01654)

45-50 F 0.00066* 0.00224 0.00061* 0.00961(0.00037) (0.00138) (0.00037) (0.00778)

50-55 F 0.00078** 0.00139 0.00096*** 0.01494**(0.00032) (0.00106) (0.00032) (0.00642)

55-60 F 0.00084*** 0.00024 0.00074** 0.00973(0.00031) (0.00096) (0.00031) (0.00607)

60-65 F 0.00125*** 0.00161* 0.00112*** 0.02820***(0.00030) (0.00086) (0.00030) (0.00597)

65-70 F 0.00168*** 0.00381*** 0.00151*** 0.04173***(0.00035) (0.00106) (0.00034) (0.00709)

70-75 F 0.00171*** 0.00383** 0.00164*** 0.04067***(0.00046) (0.00162) (0.00048) (0.01195)

≥75 F 0.00149** 0.00320* 0.00100* 0.02648(0.00059) (0.00187) (0.00055) (0.01830)

Observations 932,028 932,028 932,028 543,482# Athletes 101,875 101,875 101,875 85,412Adjusted R2 0.886 0.886 0.886 0.886

Notes: This table presents the coefficient estimates for the interaction terms between the competition temperaturestep function and a function of one-week average temperature at athlete’s home institutions immediately pre-ceding the competitions, including the difference in the pre-competition average temperature exposure and com-petition temperature (Column 1), the count of days within one week prior to the competition for which averagetemperature exceeded 60◦F (Column 2), the average temperature during the pre-competition exposure period(Columns 3), and an indicator for whether the pre-competition average temperature exceeds 60◦F (Column 4).In Column 4, we compare the performance of the athletes who experienced the coolest and the warmest third ofpre-competition temperature exposure. In each column, we include the competition temperature step function.We also control for fixed effects by athlete, year-of-eligibility, event-venue-home, and week of competitive sea-son. The standard errors in parentheses are two-way clustered at the athlete and competition level. *** p < 0.01,** p < 0.05, * p < 0.1.

45

Table A10: Adaptation from One-Week Exposure to Warm Temperatures–Use Relative Humidity

Variables (1) (2) (3) (4)Interact With: Temperature # Days > 60 F Mean Training Hottest 3rd of

Difference in One Week Temperature Pre Exposure

≤40 F 0.00067 0.00450 0.00196** 0.12903***(0.00092) (0.00508) (0.00096) (0.03101)

40-45 F 0.00007 0.00259 0.00081 -0.00435(0.00065) (0.00263) (0.00063) (0.01629)

45-50 F 0.00049 0.00164 0.00045 0.00628(0.00037) (0.00137) (0.00036) (0.00772)

50-55 F 0.00049 0.00030 0.00066** 0.00862(0.00032) (0.00105) (0.00032) (0.00643)

55-60 F 0.00054* -0.00063 0.00044 0.00363(0.00031) (0.00096) (0.00031) (0.00612)

60-65 F 0.00104*** 0.00082 0.00089*** 0.02314***(0.00030) (0.00087) (0.00030) (0.00607)

65-70 F 0.00150*** 0.00315*** 0.00132*** 0.03677***(0.00036) (0.00107) (0.00035) (0.00716)

70-75 F 0.00176*** 0.00386** 0.00166*** 0.03991***(0.00046) (0.00160) (0.00047) (0.01186)

≥75 F 0.00163*** 0.00340* 0.00104* 0.02625(0.00063) (0.00191) (0.00057) (0.01832)

Observations 929,470 929,470 929,470 541,665Number of Athletes 101,798 101,798 101,798 85,280Adjusted R2 0.886 0.886 0.886 0.886

Notes: This table presents the coefficient estimates for the interaction terms between the competition temperature stepfunction and a function of one-week average temperature at athlete’s home institutions immediately preceding the com-petitions, including the difference in the pre-competition average temperature exposure and competition temperature(Column 1), the count of days within one week prior to the competition for which average temperature exceeded 60◦F(Column 2), the average temperature during the pre-competition exposure period (Columns 3), and an indicator forwhether the pre-competition average temperature exceeds 60◦F (Column 4). In Column 4, we compare the performanceof the athletes who experienced the coolest and the warmest third of pre-competition temperature exposure. In each col-umn, we include the competition temperature step function, precipitation, relative humidity, wind assist, ozone, and theshortest distance between athlete’s home institution and competition venue. We also control for fixed effects by athlete,year-of-eligibility, event-venue-home, and week of competitive season. The standard errors in parentheses are two-wayclustered at the athlete and competition level. *** p < 0.01, ** p < 0.05, * p < 0.1.

46

Table A11: Adaptation from Two-Week Exposure to Warm Temperatures

Variables (1) (2) (3) (4)Interact With: Temperature # Days > 60 F Mean Training Hottest 3rd of

Difference in One Week Temperature Pre Exposure

≤40 F 0.00192** 0.00545** 0.00357*** 0.06009(0.00097) (0.00272) (0.00102) (0.04178)

40-45 F -0.00044 -0.00079 0.00034 -0.01975(0.00067) (0.00162) (0.00067) (0.01978)

45-50 F 0.00203*** 0.00325*** 0.00195*** 0.03141***(0.00043) (0.00086) (0.00043) (0.00902)

50-55 F 0.00176*** 0.00114* 0.00202*** 0.02050***(0.00035) (0.00064) (0.00035) (0.00669)

55-60 F 0.00143*** 0.00036 0.00136*** 0.01856***(0.00034) (0.00059) (0.00035) (0.00657)

60-65 F 0.00166*** 0.00073 0.00154*** 0.02198***(0.00033) (0.00052) (0.00034) (0.00629)

65-70 F 0.00216*** 0.00183*** 0.00200*** 0.03939***(0.00039) (0.00063) (0.00039) (0.00753)

70-75 F 0.00255*** 0.00236*** 0.00246*** 0.03290***(0.00048) (0.00083) (0.00049) (0.01183)

≥75 F 0.00233*** 0.00156 0.00196*** 0.07551***(0.00068) (0.00117) (0.00065) (0.01804)

Observations 911,518 911,518 911,518 514,696# Athletes 100,888 100,888 100,888 83,575Adjusted R2 0.886 0.886 0.886 0.887

Notes: This table presents the coefficient estimates for the interaction terms between the competition temperature stepfunction and a function of two-week average temperature at athlete’s home institutions immediately preceding thecompetitions, including the difference in the pre-competition average temperature exposure and competition tem-perature (Column 1), the count of days within two week prior to the competition for which average temperature ex-ceeded 60◦F (Column 2), the average temperature during the pre-competition exposure period (Columns 3), and anindicator for whether the pre-competition average temperature exceeds 60◦F (Column 4). In Column 4, we comparethe performance of the athletes who experienced the coolest and the warmest third of pre-competition temperatureexposure. In each column, we include the competition temperature step function, precipitation, dew point, wind as-sist, ozone, and the shortest distance between athlete’s home institution and competition venue. We also control forfixed effects by athlete, year-of-eligibility, event-venue-home, and week of competitive season. The standard errors inparentheses are two-way clustered at the athlete and competition level. *** p < 0.01, ** p < 0.05, * p < 0.1.

47

Table A12: Adaptation from One-Week Exposure to Warm Temperatures-Add Team by Venue FE

Variables (1) (2) (3) (4)Interact With: Temperature # Days > 60 F Mean Training Hottest 3rd of

Difference in One Week Temperature Pre Exposure

≤40 F 0.00019 -0.00208 0.00156 0.01206(0.00102) (0.00579) (0.00104) (0.05627)

40-45 F 0.00011 0.00152 0.00082 -0.03315(0.00068) (0.00281) (0.00067) (0.02015)

45-50 F 0.00065 0.00166 0.00060 0.00396(0.00041) (0.00153) (0.00041) (0.00965)

50-55 F 0.00047 0.00081 0.00061* 0.01248(0.00035) (0.00118) (0.00035) (0.00780)

55-60 F 0.00079** 0.00026 0.00067** 0.00769(0.00034) (0.00104) (0.00034) (0.00741)

60-65 F 0.00150*** 0.00123 0.00129*** 0.03877***(0.00032) (0.00095) (0.00032) (0.00756)

65-70 F 0.00207*** 0.00482*** 0.00179*** 0.05250***(0.00037) (0.00116) (0.00037) (0.00927)

70-75 F 0.00302*** 0.00757*** 0.00272*** 0.08593***(0.00048) (0.00171) (0.00049) (0.01731)

≥75 F 0.00203*** 0.00515** 0.00141* 0.05636*(0.00073) (0.00254) (0.00075) (0.03067)

Observations 924,679 924,679 924,679 537,504# Athletes 101,522 101,522 101,522 84,916Adjusted R2 0.891 0.891 0.891 0.891

Notes: This table presents the coefficient estimates for the interaction terms between the competition temperature stepfunction and a function of one-week average temperature at athlete’s home institutions immediately preceding thecompetitions, including the difference in the pre-competition average temperature exposure and competition tem-perature (Column 1), the count of days within one week prior to the competition for which average temperature ex-ceeded 60◦F (Column 2), the average temperature during the pre-competition exposure period (Columns 3), and anindicator for whether the pre-competition average temperature exceeds 60◦F (Column 4). In Column 4, we comparethe performance of the athletes who experienced the coolest and the warmest third of pre-competition temperatureexposure. In each column, we include the competition temperature step function. We also control for fixed effects byathlete, year-of-eligibility, event-venue-home, team-venue, and week of competitive season. The standard errors inparentheses are two-way clustered at the athlete and competition level. *** p < 0.01, ** p < 0.05, * p < 0.1.

48

Table A13: Adaptation from One-Week Exposure to Warm Temperatures - Maximum Temperature

Variables (1) (2) (3) (4)Interact With: Temperature # Days > 60 F Mean Training Hottest 3rd of

Difference in One Week Temperature Pre Exposure

≤40 F 0.00364 0.00911 0.00320 0.00000(0.00234) (0.00980) (0.00278) (0.00000)

40-45 F 0.00285** 0.01229*** 0.00340*** 0.12040***(0.00125) (0.00387) (0.00121) (0.04422)

45-50 F 0.00014 0.00210 0.00069 -0.00053(0.00079) (0.00284) (0.00083) (0.01863)

50-55 F 0.00068 0.00267 0.00100** -0.00007(0.00048) (0.00167) (0.00049) (0.01079)

55-60 F 0.00024 0.00019 0.00036 0.00664(0.00036) (0.00120) (0.00036) (0.00732)

60-65 F -0.00020 -0.00024 0.00006 0.00407(0.00029) (0.00100) (0.00029) (0.00607)

65-70 F 0.00028 0.00080 0.00024 0.00676(0.00028) (0.00107) (0.00028) (0.00581)

70-75 F 0.00063** 0.00280*** 0.00064** 0.02464***(0.00026) (0.00104) (0.00027) (0.00564)

75-80 F 0.00087*** 0.00466*** 0.00094*** 0.02345***(0.00032) (0.00129) (0.00033) (0.00732)

80-85 F 0.00111*** 0.00566*** 0.00093*** 0.03583***(0.00036) (0.00172) (0.00036) (0.00945)

85-90 F 0.00260*** 0.01283*** 0.00235*** 0.06085***(0.00055) (0.00326) (0.00056) (0.01360)

≥90 F -0.00033 -0.00269 -0.00048 0.03045(0.00080) (0.00500) (0.00075) (0.02863)

Observations 929,470 929,470 929,470 564,093# Athletes 101,798 101,798 101,798 85,851Adjusted R2 0.886 0.886 0.886 0.886

Notes: This table presents the coefficient estimates for the interaction terms between the competition temperature stepfunction and a function of one-week average temperature at athlete’s home institutions immediately preceding thecompetitions, including the difference in the pre-competition average maximum temperature exposure and competi-tion maximum temperature (Column 1), the count of days within one week prior to the competition for which aver-age maximum temperature exceeded 60◦F (Column 2), the average maximum temperature during the pre-competitionexposure period (Columns 3), and an indicator for whether the pre-competition average maximum temperature ex-ceeds 70◦F (Column 4). In Column 4, we compare the performance of the athletes who experienced the coolest andthe warmest third of pre-competition temperature exposure. In each column, we include the competition temperaturestep function, precipitation, dew point, wind assist, ozone, and the shortest distance between athlete’s home institutionand competition venue. We also control for fixed effects by athlete, year-of-eligibility, event-venue-home, and week ofcompetitive season. The standard errors in parentheses are two-way clustered at the athlete and competition level. ***p < 0.01, ** p < 0.05, * p < 0.1.

49

Table A14: Adaptation from One-Week Exposure to Warm Temperatures-No Weather Interpolation

Variables (1) (2) (3) (4)Interact With: Temperature # Days > 60 F Mean Training Hottest 3rd of

Difference in One Week Temperature Pre Exposure

≤40 F 0.00076 0.00438 0.00191** 0.12262***(0.00094) (0.00508) (0.00096) (0.03129)

40-45 F 0.00004 0.00239 0.00073 -0.00729(0.00065) (0.00260) (0.00063) (0.01596)

45-50 F 0.00044 0.00155 0.00038 0.00529(0.00037) (0.00138) (0.00037) (0.00773)

50-55 F 0.00048 0.00020 0.00063* 0.00753(0.00032) (0.00105) (0.00032) (0.00645)

55-60 F 0.00064** -0.00039 0.00051 0.00585(0.00031) (0.00096) (0.00031) (0.00614)

60-65 F 0.00107*** 0.00092 0.00090*** 0.02516***(0.00030) (0.00087) (0.00030) (0.00602)

65-70 F 0.00141*** 0.00279*** 0.00120*** 0.03575***(0.00035) (0.00108) (0.00035) (0.00721)

70-75 F 0.00181*** 0.00404** 0.00168*** 0.03938***(0.00046) (0.00157) (0.00047) (0.01210)

≥75 F 0.00162*** 0.00357* 0.00113* 0.02775(0.00061) (0.00199) (0.00059) (0.01819)

Observations 929,430 929,430 929,430 541,449# Athletes 101,798 101,798 101,798 85,269Adjusted R2 0.886 0.886 0.886 0.886

Notes: This table presents the coefficient estimates for the interaction terms between the competition temperature stepfunction and a function of one-week average temperature at athlete’s home institutions immediately preceding thecompetitions, including the difference in the pre-competition average temperature exposure and competition tempera-ture (Column 1), the count of days within one week prior to the competition for which average temperature exceeded60◦F (Column 2), the average temperature during the pre-competition exposure period (Columns 3), and an indicatorfor whether the pre-competition average temperature exceeds 60◦F (Column 4). In Column 4, we compare the perfor-mance of the athletes who experienced the coolest and the warmest third of pre-competition temperature exposure. Ineach column, we include the competition temperature step function. We also control for fixed effects by athlete, year-of-eligibility, event-venue-home, and week of competitive season. In this data sample, we do not interpolate missingweather and use the remaining weather data to construct zipcode-level measures. The standard errors in parenthesesare two-way clustered at the athlete and competition level. *** p < 0.01, ** p < 0.05, * p < 0.1.

50

Table A15: Adaptation from One-Week Exposure to Warm Temperatures-Other Events

Variables Sprint Events Strength Events

Interact With: Temperature # Days > 60 F Mean Training Hottest 3rd of Temperature # Days > 60 F Mean Training Hottest 3rd ofDifference in One Week Temperature Pre Exposure Difference in One Week Temperature Pre Exposure

≤40 F -0.00068 0.01757*** 0.00320*** 0.08191* -0.00022 0.00427 0.00128* 0.06755*(0.00129) (0.00552) (0.00109) (0.04783) (0.00074) (0.00364) (0.00077) (0.04076)

40-45 F -0.00090 0.00392 0.00030 0.02869* 0.00007 0.00582** 0.00080 0.06060***(0.00064) (0.00281) (0.00066) (0.01581) (0.00056) (0.00242) (0.00056) (0.01388)

45-50 F -0.00050 -0.00178 -0.00010 0.00458 -0.00024 0.00036 0.00025 0.00664(0.00042) (0.00156) (0.00041) (0.00931) (0.00033) (0.00131) (0.00033) (0.00715)

50-55 F 0.00016 0.00100 0.00075** 0.01886*** -0.00041 -0.00158 -0.00010 0.00494(0.00034) (0.00119) (0.00034) (0.00670) (0.00028) (0.00100) (0.00028) (0.00585)

55-60 F -0.00002 -0.00016 0.00030 0.01231** -0.00011 0.00050 0.00014 0.00665(0.00029) (0.00094) (0.00030) (0.00599) (0.00025) (0.00079) (0.00025) (0.00527)

60-65 F -0.00029 -0.00109 -0.00004 0.02066*** -0.00013 0.00012 0.00014 0.00972*(0.00031) (0.00092) (0.00031) (0.00611) (0.00026) (0.00078) (0.00026) (0.00535)

65-70 F -0.00069** -0.00116 -0.00036 0.01191* -0.00003 0.00085 0.00026 0.01398**(0.00032) (0.00096) (0.00032) (0.00703) (0.00028) (0.00088) (0.00028) (0.00618)

70-75 F -0.00057 -0.00070 -0.00033 0.01431 -0.00105*** -0.00253** -0.00081** -0.01219(0.00039) (0.00122) (0.00038) (0.01061) (0.00039) (0.00123) (0.00038) (0.00953)

≥75 F -0.00096** -0.00354** -0.00118*** 0.00345 -0.00041 -0.00045 -0.00039 0.02782*(0.00046) (0.00158) (0.00045) (0.01522) (0.00048) (0.00175) (0.00048) (0.01627)

Observations 1,127,162 1,127,162 1,127,162 678,057 1,289,459 1,289,459 1,289,459 766,302# Athletes 100,511 100,511 100,511 84,801 95,473 95,473 95,473 82,294Adjusted R2 0.854 0.854 0.854 0.861 0.837 0.837 0.837 0.840

Notes: This table presents the coefficient estimates for the interaction terms between the competition temperature step function and a function of one-week average temper-ature at athlete’s home institutions immediately preceding the competitions, including the difference in the pre-competition average temperature exposure and competitiontemperature (Column 1 & 5), the count of days within one week prior to the competition for which average temperature exceeded 60◦F (Column 2 & 6), the average temper-ature during the pre-competition exposure period (Columns 3 & 7), and an indicator for whether the pre-competition average temperature exceeds 60◦F (Column 4 & 8). InColumn 4 & 8, we compare the performance of the athletes who experienced the coolest and the warmest third of pre-competition temperature exposure. In each column, weinclude the competition temperature step function, precipitation, dew point, wind assist, ozone, and the shortest distance between athlete’s home institution and competitionvenue. We also control for fixed effects by athlete, year-of-eligibility, event-venue-home, and week of competitive season. The standard errors in parentheses are two-wayclustered at the athlete and competition level. *** p < 0.01, ** p < 0.05, * p < 0.1.

51

A3 Appendix Figures

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Figure A1: Distribution of Competition and Training Temperatures

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(a) Linear Spline with 3 Knots

(b) Alternative Functional Forms

Figure A2: Predicted Temperature-Performance Relationship

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-2.4

-2.3

30 35 40 45 50 55 60 65 70 75 80 85 90Temperature (F)

35

45

55

65

75

Pre-Exposure (F)

Cubic Spline

-2.8

-2.7

-2.6

-2.5

-2.4

30 35 40 45 50 55 60 65 70 75 80 85 90Temperature (F)

35

45

55

65

75

Pre-Exposure (F)

Quadratic

-2.8

-2.7

-2.6

-2.5

-2.4

30 35 40 45 50 55 60 65 70 75 80 85 90Temperature (F)

35

45

55

65

75

Pre-Exposure (F)

Cubic

(b) Alternative Functional Forms

Figure A3: Predicted Temperature-Performance Relationship

54

-.2-.1

5-.1

-.05

0.0

5Pe

rform

ance

Cha

nge

Rel

ativ

e to

55-

60F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 >75

Estimate 95% CI

Endurance

-.2-.1

5-.1

-.05

0.0

5Pe

rform

ance

Cha

nge

Rel

ativ

e to

55-

60F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 >75

Estimate 95% CI

Sprint

-.2-.1

5-.1

-.05

0.0

5Pe

rform

ance

Cha

nge

Rel

ativ

e to

55-

60F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 >75

Estimate 95% CI

Strength

0.0

1.02

.03.

04.0

5D

ensi

ty

40 45 50 55 60 65 70 75Mean Daily Temperature (F)

0.0

1.02

.03.

04.0

5D

ensi

ty

40 45 50 55 60 65 70 75Mean Daily Temperature (F)

0.0

1.02

.03.

04.0

5D

ensi

ty

40 45 50 55 60 65 70 75Mean Daily Temperature (F)

(a) Exclude Covariates

-.2-.1

5-.1

-.05

0.0

5Pe

rform

ance

Cha

nge

Rel

ativ

e to

55-

60F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 >75

Estimate 95% CI

Endurance

-.2-.1

5-.1

-.05

0.0

5Pe

rform

ance

Cha

nge

Rel

ativ

e to

55-

60F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 >75

Estimate 95% CI

Sprint

-.2-.1

5-.1

-.05

0.0

5Pe

rform

ance

Cha

nge

Rel

ativ

e to

55-

60F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 >75

Estimate 95% CI

Strength

0.0

1.02

.03.

04.0

5D

ensi

ty

40 45 50 55 60 65 70 75Mean Daily Temperature (F)

0.0

1.02

.03.

04.0

5D

ensi

ty

40 45 50 55 60 65 70 75Mean Daily Temperature (F)

0.0

1.02

.03.

04.0

5D

ensi

ty40 45 50 55 60 65 70 75

Mean Daily Temperature (F)

(b) Replace Dew Point with Relative Humidity

-.2-.1

5-.1

-.05

0.0

5Pe

rform

ance

Cha

nge

Rel

ativ

e to

55-

60F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 >75

Estimate 95% CI

Endurance

-.2-.1

5-.1

-.05

0.0

5Pe

rform

ance

Cha

nge

Rel

ativ

e to

55-

60F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 >75

Estimate 95% CI

Sprint

-.2-.1

5-.1

-.05

0.0

5Pe

rform

ance

Cha

nge

Rel

ativ

e to

55-

60F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 >75

Estimate 95% CI

Strength

0.0

1.02

.03.

04.0

5D

ensi

ty

40 45 50 55 60 65 70 75Mean Daily Temperature (F)

0.0

1.02

.03.

04.0

5D

ensi

ty

40 45 50 55 60 65 70 75Mean Daily Temperature (F)

0.0

1.02

.03.

04.0

5D

ensi

ty

40 45 50 55 60 65 70 75Mean Daily Temperature (F)

(c) Add Team-Venue Fixed Effect

Figure A4: Robustness of Nonlinear Relation between Temperature and Performance byEvent Type

55

-.2-.1

5-.1

-.05

0.0

5Pe

rform

ance

Cha

nge

Rel

ativ

e to

55-

60F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 >75

Estimate 95% CI

Endurance

-.2-.1

5-.1

-.05

0.0

5Pe

rform

ance

Cha

nge

Rel

ativ

e to

55-

60F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 >75

Estimate 95% CI

Sprint

-.2-.1

5-.1

-.05

0.0

5Pe

rform

ance

Cha

nge

Rel

ativ

e to

55-

60F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 >75

Estimate 95% CI

Strength

0.0

1.02

.03.

04.0

5D

ensi

ty

40 45 50 55 60 65 70 75Mean Daily Temperature (F)

0.0

1.02

.03.

04.0

5D

ensi

ty

40 45 50 55 60 65 70 75Mean Daily Temperature (F)

0.0

1.02

.03.

04.0

5D

ensi

ty

40 45 50 55 60 65 70 75Mean Daily Temperature (F)

(a) Alternative Clustered SE at Team and Week-of-Season

-.2-.1

5-.1

-.05

0.0

5.1

Perfo

rman

ce C

hang

e R

elat

ive

to 5

5-60

F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 >95

Estimate 95% CI

Endurance

-.2-.1

5-.1

-.05

0.0

5.1

Perfo

rman

ce C

hang

e R

elat

ive

to 5

5-60

F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 >95

Estimate 95% CI

Sprint

-.2-.1

5-.1

-.05

0.0

5.1

Perfo

rman

ce C

hang

e R

elat

ive

to 5

5-60

F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 >95

Estimate 95% CI

Strength

0.0

1.0

2.0

3.0

4D

ensi

ty

40 45 50 55 60 65 70 75 80 85 90 95Max Daily Temperature (F)

0.0

1.0

2.0

3.0

4D

ensi

ty

40 45 50 55 60 65 70 75 80 85 90 95Max Daily Temperature (F)

0.0

1.0

2.0

3.0

4D

ensi

ty40 45 50 55 60 65 70 75 80 85 90 95

Max Daily Temperature (F)

(b) Use Maximum Temperature

-.2-.1

5-.1

-.05

0.0

5Pe

rform

ance

Cha

nge

Rel

ativ

e to

55-

60F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 >75

Estimate 95% CI

Endurance

-.2-.1

5-.1

-.05

0.0

5Pe

rform

ance

Cha

nge

Rel

ativ

e to

55-

60F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 >75

Estimate 95% CI

Sprint

-.2-.1

5-.1

-.05

0.0

5Pe

rform

ance

Cha

nge

Rel

ativ

e to

55-

60F

<40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 >75

Estimate 95% CI

Strength

0.0

1.02

.03.

04.0

5D

ensi

ty

40 45 50 55 60 65 70 75Mean Daily Temperature (F)

0.0

1.0

2.0

3.0

4D

ensi

ty

40 45 50 55 60 65 70 75Mean Daily Temperature (F)

0.0

1.02

.03.

04.0

5D

ensi

ty

40 45 50 55 60 65 70 75Mean Daily Temperature (F)

(c) No Weather Interpolation

Figure A5: Further Robustness of Nonlinear Relation between Temperature and Perfor-mance by Event Type

56

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Quadratic

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Cubic

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Linear Spline

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Cubic Spline

+/- 2SE Warmest Pre-Exposure

+/- 2SE Coolest Pre-Exposure

(a) Exclude Covariates

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Quadratic

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Cubic

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Linear Spline

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Cubic Spline

+/- 2SE Warmest Pre-Exposure

+/- 2SE Coolest Pre-Exposure

(b) Replace Dew Point with Relative Humidity

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Quadratic

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Cubic

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Linear Spline

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Cubic Spline

+/- 2SE Warmest Pre-Exposure

+/- 2SE Coolest Pre-Exposure

(c) Add Team-Venue Fixed Effect

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Quadratic

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Cubic

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Linear Spline

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Cubic Spline

+/- 2SE Warmest Pre-Exposure

+/- 2SE Coolest Pre-Exposure

(d) Alternative Clustered SE at Team and Week-of-Season

Figure A6: Robustness of Nonlinear Relationship Between Temperature and Performance57

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

atve

to W

orld

Rec

ord

40 45 50 55 60 65 70 75 80 85 90 95Temperature (F)

Quadratic

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

atve

to W

orld

Rec

ord

40 45 50 55 60 65 70 75 80 85 90 95Temperature (F)

Cubic

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

atve

to W

orld

Rec

ord

40 45 50 55 60 65 70 75 80 85 90 95Temperature (F)

Linear Spline

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

atve

to W

orld

Rec

ord

40 45 50 55 60 65 70 75 80 85 90 95Temperature (F)

Cubic Spline

+/- 2SE Warmest Pre-Exposure

+/- 2SE Coolest Pre-Exposure

(a) Use Maximum Temperature

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Quadratic

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Cubic

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Linear Spline

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Cubic Spline

+/- 2SE Warmest Pre-Exposure

+/- 2SE Coolest Pre-Exposure

(b) Two Week Pre-Competition Period

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Quadratic

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Cubic

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Linear Spline

-2.6

-2.5

-2.4

-2.3

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Cubic Spline

+/- 2SE Warmest Pre-Exposure

+/- 2SE Coolest Pre-Exposure

(c) No Weather Interpolation

Figure A7: Further Robustness of Nonlinear Relationship Between Temperature and Per-formance

58

-2.7

5-2

.65

-2.5

5St

anda

rdiz

ed P

erfo

rman

ce R

elat

ive

to W

orld

Rec

ord

40 45 50 55 60 65 70 75 80Temperature (F)

Quadratic

-2.7

5-2

.65

-2.5

5St

anda

rdiz

ed P

erfo

rman

ce R

elat

ive

to W

orld

Rec

ord

40 45 50 55 60 65 70 75 80Temperature (F)

Cubic

-2.7

5-2

.65

-2.5

5St

anda

rdiz

ed P

erfo

rman

ce R

elat

ive

to W

orld

Rec

ord

40 45 50 55 60 65 70 75 80Temperature (F)

Linear Spline

-2.7

5-2

.65

-2.5

5St

anda

rdiz

ed P

erfo

rman

ce R

elat

ive

to W

orld

Rec

ord

40 45 50 55 60 65 70 75 80Temperature (F)

Cubic Spline

+/- 2SE Warmest Pre-Exposure

+/- 2SE Coolest Pre-Exposure

(a) Sprint Events

-4.6

-4.5

-4.4

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Quadratic

-4.6

-4.5

-4.4

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Cubic

-4.6

-4.5

-4.4

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Linear Spline

-4.6

-4.5

-4.4

Stan

dard

ized

Per

form

ance

Rel

ativ

e to

Wor

ld R

ecor

d

40 45 50 55 60 65 70 75 80Temperature (F)

Cubic Spline

+/- 2SE Warmest Pre-Exposure

+/- 2SE Coolest Pre-Exposure

(b) Strength Events

Figure A8: Nonlinear Relation Between Temperature and Performance of Other EventTypes

59