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 2006-2012 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 ≤ -20400.0% -20 < β i – β j ≤ -1510220.0% -15 < β i – β j ≤ -1031825.8% -10 < β i – β j ≤ -5984646.9% -5 < β i – β j ≤ 01085651.9% 0 < β i – β j ≤ 51127667.9% 5 < β i – β j ≤ 10946670.2% 10 < β i – β j ≤ 15343397.1% 15 < β i – β j ≤ 2010 100.0% β i – β j > 2033100.0% 2006-2012 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 2006-2012 –“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

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 –willoughby@edwards.usask.cawilloughby@edwards.usask.ca