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Who’s on First: Simulating the Canadian Football League regular season Keith A. Willoughby, Ph.D. University of Saskatchewan Joint Statistical Meetings (2014)

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Research questions Can we develop a spreadsheet model to simulate the outcome of professional football games? Can we use this model to determine the probabilities of a team finishing first in their division?

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Overview of presentation 1. CFL background 2. Power rankings model 3. CFL simulation model 4. Results

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Western Division Eastern Division CFL teams (2014)

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Why do teams want to finish 1 st in their division? The 1 st place team hosts the divisional championship game Winners of each divisional championship game meet in the Grey Cup

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Financial impact Hosting a playoff game can yield over $1 million in profit for the home team –Ticket sales, concession sales Annual salary cap for each team is about $5 million

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Power rankings model In order to develop the simulation model, we needed to determine the probability of victory for any team during all regular season games Need a way to quantitatively establish the “strength” of each team

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“Strength” values Considers two items: –Particular opponent Defeating a stronger opponent increases a team’s strength value –Outcome of each game (margin of victory) Defeating an opponent by a larger margin of victory increases a team’s strength value

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Power rankings model For each game, let: S i = score of winning team S j = score of losing team Margin of victory (MOV i,j ) = S i - S j

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Power rankings model

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Simulation model How well do the strength values (β’s) correlate with game outcomes? Analyzed game results from seasons –504 CFL games

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Simulation model Using the optimization model, we determined the strength values (β’s) for each team Calculated β i – β j for each game in each season –Team i represented the home team

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β i – β j Total games Total wins by home team Probability of victory β i – β j ≤ % -20 < β i – β j ≤ % -15 < β i – β j ≤ % -10 < β i – β j ≤ % -5 < β i – β j ≤ % 0 < β i – β j ≤ % 5 < β i – β j ≤ % 10 < β i – β j ≤ % 15 < β i – β j ≤ % β i – β j > % results

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Simulation model Logistic regression model: –Explanatory variable (X) = β h – β v where h = home team; v = visiting team –Response variable (Y) = outcome of game 1 if home team won; 0 if home team lost Tie games: 3 (out of 504) – Assigned the visiting team as the winner

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Probability of victory Applied simulation model for 2013 regular season Calculated β h – β v for all games yet to be played Added 3.4 to the resulting difference –Reflects average home team margin of victory from –“Home field advantage”

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Simulation model Used the logistic regression equation to determine the probability of victory Generate random numbers using the RAND() function If RAND() ≤ Calculated probability, then home team wins Else, visiting team wins

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Simulation model Require the following inputs: –Current number of wins –Remaining games –Strength values from the power rankings optimization model

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Simulation model It will calculate the expected number of wins for each team By simply counting how many times a specific team has the most wins, we can determine the probability that each team finishes first in its four-team division

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2013 CFL regular season

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Conclusions Western Division: –Calgary overtook Saskatchewan –Saskatchewan lost 4 straight games in September Eastern Division: –Toronto was the dominant team all year

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Next steps Currently, each game is equally weighted However, the relatively recent games may have more influence on a team’s performance than games that occurred much earlier in the season Could adopt a weighting scheme that gives less emphasis to games earlier in the season

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Thank you for your time! Contact information: –Keith A. Willoughby, Ph.D. –University of Saskatchewan

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