Summary of Articles on Statistics in Sports

I own a book called Anthology of Statistics in Sports, edited by Jim Albert, Jay Bennett, and James J. Cochran. It contains 44 statistical articles on football, baseball, basketball, hockey, and other miscellaneous sports. Most of the statistics involved in these articles is far over my head, so I will simply summarize some of the more interesting findings in the books. When possible, I will provide a link to the article itself.

On the Probability of Winning a Football Game
by Hal Stern, Assistant Professor, Department of Statistics, Harvard
Stern examines methods that can be used to predict the outcome of a NFL football game. One method is based on the point spread. It was found that the true margin of victory for a favored team is a normal random variable with mean at the point spread and standard deviation of 13.86. So, one can approximate the probability of the favored (or underdog) team winning a particular game based on the point spread. Below is a table of various point spreads and probabilities of favored team winning:

Spread	P(Favored Wins)	Spread	P(Favored Wins)
0	0.5000	11	0.7852
1	0.5279	12	0.8078
2	0.5557	13	0.8264
3	0.5871	14	0.8438
4	0.6141	15	0.8599
5	0.6406	16	0.8749
6	0.6664	17	0.8907
7	0.6950	20	0.9251
8	0.7190	25	0.9641
9	0.7422	30	0.9846
10	0.7642	35	0.9943

These values are also useful retrospectively, as one can go back and look at point spreads for an entire season and see what the probability of a team winning their division or making the playoffs. Stern did this with the 1984 NFL season, simulating it 10,000 times based on the probabilities given by the point spreads. It proved effective, as the team with highest probability of winning their division did so in five out of six divisions. The New York Giants made the playoffs despite only having a 0.2291 probability of doing so. In 12% of the simulations, the San Francisco 49ers did not make the playoffs, even though they won the Super Bowl in real life.

Article appeared in The American Statistician, August 1991

Did Shoeless Joe Jackson Throw the 1919 World Series?
By Jay Bennett
In 1919 World Series, the Cincinnati Reds upset the favored Chicago White Sox 5-3 in a best of nine series. A year later, Joe Jackson and seven other "Black Sox" were banned from baseball forever for throwing the series, even though they were all tried and found innocent in court. Joe Jackson had a .356 lifetime average at the time, and Bennett looks to examine whether or not Shoeless Joe played below his ability in the Series, to see if he was knowingly trying to throw the games. Jackson hit .375 in the Series, while hitting .357 with runners in scoring position and .400 with two outs and runners in scoring position, so even just on the surface it appears he played to his full ability.
Bennett also looks at a statistic, PWA (Player Win Average), which is virtually identical to the Win Percentage Added discussed in this post. It simply measures how much the probability of a team winning increased due to the performance of a particular player. A related statistic is PGP, which more accurately measures the effect of a player on victory or defeat. A player has a PGP value for each game, and when they were averaged over the entire 1919 World Series, Jackson's came out to be not only the third best on his team, but the seventh best in the entire World Series, and he had the most positive impact of all hitters in the Series. All other "Black Sox" had negative impacts on their team in the Series. It appears that Joe Jackson played to his full potential in the Series, and did not make an attempt to throw it. However, it is still possible that he bet on the Series but could not bring himself to actively try to lose it. Whatever the case, it is an absolute shame that Joe Jackson's career was cut so short by this scandal.

Article appeared in The American Statistician, 1993.

Drive for Show and Putt for Dough
by Scott M. Berry
Berry, an avid golfer, examines what type of shots one must excel at to be a great golfer. He looks only at those at the highest level of golf, the ones on the United States Professional Golfer's Association Tour (PGA Tour). Unfortunately much of the statistics in this article fly over my head like a pop culture reference, but the conclusion is simple enough: "You drive for dough and putt for more dough!" It appears that putting and overall score are correlated most strongly in a group of variables such as distance on drive, driving accuracy, putting, chipping, and iron play. Iron play appears to be second most important. Still, driving is very important, as evidenced by the fact that the PGA Tour ranks golfers in driving distance and accuracy, and they are the most popular rankings.

Article appeared in Chance, 1999.

Interesting Baseball Fact of the Day: The longest streak of games with a balk is 6, set by Dave Stewart at the beginning of the 1988 season. He totaled 11 balks in the span. This came after Major League Baseball declared they would be watching balks closely in the 1988 season. Thus, four of the seven longest "balk streaks" involve the beginning of the 1988 season. There were 924 balks in the majors in 1988, up from only 356 in 1987.