Mathematical Modeling Transfers to Football. Dr. Roger Kaufmann May 2014

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1 Mathematical Modeling Transfers to Football Dr. Roger Kaufmann May 2014

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 Switzerland vs. Ecuador Up-to-date figures for the first match of Switzerland Part 4 backtesting and further applications Backtesting Outlook May

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

4 The favorites: Wanted: World Champion Brazil 21.8% Argentina 10.1% Germany 8.0% Spain 7.5% Colombia 5.2% Uruguay 4.3% Chile 4.1% Netherlands 3.7% Ecuador 3.5% Portugal 3.3% France 2.9% England 2.8% Italy 2.4% Russia 2.2% USA 2.0% Belgium 1.8% Switzerland 1.8% Others 13.3% Probabilities Brazil Argentina Germany Spain Colombia Uruguay Chile Netherlands Ecuador Portugal France England Italy Russia USA May 2014 Belgium Switzerland 4 Others

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 Switzerland vs. Ecuador Up-to-date figures for the first match of Switzerland Part 4 backtesting and further applications Backtesting Outlook May

6 Mathematical Ingredients Strength of a team Ranking lists Matches won, tied, lost Goals scored, goals received Elo rating (more stable than FIFA 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 May

7 Elo Rating Both friendly and qualifying matches considered Daily update May

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 May

9 A Single Match Known: Strength of both teams Average number of goals in international matches Calculate: Expected number of goals for both teams (n 1, n 2 ) Account for random effects and their correction: Use Poisson distributions (with expected values n 1, n 2 ) 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] May

10 Dynamic Sports Analysis Original Output May

11 Dynamic Sports Analysis iphone App Link: May

12 Putting the Puzzle together Calculation of a Championship The steps for calculating a whole championship (e.g. national championship, world cup): 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 May

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

14 Betting Advice Comparison: calculated probability vs. odds [all odds and probabilities as of March 2014] Brazil 21.8% x 3 = 65.4% Argentina 10.1% x 4 = 40.4% Germany 8.0% x 4 = 32.0% Spain 7.5% x 5 = 37.5% Chile 4.1% x 33 = 135.3% Switzerland 1.8% x 50 = 90.0% Ecuador 3.5% x 95 = 332.5% USA 2.0% x 140 = 280.0% Greece 1.3% x 180 = 234.0% Iran 0.8% x 750 = 600.0% Costa Rica 0.6% x 850 = 510.0% Honduras 0.6% x 900 = 540.0% May % 100% 200% 300% 400% 500% 600%

15 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 Switzerland vs. Ecuador Up-to-date figures for the first match of Switzerland Part 4 backtesting and further applications Backtesting Outlook May

16 Group E First Round Switzerland Ecuador 30.7% Switzerland wins 31.1% draw 38.2% Ecuador wins France Honduras 43.5% France wins 30.4% draw 26.2% Honduras wins Group Winner Round of 16 Quarter Finals Semi Finals Final Champion Ecuador 31.4% 58.3% 31.2% 16.6% 7.5% 3.5% France 29.3% 56.2% 28.9% 15.1% 6.6% 2.9% Switzerland 24.0% 49.3% 23.6% 11.4% 4.6% 1.8% Honduras 15.3% 36.2% 14.0% 5.4% 1.8% 0.6% May

17 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 Switzerland vs. Ecuador Up-to-date figures for the first match of Switzerland Part 4 backtesting and further applications Backtesting Outlook May

18 Backtesting Online betting pools About 60 participations. Always among first 1 / 3 Several 1 st 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 May

19 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 May

20 Example of a Manager Decision EURO 2008, Qualification for Quarter Finals Assumed results CZE POR 2:1 CZE POR 1:1 CZE POR 1:3 1:2 CZE 100.0% CZE 96.6% CZE 64.9% 75.1% SUI TUR 2:1 POR 72.5% POR 78.4% POR 99.8% 95.6% SUI 27.5% SUI 25.0% SUI 28.1% 22.6% TUR 0.0% TUR 0.0% TUR 7.3% 6.7% CZE 100.0% CZE 83.8% CZE 79.9% 80.7% SUI TUR 1:1 POR 76.5% POR 81.9% POR 100.0% SUI 23.0% SUI 19.8% SUI 2.8% TUR 0.5% TUR 14.5% TUR 17.3% 16.5% CZE 97.1% CZE 79.7% CZE 61.9% 76.8% SUI TUR 1:2 POR 81.1% POR 99.6% POR 100.0% SUI 4.5% SUI 0.0% SUI 0.0% TUR 17.3% TUR 20.6% TUR 38.1% 23.2% May

21 Thank you for your attention! Questions? Enjoy the FIFA World Cup 2014! May

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