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Monte carlo simulation for floorball results
- 1. Monte Carlo Simulation for Floorball results Simulation 30E00400 Course project Ville Lehtonen (K93890), Miikka Kataja (239680)
- 2. Introduction What are we doing?
- 3. Salibandyliiga in a nutshell ?? 14 teams ?? A twofold regular season - 182 games ?? Top 8 teams continue in playoffs ?? Weakest team will be relegated from the league ?? Teams placing 12. and 13. face elimination rounds This project simulates results of the regular season, based on game results during 1990-2015
- 4. Research question ”What are the final standings and which team will win Salibandyliiga regular season 2015-2016?”
- 5. Assumptions ?? Amount of goals scored in a single match follow truncated Poisson distribution – based on data (1990-2015) ?? Statistically siginficant difference in scored home goals vs. scored away goals – F-test, t-test ?(?; ?)=?Pr?( ?= ?)?= ?? ?↑??? ?↑? ??/?!?, where x = {1,2,3, …, 25} 0% 5% 10% 15% 20% 1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526 Figure 1: Realized goal distribution vs. Poisson distribution truncated Poisson distribution Realized goal distribution 5.33 4.90 3 3.5 4 4.5 5 5.5 6 Home team Away team Figure 2: Avg. number of goals for home and away team
- 6. Building the model How did we do it?
- 7. Step 1: Averages for goal distributions ?λ↓( ? ??. ?)?=? ?? Goal averages for each matchpair are derived from historical data
- 8. Step 2: How is a single match simulated? Un ~ U(0,1) Um ~ U(0,1) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 pdf: goal distributions for team n vs. team m Team n Team m
- 9. Step 2: How is a single match simulated? Un ~ U(0,1) Um ~ U(0,1) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 cdf: goal distributions for team n vs. team m Team n Team m
- 10. Step 2: How is a single match simulated? Un = 0,65 Um = 0,79 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 cdf: goal distributions for team n vs. team m Team n Team m
- 11. Step 2: How is a single match simulated? Un = 0,65 Um = 0,79 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 cdf: goal distributions for team n vs. team m Team n Team m
- 12. Step 2: How is a single match simulated? Un = 0,65 Um = 0,79 Match result 5 - 9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 cdf: goal distributions for team n vs. team m Team n Team m
- 13. Step 3: Match outcome probabilities ?? Simulation of each match pair x 1000 times to gain probabilities for different match outcomes Team n wins 68% of the time Match ends as a draw 10% of the time Team m wins 22% of the time
- 14. Step 4: Simulation of one season ?? The outcome of each match is determined with a LOOKUP function and a uniformly distributed random number U ~ U(0,1) ?? Cumulative match outcome probabilities Team n wins 0,68 Draw 0,78 Team m wins 1,0
- 15. Step 4: Simulation of one season ?? The outcome of each game is determined with a LOOKUP function and a uniformly distributed random number U ~ U(0,1) ?? Cumulative match outcome probabilities Team n wins 0,68 Draw 0,78 Team m wins 1,0 U = 0,82
- 16. Step 4: Simulation of one season ?? The outcome of each game is determined with a LOOKUP function and a uniformly distributed random number U ~ U(0,1) ?? Cumulative match outcome probabilities Team n wins 0,68 Draw 0,78 Team m wins 1,0 ?? 182 matches ?? Win = +2p, draw = +1p U = 0,82 Team m wins!
- 17. Step 5: Outcomes of the model ?? After 1000 simulation runs of a single season Points per team per season Average, max and min points per team after 1000 simulation runs Variance, standard deviation and standard error of mean of points per team after 1000 simulation runs
- 18. Findings What did we find out?
- 19. Iteration 1 ?? Data: Past 3 seasons ?? Assumptions: Home advantage does not exist ?? Problems: Older data has too much weight on results 14% 49% 26% 9% 2% Probability of placing top 1 in regular season - iteration 1 Classic Happee SPV SSV Oilers 0 5 10 15 20 25 30 35 40 45 Team performance: Avg. points per team - iteration 1
- 20. Iteration 2 ?? Data: Past 1? seasons ?? Assumptions: Home advantage does exist ?? Problems: Poisson distribution with too low sample size 61% 10% 2% 3% 26% Probability of placing top 1 in regular season - iteration 2 Happee SPV Oilers SSV Classic 0 5 10 15 20 25 30 35 40 45 Team performance: Avg. points - Iteration 1 & 2 Iteration 2 Iteration 1
- 21. Iteration 3 ?? Data: 3? seasons with weights (0,6 / 0,25 / 0,15) ?? Assumptions: Home advantage does exist ?? Problems: Are weights accurate? 54% 15%3% 7% 21% Probability of placing top 1 in regular season - Iteration 3 Happee SPV Oilers SSV Classic
- 22. Comparison: Team performance 41 37 39 36 32 25 25 22 22 22 18 18 15 12 40 38 35 33 32 24 25 20 23 19 23 18 18 14 40 38 37 35 33 26 24 22 21 20 19 17 16 16 0 5 10 15 20 25 30 35 40 45 Happee Classic SPV SSV Oilers Er? KooVee TPS Indians NST OLS Nokian KrP M-team SalBa Comparsion of iterations: Team perforamnce - avg. of points Iteration 1 Iteration 2 Iteration 3 Lineaarinen (Iteration 1) Lineaarinen (Iteration 3)
- 23. Comparison: Variance 0 5 10 15 20 25 Happee SPV Oilers SSV Classic Er? KooVee OLS Indians M-team Nokian KrP TPS NST SalBa Comparison of iterations: Variances Iteration 1 Iteration 2 Iteration 3
- 24. Conclusion What did we learn?
- 25. Predicted final standings 54% 15% 3% 7% 21% Probability of placing top 1 in regular season Happee SPV Oilers SSV Classic
- 26. Limitations ?? There is no perfect data set available ?? teams and their relative strenghts change between seasons ?? Salibandyliiga is probably not the most optimal sports league to use the model for ?? Only 182 games per season (vs. NHL 1230 games per season) ?? Different teams each season à Timeliness of data vs. sample size
- 27. Comparison to current standings Current Prediction
- 28. Questions?