1 / 23

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

marcy
Télécharger la présentation

Mathematical Modeling Transfers to Football

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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!

More Related