the correlation between turnover differential and winning in the national football league
TRANSCRIPT
The Correlation between Turnover Differential and Winning in the National Football League
©2010 Hank Koebler, IV
Table of Contents Cover Page........................................................................................................................................... 1
Table of Contents .........................................................................................................................................2 Preface .........................................................................................................................................................3 Introduction .................................................................................................................................................5 Review of Literature ....................................................................................................................................6 Research Question .......................................................................................................................................7 Hypotheses ..................................................................................................................................................7 Treatment of the Data .................................................................................................................................8 Pearson’s Correlation Coefficient................................................................................................................8 Chi-‐squared Test of Independence..............................................................................................................9 Scatter Plot of the Data .............................................................................................................................10 Best-‐Fit Line................................................................................................................................................11 Determining the Accuracy of the Best-‐Fit Line Equation ..........................................................................12 Conclusion ..................................................................................................................................................14 Validity of the Investigation’s Mathematical Processes and Conclusions ...............................................16 Turnover Differential and Predicted Wins for NFL Teams in 2000 ...........................................................17 Turnover Differential and Predicted Wins for NFL Teams in 2001 ...........................................................18 Turnover Differential and Predicted Wins for NFL Teams in 2002 ...........................................................19 Turnover Differential and Predicted Wins for NFL Teams in 2003 ...........................................................20 Turnover Differential and Predicted Wins for NFL Teams in 2004 ...........................................................21 Turnover Differential and Predicted Wins for NFL Teams in 2005 ...........................................................22 Turnover Differential and Predicted Wins for NFL Teams in 2006 ...........................................................23 Turnover Differential and Predicted Wins for NFL Teams in 2007 ...........................................................24 Turnover Differential and Predicted Wins for NFL Teams in 2008 ...........................................................25 Turnover Differential and Predicted Wins for NFL Teams in 2009 ...........................................................26 Notes ..........................................................................................................................................................27 Works Cited................................................................................................................................................28
Preface
One of the greatest of all time. Precise, accurate, unflappable in the face of pressure.
Able to read a defense both better and quicker than any other quarterback in a league.
Considered by some one of the best to ever play the game. He had already won one Super Bowl
ring, and many more were sure to come. Yet something was still missing.
By any statistical measure, he has consistently been the best quarterback in the league for
years, putting up all kinds of records every season. But when the regular season ended, he
collapsed annually. Every year his team entered the playoffs with high expectations, and every
year his play fizzled and the playoffs ended with heartbreak and disappointment. It was possible
to make the case that one of the greatest quarterbacks of all time was also a perennial
disappointment in the playoffs. Even in the one year that his team did win a Super Bowl, he had
played terribly and the team’s defense won the game for them. For this reason, even his Super
Bowl ring wasn’t enough to allay concerns that he couldn’t win a big game.
On this night, he can lay all those claims to rest, and establish once and for all that he is
worthy of being considered the best quarterback of all time. It is his second Super Bowl
appearance, and this time, the defense can’t save the day for him. The spotlight is now on him,
and he has to put the team on his shoulders and win this game.
His team is down 24-17, a margin of only one touchdown, with 3 minutes and 24 seconds
left in the Super Bowl. His team has possession of the ball, and is quickly moving downfield. A
few short completions bring the ball into the opposing team’s side of the field. Like sharks
smelling blood, he and his team can smell the endzone getting closer and closer. This is it. Tying
the game with a touchdown will be huge – he will then have a chance to win the game in
overtime, providing a dramatic finish to the biggest game of his career. This is his moment, his
time to shine.
He drops back to pass and spots his top receiver apparently wide-open at the 26-yard line.
He releases a pass with the velocity of a rocket and precision of a laser. Another completion,
another first down, and another few yards closer to tying the game.
Except the pass isn’t completed. He has misread the defense, and a defensive back leaps
in front of his receiver and intercepts the pass. He watches, helpless, as the interception is
returned 74 yards for a touchdown. His team is now down by a score of 31-17, and when they
get the ball back, their drive ends as they are stopped on fourth down near the goal line with just
over a minute left. As soon as this happens, he walks off the field and into the locker room, not
even waiting for the customary postgame handshakes.
He now has an entire offseason to cope with the all-too-familiar bitterness of a postseason
ending in disappointment yet again. This isn’t how it was supposed to turn out. Instead of
basking in the glory of a Super Bowl win, he now has to wallow in defeat. He has failed once
more in the postseason, adding fuel to the fire of the claims that he is a big-game choker. In the
blink of an eye, his mistake cost his team the Super Bowl in front of a record-setting television
audience. On the world’s biggest stage, they have come up short because of one play.
This narrative is no mere dramatization. It is a real-life account of the most important
play of Super Bowl XLIV, the most recent championship game of the National Football League.
This study will examine game-changing moments like these. Turnovers, and their enormous
impact on American football.
Introduction
Sports have always played an enormous role in the culture and psyche of nations. From
the days of the ancient Olympics, to the modern era where millions, if not billions, of dollars are
spent worldwide on professional sports, human culture has always relied on sport for spectacle.
For this reason, the National Football League, the United States’ professional American football
league, is one of the most popular sporting institutions in the United States of America.
This study hopes to highlight one aspect of winning American football, using the
National Football League and determine that aspect’s importance in deciding the outcome of
football games. Specifically, it probes the issue of turnovers, defined for the purposes of this
study as when the team with possession of the ball loses possession, either throwing an
interception or fumbling the ball.
A team’s turnover differential is defined as the amount of times their opponents turned
the ball over against them that season, minus the amount of times that they turned the ball over
that season.
Conventional coaching wisdom suggests a high turnover differential is a good thing, but
this study examines the mathematical correlation between a team’s turnover differential and their
winning percentage that season in order to test the validity of that commonly held belief.
The task of this investigation is to determine the correlation between turnover differential
and winning percentage. This task will be achieved through use of Pearson’s p-test along with a
chi-squared test to determine the link between turnover differential and winning percentage in
the National Football League.
Review of Literature
Conventional wisdom holds turnover differential to be one of the most important factors
in determining which team will win a football game. According to NFL Hall of Fame inductee
and NFL Network analyst Rod Woodson, “If you look at the history of games in general, the
more turnovers [a team commits], the less likely that team will win. Turnovers can come in
critical situations where a quarterback can either throw an interception or a defensive back can
get an interception or a fumble can happen – all of those things play a huge role in a momentum
swing or outcome of a game.”(1) In the 2008 NFL season, the five teams with the highest
turnover differential each made the playoffs, won at least 11 of the 16 games they played in the
regular season, and had a combined record of 59-21.(2)
Team Takeaways Giveaways Differential Record
Source: National Football League
Miami 30 13 +17 11-5
Tennessee 31 17 +14 13-3
Baltimore 34 21 +13 11-5
New York Giants 22 13 +9 12-4
Indianapolis 26 17 +9 12-4
(3)
In the history of the Super Bowl, the NFL’s league championship game, teams with a
turnover differential of zero in the Super Bowl have a combined 9-9 record, while teams with a
positive turnover differential have a combined record of 30-3(4).
According to Sportscapping.com writer Steve Janus, “Turnovers are one of the most
basic fundamentals of winning football.”(5) This sentiment is shared by Miami Dolphins head
coach Tony Sparano, who explained the importance of turnovers in a September 2009 interview,
saying “turnovers not only can kill a drive if you lose the ball or start one if you recover it, but it
can also reverse the momentum of a game like no other play, instantly changing field position
and giving one team a huge advantage over the other."(6)
Research Question
What correlation exists between an NFL team’s turnover differential in a given season
and their percentage of games won that season?
Hypotheses
Null Hypothesis
There is no significant correlation between a team’s turnover differential and their
winning percentage, and winning percentage is independent of turnover differential.
Alternative Hypothesis
There is a significant correlation between a team’s turnover differential and their
winning percentage, and winning percentage is dependent on turnover differential.
Treatment of the Data
Using the NFL’s official statistics found on their website, I took each team in the NFL,
and listed their turnover differential and winning percentage each season from the 2000 NFL
season to the 2009 NFL season. As there are 32 teams in the NFL, this should have provided
320 sets of data to analyze. However, because the Houston Texans did not exist until the 2002
season, there were 2 years (2000-2001) with only 31 teams, leaving the total sample size at 318.
Pearson’s Correlation Coefficient
Using the data gathered in the manner described above, a two-tailed Pearson’s p-test was
run in SPSS, Inc.’s PASW Statistics to find Pearson’s product–moment correlation coefficient
according to the formula for product-moment correlation coefficient as listed in the IBO
Diploma Programme Mathematical Studies SL Information Booklet:
Correlations
Winning
Percentage
Turnover
Differential
Pearson Correlation 1 .646
Sig. (2-tailed) .000
Winning Percentage
N 318 318
Pearson Correlation .646 1
Sig. (2-tailed) .000 Turnover Differential
N 318 318
According to the results of this p-test, the value of the correlation between winning
percentage and turnover differential is equal to 0.646 (3SF). This suggests a strong positive
correlation between turnover differential and win percentage.
Chi-Squared Test of Independence
Running a chi-squared test also supports the conclusion that turnover differential and
winning percentage are not independent of each other. For the purpose of organizing the data
into a format that can best be implemented into a chi-squared test, I listed teams as having a
losing record if they won 8 or less games in a season, and a winning record if they won more
than 50% games. Additionally, I listed a team as having a positive turnover differential if their
turnover differential is greater than zero and a negative turnover differential if their turnover
differential was zero or less. These are the charts for the Observed and Expected values:
Observed Values Losing record Winning record Total
positive TOD 53 102 155
negative TOD 121 42 163 Total 174 144 318
Expected Values Losing record Winning record Total
positive TOD 84.8 70.2 155 negative TOD 89.2 73.8 163
Total 174 144 318 As the values resulted in a two-by-two matrix, the number of degrees of freedom of this
chi-squared test is equal to 1. Running a chi-squared test resulted in a chi-squared value of 51.4,
according to the IBO Diploma Programme Mathematical Studies SL Information Booklet’s
formula:
The Mathematical Studies SL Information Booklet also provides a chart to determine
critical values of chi-squared:
This chi-squared value exceeds the critical value of 7.879 for testing dependence at a
99.5% significance level with one degree of freedom. This suggests that winning percentage is
strongly dependent on turnover differential.
Scatter Plot of the Data
The data for teams’ winning percentage and turnover differential was also put into a
scatter plot, with each team’s turnover differential as the x-axis, and their winning percentage as
the y-axis.
Best-Fit Line
In order to predict team’s winning percentage based on their turnover differential,
Microsoft Excel’s best-fit line feature was applied to the scatter plot of the data. This resulted in
the creation of a line with the equation f(x) = 0.0127x + 0.5004. To test the accuracy of this
equation, each team’s turnover differential was substituted into the equation to determine the
team’s Predicted Winning Percentage for that season. For example, the 2003 Tennessee Titans
had a turnover differential of 13, meaning that in the 2003 season their opponents turned the ball
over against the Titans a total of 13 more times than the Titans turned the ball over. Substituting
the 2003 Titans’ turnover differential into the function results in the following equation:
f(13) = 0.0127(13) + 0.5004
f(13) = 0.01651+0.5004
f(13) = 0.6655
Therefore, the 2003 Titans’ Predicted Winning Percentage was 66.55%. In actuality, the
Titans won 75% of their games that season, with a difference of 8.4% between the real winning
percentage and the Predicted Winning percentage. There are sixteen games in the NFL season,
which means that this formula projected the 2003 Titans to win 10.648 games that year, as
66.55% of 16 is equal to 10.648. Because there are only two outcomes of a game, a win or a
loss, a decimal value would suggest a partial win, which is impossible in the scope of this study.
Therefore, the predicted number of wins for each team was rounded to the nearest whole number
for the purposes of determining the difference between Predicted Wins and Actual Wins.
Determining the Accuracy of the Best-Fit Line Equation
These calculations were performed on all 318 of the collected data sets to find the
predicted number of games won by each team in each season from the 2000 season to the 2009
season. The differences between predicted wins and actual wins ranged from -7 to 8, for a total
range of 15. For a sixteen-game season, an error margin of fifteen is highly unimpressive and
gives the impression that the equation of the best-fit line is not a remotely accurate predictor of a
team’s win-loss record. However, closer examination of the statistics disproves this theory and
upholds the validity of the equation in question.
The mean Difference in Games Won is -0.00377, suggesting that this equation is
extremely accurate. To account for the possible presence of outliers, the median was taken as
well, and the median was equal to zero, further confirming the accuracy of the equation. The
lower quartile of the differences was -2, and the upper quartile was 2.
The standard deviation of the values of difference in games won is 2.37 games. Out of
the 318 data sets, 223 of them had a difference in games won that ranged from -2 to 2.
Therefore, 70.1% (223/318) of the sample size falls within only one standard deviation. As there
are five possible values that fit this margin of error (a difference of 2, 1, 0, -1, or -2), this
equation has a five in sixteen (31.3%) probability of being correct within one standard deviation
In theory, any prediction of the amount of games a team wins in a season has a 31.3%
probability of being correct within 2 games. However, this equation predicted the correct
number of wins within two games 70.1% of the time. 70.1 divided by 31.3 is equal to 2.23, so
the equation predicted the correct number of games won 2.23 times as frequently as it would
have if its predictions were not accurate.
When allowing for a margin of error of plus or minus one game, the equation is correct
45.9% of the time. As there are three possible values that fit this margin of error (a difference of
1, 0, or -1), this equation has a three in sixteen (18.8%) probability of being correct within one
game. 45.9/18.8 = 2.44, so this equation is correct within one game 2.44 times as frequently as it
would have if its predictions had no significant accuracy.
Out of the 318 sets of data, there were 50 instances where the predicted number of wins
was equal to the actual number of wins. This means that the equation predicted the exact number
of wins 15.7% of the time. As there is only a 1 in 16 (6.25%) chance of accurately guessing the
exact number of games won in a season, and 15.7/6.25 = 2.51, this formula is exactly right 2.51
times as often as it would be if win percentage were independent of turnover differential.
Conclusion
Given the pre-existing literature suggesting that turnover differential is one of the key
aspects of winning in American football, and the mathematical evidence from this investigation
that strongly supports this theory, it is evident that turnover differential plays an enormous role in
a team’s winning percentage.
The Pearson’s product-moment correlation coefficient of 0.646, obtained from the two-
tailed p-test, suggests a strong positive correlation among turnover differential and winning
percentage. In other words, the teams with higher turnover differentials in a season tend to win
more games.
The chi-squared test results further suggest that winning percentage is highly dependent
on turnover differential. The chi-squared value of 51.4 greatly exceeds the critical value for 1
degree of freedom at the 99.5% significance level, which is indicative of a major discrepancy
between observed and expected values in the chi-squared data tables.
For these reasons, this investigation rejects the null hypothesis that there is no significant
correlation between a team’s turnover differential and their winning percentage, and winning
percentage is independent of turnover differential.
Without a doubt, there is a statistically significant correlation between a team’s turnover
differential and their winning percentage, and winning percentage is indeed dependent on
turnover differential.
Though there is no way to determine the cause of this correlation, it is possible to
hypothesize as to the reasons that these two variables are so closely tied to each other. As
mentioned before, teams that obtain a higher turnover differential tend to win more of their
games. There are two potential causes of this. It is possible that these teams that win the most
games are simply the best teams, and therefore, they are better at achieving a high turnover
differential. On the other hand, it is possible that a high turnover differential makes a team much
more likely to win the game. In reality, it is probably a combination of these two factors that
explains why turnover differential and winning percentage are so closely linked.
Validity of the Investigation’s Mathematical Processes and Conclusions
The amount of data for this investigation was adequate enough to prevent outliers from
skewing the data. 318 sets of data was more than enough to avoid this, although the study is
limited in the sense that it only evaluates the past 10 years. For a more thorough and informative
investigation, one could examine one could examine turnover differential on a team-by-team
basis, and determine if there are some teams with consistently high or low turnover differentials.
One could then discuss the teams’ winning percentage over this period of time, and determine
each team’s correlation between turnover differential and winning percentage.
The reason this correlation could differ by team is because all teams perform differently.
Some teams are able to capitalize on turnovers and exploit even their opponents’ smallest
mistakes, while other teams are so ineffective that they have difficulty scoring no matter what the
situation. Therefore, teams vary in their ability to obtain points from turnovers, and that could
affect their winning percentage as well.
As far as mathematical processes, this investigation used both a two-tailed p-test and a
chi-squared test, which both resulted in an incredibly strong correlation between the two
variables. These were appropriate methods of determining the correlation and dependence, and
their results were very convincing.
The best-fit line equation appeared to be quite accurate, but it only works within the
range of -39 < TOD < 39; otherwise it results that are nonsensical in the context of this
investigation – winning percentages that are either negative numbers or over 100%. Since the
largest value of TOD was 24, and the lowest was -28, this does not appear to have affected the
validity of the results.
Turnover Differential and Predicted Wins for NFL Teams in 2000
Team TOD Predicted Win % Wins Predicted Wins Difference in Wins 49ers 2 52.58% 6 8 -‐2 Bears -‐9 38.61% 5 6 -‐1
Bengals -‐14 32.26% 4 5 -‐1 Bills 6 57.66% 8 9 -‐1
Broncos 19 74.17% 11 12 -‐1 Browns -‐3 46.23% 3 7 -‐4
Buccaneers 17 71.63% 10 11 -‐1
Cardinals -‐24 19.56% 3 3 0 Chargers -‐28 14.48% 1 2 -‐1 Chiefs 3 53.85% 7 9 -‐2
Colts -‐7 41.15% 10 7 3 Cowboys -‐14 32.26% 5 5 0
Dolphins 15 69.09% 11 11 0 Eagles 2 52.58% 11 8 3 Falcons -‐9 38.61% 4 6 -‐2
Giants 8 60.20% 12 10 2 Jaguars 1 51.31% 7 8 -‐1 Jets -‐5 43.69% 9 7 2
Lions 11 64.01% 9 10 -‐1 Packers -‐5 43.69% 9 7 2
Panthers 3 53.85% 7 9 -‐2 Patriots -‐2 47.50% 5 8 -‐3 Raiders 17 71.63% 12 11 1
Rams -‐10 37.34% 10 6 4 Ravens 23 79.25% 12 13 -‐1 Redskins 0 50.04% 8 8 0
Saints 9 61.47% 10 10 0 Seahawks -‐9 38.61% 6 6 0
Steelers 12 65.28% 9 10 -‐1 Titans 2 52.58% 13 8 5 Vikings -‐11 36.07% 11 6 5
• TOD = Turnover Differential, defined in the introduction as the amount of times a team’s opponents lose possession of the ball (via an interception or a fumble) in one season, minus the amount of times the team loses possession of the ball in one season
• Predicted Win % is according to the function f(x) = 0.0127x + 0.5004 • Difference in Wins = Actual Wins – Predicted Wins
Turnover Differential and Predicted Wins for NFL Teams in 2001
Team TOD Predicted Win % Wins Predicted Wins Difference in Wins 49ers 15 69.09% 12 11 1
Bears 13 66.55% 13 11 2 Bengals -‐9 38.61% 6 6 0
Bills -‐14 32.26% 3 5 -‐2
Broncos 10 62.74% 8 10 -‐2 Browns 9 61.47% 7 10 -‐3
Buccaneers 17 71.63% 9 11 -‐2 Cardinals -‐3 46.23% 7 7 0
Chargers 2 52.58% 5 8 -‐3 Chiefs -‐7 41.15% 6 7 -‐1
Colts -‐13 33.53% 6 5 1
Cowboys -‐9 38.61% 5 6 -‐1 Dolphins -‐10 37.34% 11 6 5
Eagles 9 61.47% 11 10 1 Falcons 2 52.58% 7 8 -‐1
Giants -‐1 48.77% 7 8 -‐1
Jaguars -‐3 46.23% 6 7 -‐1 Jets 18 72.90% 10 12 -‐2
Lions -‐16 29.72% 2 5 -‐3 Packers 12 65.28% 12 10 2
Panthers 1 51.31% 1 8 -‐7 Patriots 7 58.93% 11 9 2
Raiders -‐1 48.77% 10 8 2
Rams -‐10 37.34% 14 6 8 Ravens -‐8 39.88% 10 6 4
Redskins 6 57.66% 8 9 -‐1 Saints -‐5 43.69% 7 7 0
Seahawks 6 57.66% 9 9 0
Steelers 7 58.93% 13 9 4 Titans -‐4 44.96% 7 7 0
Vikings -‐21 23.37% 5 4 1
• TOD = Turnover Differential, defined in the introduction as the amount of times a team’s
opponents lose possession of the ball (via an interception or a fumble) in one season, minus the amount of times the team loses possession of the ball in one season
• Predicted Win % is according to the function f(x) = 0.0127x + 0.5004 • Difference in Wins = Actual Wins – Predicted Wins
Turnover Differential and Predicted Wins for NFL Teams in 2002
Team TOD Predicted Win % Wins Predicted Wins Difference in Wins 49ers 10 62.74% 10 10 0
Bears -‐7 41.15% 4 7 -‐3 Bengals -‐15 30.99% 2 5 -‐3
Bills -‐12 34.80% 8 6 2
Broncos -‐5 43.69% 9 7 2 Browns -‐2 47.50% 9 8 1
Buccaneers 17 71.63% 12 11 1 Cardinals -‐10 37.34% 5 6 -‐1
Chargers 3 53.85% 8 9 -‐1 Chiefs 16 70.36% 8 11 -‐3
Colts -‐5 43.69% 4 7 -‐3
Cowboys -‐4 44.96% 5 7 -‐2 Dolphins 0 50.04% 9 8 1
Eagles 14 67.82% 12 11 1 Falcons 12 65.28% 9.5 10 -‐0.5
Giants -‐2 47.50% 10 8 2
Jaguars 12 65.28% 6 10 -‐4 Jets 4 55.12% 9 9 0
Lions -‐7 41.15% 3 7 -‐4 Packers 17 71.63% 12 11 1
Panthers -‐7 41.15% 7 7 0 Patriots 5 56.39% 9 9 0
Raiders 12 65.28% 11 10 1
Rams -‐19 25.91% 7 4 3 Ravens -‐1 48.77% 7 8 -‐1
Redskins -‐14 32.26% 7 5 2 Saints 8 60.20% 9 10 -‐1
Seahawks 2 52.58% 7 8 -‐1
Steelers 0 50.04% 10.5 8 2.5 Texans -‐8 39.88% 4 6 -‐2
Titans 4 55.12% 11 9 2 Vikings -‐18 27.18% 6 4 2 • TOD = Turnover Differential, defined in the introduction as the amount of times a team’s
opponents lose possession of the ball (via an interception or a fumble) in one season, minus the amount of times the team loses possession of the ball in one season
• Predicted Win % is according to the function f(x) = 0.0127x + 0.5004 • Difference in Wins = Actual Wins – Predicted Wins
Turnover Differential and Predicted Wins for NFL Teams in 2003
Team TOD Predicted Win % Wins Predicted Wins Difference in Wins 49ers 12 65.28% 7 10 -‐3
Bears -‐9 38.61% 7 6 1 Bengals 2 52.58% 8 8 0
Bills -‐16 29.72% 6 5 1
Broncos -‐4 44.96% 10 7 3 Browns -‐11 36.07% 5 6 -‐1
Buccaneers 2 52.58% 7 8 -‐1 Cardinals -‐13 33.53% 4 5 -‐1
Chargers -‐11 36.07% 4 6 -‐2 Chiefs 19 74.17% 13 12 1
Colts 10 62.74% 12 10 2
Cowboys -‐4 44.96% 10 7 3 Dolphins 2 52.58% 10 8 2
Eagles 4 55.12% 12 9 3 Falcons 0 50.04% 5 8 -‐3
Giants -‐16 29.72% 4 5 -‐1
Jaguars -‐4 44.96% 5 7 -‐2 Jets 0 50.04% 6 8 -‐2
Lions 0 50.04% 5 8 -‐3 Packers 0 50.04% 10 8 2
Panthers -‐5 43.69% 11 7 4 Patriots 17 71.63% 14 11 3
Raiders -‐1 48.77% 4 8 -‐4
Rams 7 58.93% 12 9 3 Ravens 3 53.85% 10 9 1
Redskins 2 52.58% 5 8 -‐3 Saints -‐1 48.77% 8 8 0
Seahawks -‐1 48.77% 10 8 2
Steelers -‐3 46.23% 6 7 -‐1 Texans -‐5 43.69% 5 7 -‐2
Titans 13 66.55% 12 11 1 Vikings 11 64.01% 9 10 -‐1 • TOD = Turnover Differential, defined in the introduction as the amount of times a team’s
opponents lose possession of the ball (via an interception or a fumble) in one season, minus the amount of times the team loses possession of the ball in one season
• Predicted Win % is according to the function f(x) = 0.0127x + 0.5004 • Difference in Wins = Actual Wins – Predicted Wins
Turnover Differential and Predicted Wins for NFL Teams in 2004
Team TOD Predicted Win % Wins Predicted Wins Difference in Wins 49ers -‐19 25.91% 2 4 -‐2
Bears -‐8 39.88% 5 6 -‐1 Bengals 4 55.12% 8 9 -‐1
Bills 10 62.74% 9 10 -‐1
Broncos -‐9 38.61% 10 6 4 Browns -‐11 36.07% 4 6 -‐2
Buccaneers -‐9 38.61% 5 6 -‐1 Cardinals 1 51.31% 6 8 -‐2
Chargers 15 69.09% 12 11 1 Chiefs -‐6 42.42% 7 7 0
Colts 19 74.17% 12 12 0
Cowboys -‐15 30.99% 6 5 1 Dolphins -‐18 27.18% 4 4 0
Eagles 6 57.66% 13 9 4 Falcons 2 52.58% 11 8 3
Giants 4 55.12% 6 9 -‐3
Jaguars 5 56.39% 9 9 0 Jets 18 72.90% 10 12 -‐2
Lions 4 55.12% 6 9 -‐3 Packers -‐13 33.53% 10 5 5
Panthers 12 65.28% 7 10 -‐3 Patriots 9 61.47% 12 10 2
Raiders -‐17 28.45% 5 5 0
Rams -‐24 19.56% 8 3 5 Ravens 11 64.01% 9 10 -‐1
Redskins -‐1 48.77% 6 8 -‐2 Saints 7 58.93% 8 9 -‐1
Seahawks 7 58.93% 9 9 0
Steelers 11 64.01% 15 10 5 Texans 5 56.39% 7 9 -‐2
Titans -‐1 48.77% 5 8 -‐3 Vikings 1 51.31% 8 8 0 • TOD = Turnover Differential, defined in the introduction as the amount of times a team’s
opponents lose possession of the ball (via an interception or a fumble) in one season, minus the amount of times the team loses possession of the ball in one season
• Predicted Win % is according to the function f(x) = 0.0127x + 0.5004 • Difference in Wins = Actual Wins – Predicted Wins
Turnover Differential and Predicted Wins for NFL Teams in 2005
Team TOD Predicted Win % Wins Predicted Wins Difference in Wins 49ers -‐9 38.61% 4 6 -‐2
Bears 6 57.66% 11 9 2 Bengals 24 80.52% 11 13 -‐2
Bills 4 55.12% 5 9 -‐4
Broncos 20 75.44% 13 12 1 Browns -‐7 41.15% 6 7 -‐1
Buccaneers 7 58.93% 11 9 2 Cardinals -‐11 36.07% 5 6 -‐1
Chargers -‐8 39.88% 9 6 3 Chiefs 8 60.20% 10 10 0
Colts 12 65.28% 14 10 4
Cowboys -‐5 43.69% 9 7 2 Dolphins 1 51.31% 9 8 1
Eagles -‐7 41.15% 6 7 -‐1 Falcons 0 50.04% 8 8 0
Giants 12 65.28% 11 10 1
Jaguars 11 64.01% 12 10 2 Jets -‐6 42.42% 4 7 -‐3
Lions 1 51.31% 5 8 -‐3 Packers -‐24 19.56% 4 3 1
Panthers 16 70.36% 11 11 0 Patriots -‐6 42.42% 10 7 3
Raiders -‐4 44.96% 4 7 -‐3
Rams -‐10 37.34% 6 6 0 Ravens -‐10 37.34% 6 6 0
Redskins 1 51.31% 10 8 2 Saints -‐24 19.56% 3 3 0
Seahawks 10 62.74% 13 10 3
Steelers 7 58.93% 11 9 2 Texans -‐8 39.88% 2 6 -‐4
Titans -‐6 42.42% 4 7 -‐3 Vikings 5 56.39% 9 9 0 • TOD = Turnover Differential, defined in the introduction as the amount of times a team’s
opponents lose possession of the ball (via an interception or a fumble) in one season, minus the amount of times the team loses possession of the ball in one season
• Predicted Win % is according to the function f(x) = 0.0127x + 0.5004 • Difference in Wins = Actual Wins – Predicted Wins
Turnover Differential and Predicted Wins for NFL Teams in 2006
Team TOD Predicted Win % Wins Predicted Wins Difference in Wins 49ers -‐5 43.69% 7 7 0
Bears 8 60.20% 13 10 3 Bengals 7 58.93% 8 9 -‐1
Bills -‐5 43.69% 7 7 0
Broncos 0 50.04% 9 8 1 Browns -‐15 30.99% 4 5 -‐1
Buccaneers -‐12 34.80% 4 6 -‐2 Cardinals 3 53.85% 8 9 -‐1
Chargers 13 66.55% 14 11 3 Chiefs 4 55.12% 9 9 0
Colts 7 58.93% 12 9 3
Cowboys 1 51.31% 9 8 1 Dolphins 2 52.58% 6 8 -‐2
Eagles 5 56.39% 10 9 1 Falcons 6 57.66% 7 9 -‐2
Giants 0 50.04% 8 8 0
Jaguars 1 51.31% 8 8 0 Jets 0 50.04% 10 8 2
Lions -‐9 38.61% 3 6 -‐3 Packers 0 50.04% 8 8 0
Panthers -‐5 43.69% 8 7 1 Patriots 8 60.20% 12 10 2
Raiders -‐23 20.83% 2 3 -‐1
Rams 14 67.82% 8 11 -‐3 Ravens 17 71.63% 13 11 2
Redskins -‐5 43.69% 5 7 -‐2 Saints -‐4 44.96% 10 7 3
Seahawks -‐8 39.88% 9 6 3
Steelers -‐8 39.88% 8 6 2 Texans -‐3 46.23% 6 7 -‐1
Titans 2 52.58% 8 8 0 Vikings 4 55.12% 6 9 -‐3 • TOD = Turnover Differential, defined in the introduction as the amount of times a team’s
opponents lose possession of the ball (via an interception or a fumble) in one season, minus the amount of times the team loses possession of the ball in one season
• Predicted Win % is according to the function f(x) = 0.0127x + 0.5004 • Difference in Wins = Actual Wins – Predicted Wins
Turnover Differential and Predicted Wins for NFL Teams in 2007
Team TOD Predicted Win % Wins Predicted Wins Difference in Wins 49ers -‐12 34.80% 5 6 -‐1
Bears -‐1 48.77% 7 8 -‐1 Bengals 5 56.39% 7 9 -‐2
Bills 9 61.47% 7 10 -‐3
Broncos 1 51.31% 7 8 -‐1 Browns -‐2 47.50% 10 8 2
Buccaneers 15 69.09% 9 11 -‐2 Cardinals -‐7 41.15% 8 7 1
Chargers 24 80.52% 11 13 -‐2 Chiefs -‐11 36.07% 4 6 -‐2
Colts 18 72.90% 13 12 1
Cowboys 5 56.39% 13 9 4 Dolphins -‐7 41.15% 1 7 -‐6
Eagles -‐8 39.88% 8 6 2 Falcons 4 55.12% 4 9 -‐5
Giants -‐9 38.61% 10 6 4
Jaguars 9 61.47% 11 10 1 Jets -‐4 44.96% 4 7 -‐3
Lions -‐1 48.77% 7 8 -‐1 Packers 4 55.12% 13 9 4
Panthers 1 51.31% 7 8 -‐1 Patriots 16 70.36% 16 11 5
Raiders -‐11 36.07% 4 6 -‐2
Rams -‐10 37.34% 3 6 -‐3 Ravens -‐17 28.45% 5 5 0
Redskins -‐5 43.69% 9 7 2 Saints -‐7 41.15% 7 7 0
Seahawks 10 62.74% 10 10 0
Steelers 3 53.85% 10 9 1 Texans -‐13 33.53% 8 5 3
Titans 0 50.04% 10 8 2 Vikings 1 51.31% 8 8 0 • TOD = Turnover Differential, defined in the introduction as the amount of times a team’s
opponents lose possession of the ball (via an interception or a fumble) in one season, minus the amount of times the team loses possession of the ball in one season
• Predicted Win % is according to the function f(x) = 0.0127x + 0.5004 • Difference in Wins = Actual Wins – Predicted Wins
Turnover Differential and Predicted Wins for NFL Teams in 2008
Team TOD Predicted Win % Wins Predicted Wins Difference in Wins 49ers -‐17 28.45% 7 5 2
Bears -‐6 42.42% 9 7 2 Bengals -‐2 47.50% 4.5 8 -‐3.5
Bills -‐8 39.88% 7 6 1
Broncos -‐17 28.45% 8 5 3 Browns 5 56.39% 4 9 -‐5
Buccaneers 4 55.12% 9 9 0 Cardinals 0 50.04% 9 8 1
Chargers 4 55.12% 8 9 -‐1 Chiefs 5 56.39% 2 9 -‐7
Colts 9 61.47% 12 10 2
Cowboys -‐11 36.07% 9 6 3 Dolphins 17 71.63% 11 11 0
Eagles 3 53.85% 9.5 9 0.5 Falcons -‐3 46.23% 11 7 4
Giants 9 61.47% 12 10 2
Jaguars -‐7 41.15% 5 7 -‐2 Jets -‐1 48.77% 9 8 1
Lions -‐9 38.61% 0 6 -‐6 Packers -‐2 47.50% 6 8 -‐2
Panthers 6 57.66% 12 9 3 Patriots 1 51.31% 11 8 3
Raiders 1 51.31% 5 8 -‐3
Rams -‐5 43.69% 2 7 -‐5 Ravens 13 66.55% 11 11 0
Redskins 0 50.04% 8 8 0 Saints -‐4 44.96% 8 7 1
Seahawks -‐8 39.88% 4 6 -‐2
Steelers 4 55.12% 12 9 3 Texans -‐10 37.34% 8 6 2
Titans 14 67.82% 13 11 2 Vikings 6 57.66% 10 9 1 • TOD = Turnover Differential, defined in the introduction as the amount of times a team’s
opponents lose possession of the ball (via an interception or a fumble) in one season, minus the amount of times the team loses possession of the ball in one season
• Predicted Win % is according to the function f(x) = 0.0127x + 0.5004 • Difference in Wins = Actual Wins – Predicted Wins
Turnover Differential and Predicted Wins for NFL Teams in 2009
Team TOD Predicted Win % Wins Predicted Wins Difference in Wins 49ers 9 61.47% 8 10 -‐2
Bears -‐6 42.42% 7 7 0 Bengals 0 50.04% 10 8 2
Bills 3 53.85% 6 9 -‐3
Broncos 7 58.93% 8 9 -‐1 Browns -‐12 34.80% 5 6 -‐1
Buccaneers -‐5 43.69% 3 7 -‐4 Cardinals -‐7 41.15% 10 7 3
Chargers 8 60.20% 13 10 3 Chiefs 1 51.31% 4 8 -‐4
Colts 2 52.58% 14 8 6
Cowboys 2 52.58% 11 8 3 Dolphins -‐8 39.88% 7 6 1
Eagles 15 69.09% 11 11 0 Falcons 3 53.85% 9 9 0
Giants -‐7 41.15% 8 7 1
Jaguars 2 52.58% 7 8 -‐1 Jets 1 51.31% 9 8 1
Lions -‐18 27.18% 2 4 -‐2 Packers -‐2 47.50% 11 8 3
Panthers 6 57.66% 8 9 -‐1 Patriots 6 57.66% 10 9 1
Raiders -‐13 33.53% 5 5 0
Rams -‐13 33.53% 1 5 -‐4 Ravens 10 62.74% 9 10 -‐1
Redskins -‐11 36.07% 4 6 -‐2 Saints 11 64.01% 13 10 3
Seahawks -‐8 39.88% 5 6 -‐1
Steelers -‐3 46.23% 9 7 2 Texans -‐1 48.77% 9 8 1
Titans -‐4 44.96% 8 7 1 Vikings 6 57.66% 12 9 3 • TOD = Turnover Differential, defined in the introduction as the amount of times a team’s
opponents lose possession of the ball (via an interception or a fumble) in one season, minus the amount of times the team loses possession of the ball in one season
• Predicted Win % is according to the function f(x) = 0.0127x + 0.5004 • Difference in Wins = Actual Wins – Predicted Wins
Notes
1. Turnover Differential - Key to Victory in the NFL 2. Turnover Differential - Key to Victory in the NFL 3. Turnover Differential - Key to Victory in the NFL 4. Turnover Differential Often Determines Super Bowl Outcome 5. NFL Handicapping: Turnovers 6. Turnover Differential - Key to Victory in the NFL
Works Cited
IBO Diploma Programme Mathematical Studies SL Information Booklet. Geneva, Switzerland.
November 2004.
Janus, Steve. "NFL Handicapping: Turnovers." Sportscapping.com. 14 Oct. 2009. Web. 25 Jan. 2010.
<http://sportscapping.com/articles/nfl-handicapping-turnovers/>.
"Turnover Differential - Key to Victory in the NFL." IHaveNet.com. 7 Sept. 2009. Web. 24 Jan. 2010.
<http://www.ihavenet.com/NFL/NFL-2009-Turnovers-Key-to-Victory-in-NFL.html>.
"Turnover Differential Often Determines Super Bowl Outcome." NFL.com. National Football League,
22 Jan. 2009. Web. 24 Jan. 2010.
<http://www.nfl.com/superbowl/story?id=09000d5d80e5d3d9&template=with-
video&confirm=true>.