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Mathematical Modeling Transfers to Football

Mathematical Modeling Transfers to Football. Dr. Roger Kaufmann June 17, 2008. Mathematical Modeling Transfers to Football. Part 1 – introduction Relation football ↔ mathematics A first glance at the outcome Part 2 – mathematical approach Strength of a team Calculation of probabilities

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Mathematical Modeling Transfers to Football

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  1. Mathematical Modeling Transfers to Football Dr. Roger Kaufmann June 17, 2008

  2. Mathematical Modeling Transfers to Football Part 1 – introduction • Relation football ↔ mathematics • A first glance at the outcome Part 2 – mathematical approach • Strength of a team • Calculation of probabilities Part 3 – today's matches • Up-to-date figures for tonight Part 4 – backtesting and further applications • Backtesting • Outlook

  3. Football andMathematics • Strength of teams can be estimated • Statistics come into play • Uncertainties play an important role • Probabilities are the key element • Unexpected events change the initial situation • So-called conditional probabilities need to be considered

  4. Wanted: European Champion The favorites: Spain 24.6% Netherlands 18.9% Germany 15.6% Croatia 14.3% Portugal 9.9% Turkey 5.1% Italy 4.5% Sweden 2.3% Romania 2.2% France 1.3% Russia 1.3%

  5. Mathematical Modeling Transfers to Football Part 1 – introduction • Relation football ↔ mathematics • A first glance at the outcome Part 2 – mathematical approach • Strength of a team • Calculation of probabilities Part 3 – today's matches • Up-to-date figures for tonight Part 4 – backtesting and further applications • Backtesting • Outlook

  6. Mathematical Ingredients Strength of a team • Ranking lists • Matches won, tied, lost • Goals scored, goals received • FIFA World Ranking • Strength of a team is calculated depending on the results in each match • No consideration of single football players (injuries, etc.) • Only measurable information, no personal opinion

  7. FIFA World Ranking • Both friendly and qualifying matches considered • Monthly update

  8. Mathematical Ingredients (cont.) General football statistics • Goals scored by home teams • Goals scored by away teams • Frequency of draws • Frequency of favorites underestimating outsiders

  9. A Single Match Known: • Strength of both teams • Average number of goals in international matches Calculate: • Expected number of goals for both teams (n1, n2) Account for random effects and their correction: • Use Poisson distributions (with expected values n1, n2) to model the number of goals scored • Adapt (i.e. increase) probability of draws Output: • P[0:0], P[1:0], P[1:1], etc.; and P[win/draw/loss]

  10. Dynamic Sports Analysis – the Output

  11. Putting the Puzzle together – Calculation of a Championship The steps for calculating a whole championship (e.g. national championship, world cup, EURO): • Assess strength of each team • Calculate probability for each match • Simulate a potential result for each match • This yields one potential final ranking list • Repeat the above procedure thousands of times • Calculate probabilities for outcomes of interest

  12. National Championship vs.World Cup/EURO National championship: • Many matches • Randomness plays a minor role • Typically the strongest team wins World cup/EURO (knockout system): • A single bad day can ruin all hopes • Randomness plays an important role • Big chances for outsiders

  13. Betting Advice Compare: calculated probability vs. odds [all odds and probabilities as of end April 2008] Germany 15.0% x 5 = 75.0% Italy 13.4% x 8 = 107.2% Spain 13.2% x 7 = 92.4% Czech Rep. 11.1% x 15 = 166.5% Greece 7.5% x 26 = 195.0% Romania 3.7% x 41 = 151.7%

  14. Mathematical Modeling Transfers to Football Part 1 – introduction • Relation football ↔ mathematics • A first glance at the outcome Part 2 – mathematical approach • Strength of a team • Calculation of probabilities Part 3 – today's matches • Up-to-date figures for tonight Part 4 – backtesting and further applications • Backtesting • Outlook

  15. Today's Matches France – Italy 27.0% France wins 29.0% draw 44.0% Italy wins Netherlands – Romania 49.1% Netherlands wins 28.2% draw 22.7% Romania wins

  16. European Championevolution of probabilities over time

  17. European Championevolution of probabilities over time

  18. Comparison with UBS, DeKaBank and University of Vienna • Other researchers and risk managers performed calculations on the most probable outcome of the EURO 2008 as well. • Although based on different data sources, most results resemble each other. June 17, 2008 18

  19. Mathematical Modeling Transfers to Football Part 1 – introduction • Relation football ↔ mathematics • A first glance at the outcome Part 2 – mathematical approach • Strength of a team • Calculation of probabilities Part 3 – today's matches • Up-to-date figures for tonight Part 4 – backtesting and further applications • Backtesting • Outlook

  20. Backtesting Online betting pools • About 60 participations. Always among first 1/3 • Several 1st ranks, won many prizes Swiss lottery • Several times 12 correct results out of 13 • Return more than twice the expected one Mathematical backtesting • Backtesting possible for accumulation of predictions; not for a single match • e.g. 20 events with a probability of 80% each => expect 14 to 18 occurrences

  21. Outlook on Further Applications Live calculations during a match • Impact of: • Goals scored • Red cards given • Penalties given • Time evolved • Help manager to decide: • New forward in order to score a further goal • New defender in order to keep the current result • How much risk to take at a given moment

  22. Example of a Manager DecisionQualification for Quarter Finals June 11, 2008 22

  23. Thank you… …for your attention! • Questions? Enjoy tonight’s match!

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