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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.

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Presentation on theme: "Who’s on First: Simulating the Canadian Football League regular season Keith A. Willoughby, Ph.D. University of Saskatchewan Joint Statistical Meetings."— Presentation transcript:

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

2 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?

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

4 Western Division Eastern Division CFL teams (2014)

5 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

6 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

7 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

8 “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

9 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

10 Power rankings model 

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

13 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

14 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

15 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

16 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”

17 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

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

19 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

20 2013 CFL regular season

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

23 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

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


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