Eric Huggins, Ph.D. Fort Lewis College Durango, CO

Goals 1. To estimate the probability that a football team will win a game in advance. 2. To determine and use all relevant and significant leading information: Point Spread Over/Under Home/Away 3. To develop the best fitting equation for a large set of data. 10/14/2012INFORMS 2012

References Point Spreads = Efficient Markets Numerous How to Beat Point Spreads Numerous Questionable “On the Probability of Winning a Football Game” by Hal Stern The American Statistician, /14/2012INFORMS 2012

Stern’s Paper Data from NFL 1981, 1983 and 1984 seasons. n = 224 per year Stern developed an equation to predict the probability that the favorite wins depending on the point spread p. For p < 6, P(Favorite wins) ≈ 50% + 3%p. Example: The Arizona Cardinals are a 4.5 point favorite later today, so there is approximately a 63.5% chance that they will win. 10/14/2012INFORMS 2012

Extensions 1. The probability function is clearly non-linear: If the point spread is 0, the probability is 50% As the point spread increases, the probability should approach 100%, non-linearly. 2. NFL points spreads are usually close and there are only a couple hundred games per year. So, use NCAA college football instead: Wide variation among point spreads. Almost a thousand games per year. 10/14/2012INFORMS 2012

Data Collection: 10/14/2012INFORMS 2012 ARIZONA STATE (2010 Season) (SUR: 6-6 PSR: 10-2 O-U: 7-4) S.04* PORT. ST. W S.11* N. ARIZONA L o57 S.18 Wisconsin W u49 S.25* OREGON W o55 O.02 Oregon St. W +3' o54' O.09* Washington W +1' u59 O.23 California L o51 O.30* WASH. ST.# W -21' 42-0 u57' N.06* Southern Cal W +5' o60' N.13* STANFORD W u59' N.26 UCLA W -12' o48' D.02* Arizona-OT W o56

Data Collection Collected data from 7861 college football games from 2011 to Stopped at 2001 since data started getting sketchy. Have data for NFL, too; haven’t run it yet. Converted and cleaned data into MS Excel format. Data contains teams, date, point spread, over/under and actual score of the game. 10/14/2012INFORMS 2012

Data Highlights Lowest point spread = 0, highest point spread = 56.5 points (Louisiana Monroe at Florida 2001) Most common point spreads: 2.5 to 3.5, approximately a field goal 6.5 to 7.5, approximately a touchdown Biggest upset: Stanford beats USC (2007) despite being 40.5 point underdog. Lowest over/under = 34 (Ohio State at Penn State 2004), highest over/under = 83 (Tulsa at Rice 2007) Most common over/under: 47 points. 10/14/2012INFORMS 2012

Point Spreads and Over/Under The point spread (or Las Vegas odds) is a handicap for the underdog. The casinos want half the betting on one side and half on the other. The line can and does change. The Arizona Cardinals are a 4.5 point favorite over the Buffalo Bills later today. The over/under is a wager on the total points to be scored in a game. The over/under in the Arizona/Buffalo game is 43 points. 10/14/2012INFORMS 2012

Are the Point Spread and Actual Point Differential Correlated? 10/14/2012INFORMS 2012

Are the Point Spread and Actual Point Differential Correlated? 10/14/2012INFORMS 2012 This team was favored by 34 and won by 72.

Are the Point Spread and Actual Point Differential Correlated? 10/14/2012INFORMS 2012 This team was a 29 point underdog but won by 14.

Are the Point Spread and Actual Point Differential Correlated? 10/14/2012INFORMS 2012

So, Let’s Estimate! Given the point spread and over/under, predict the probability that the favorite wins the game. 1. Use point spread alone. 2. Use some combination of point spread and over/under. Spread Percentage = (point spread/(over/under)) Point spread and over/under as separate variables. 3. What model will fit the curve? Picture the graph from p =0 to very high p. Use logistic regression. 10/14/2012INFORMS 2012

Point Spread vs. Probability of Win 10/14/2012INFORMS 2012

Point Spread vs. Probability of Win 10/14/2012INFORMS 2012

Point Spread vs. Probability of Win 10/14/2012INFORMS 2012 n = 103, p = 21 points, prob = 94.2%

Point Spread vs. Probability of Win 10/14/2012INFORMS 2012 n = 7, p = 40.5 points, prob = 85.7%

Point Spread vs. Probability of Win 10/14/2012INFORMS 2012

Spread % vs. Probability of Win 10/14/2012INFORMS 2012 Recall that the Spread % is the point spread divided by the over/under. So, in a game with a 5 point spread and over/under of 50, the Spread % is 10%.

Spread % vs. Probability of Win 10/14/2012INFORMS 2012 n = 212, s% = 10%, prob = 61.8%

Spread % vs. Probability of Win 10/14/2012INFORMS 2012 n = 142, s% = 28%, prob = 80.3%

Spread % vs. Probability of Win 10/14/2012INFORMS 2012 n = 16, s% = 67%, prob = 93.8%

Spread % vs. Probability of Win 10/14/2012INFORMS 2012 The best fitting line, forcing the probability at x = 0 to be 50%, is y = 1/(1+e -z ) with z = 5.916x. But just look at the graph, it fits!!!

Which is Better? Point Spread: r = Spread %: r = /14/2012INFORMS 2012

Two Variables: Point Spread and Over/Under Set up a logistic regression with both point spread p and over/under o/u. Not sure how to force probability to 50% for p = 0 with two variables. Over/under is not really significant, but included it anyway. Tried several combinations: o/u, o/u – p, p/(o/u), etc. Best fit: y = 1/(1+e -z ), z = 0.128(p) (o/u) /14/2012INFORMS 2012

Linear estimator: Point Spread 10/14/2012INFORMS 2012 Three lines: p ≤ 10 → prob ≈ 50% + 3%p 10 < p ≤ 30 → prob ≈ 80% + 1%p p > 30 → prob ≈ 100%

Linear Estimator: Spread % 10/14/2012INFORMS 2012 Two lines: s% ≤ 50% → prob ≈ 50% + s% 50% < s% ≤ 100% → prob ≈ 100%

Further Research Analysis on NFL data. Factor in home/away games. Compare probabilities to Las Vegas money lines: Accuracy? Advantage? The Arizona Cardinals are at -220 to win today. (The Buffalo Bills are at +190.) 10/14/2012INFORMS 2012

Show Estimator in MS Excel 10/14/2012INFORMS 2012