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

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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 Part 3 – today's matches Up-to-date figures for tonight Part 4 – backtesting and further applications Backtesting Outlook June 17, 20082

Football and Mathematics 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 June 17, 20083

Wanted: European Champion June 17, 20084 Spain24.6% Netherlands18.9% Germany15.6% Croatia14.3% Portugal 9.9% Turkey 5.1% Italy4.5% Sweden2.3% Romania2.2% France1.3% Russia1.3% The favorites:

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 June 17, 20085

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 June 17, 20086

FIFA World Ranking Both friendly and qualifying matches considered Monthly update June 17, 2008 7

Mathematical Ingredients (cont.) General football statistics Goals scored by home teams Goals scored by away teams Frequency of draws Frequency of favorites underestimating outsiders June 17, 20088

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] June 17, 20089

Dynamic Sports Analysis – the Output June 17, 200810

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 June 17, 200811

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 June 17, 200812

Betting Advice Compare: calculated probability vs. odds [all odds and probabilities as of end April 2008] Germany15.0% x 5= 75.0% Italy13.4% x 8= 107.2% Spain13.2% 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% June 11, 200813

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 June 17, 200814

Today's Matches Netherlands – Romania 49.1% Netherlands wins 28.2% draw 22.7% Romania wins June 17, 200815 Quarter FinalsSemi FinalsFinalChampion Netherlands100.0%68.4%33.8%18.9% Italy44.8%17.7%8.8%4.5% Romania34.4%10.8%5.0%2.2% France20.8%6.7%2.9%1.3% France – Italy 27.0% France wins 29.0% draw 44.0% Italy wins

European Champion evolution of probabilities over time June 17, 200816 Group A17 June15 June11 June6 June Portugal9.9%15.4%9.7%6.8% Turkey5.1%1.8%0.5%2.6% Czech Rep. ---7.3%14.9%12.2% Switzerland --- 0.8%2.7% Group B17 June15 June11 June6 June Germany15.6%11.5%17.7%14.2% Croatia14.3%10.7%6.3%5.4% Austria---0.2%0.1%0.7% Poland---0.03%0.6%2.1%

European Champion evolution of probabilities over time June 17, 200817 Group C17 June15 June11 June6 June Netherlands 18.9%18.3%11.1%4.5% Italy4.5%4.3%5.7%15.6% Romania2.2%2.1%3.0%3.6% France1.3%1.2%4.3%5.9% Group D17 June15 June11 June6 June Spain24.6%23.9%19.5%13.2% Sweden2.3%2.1%3.5%1.3% Russia1.3% 0.5%1.7% Greece--- 1.6%7.5%

Comparison with UBS, DeKaBank and University of Vienna June 17, 200818 Quarter FinalsSemi FinalsFinalChampion UBS CZE, GER, ITA, SPA, SUI, CRO, NED, GRI CZE, SUI, ITA, NEDCZE, ITACZE DeKaBank CZE, GER, ITA, SPA, ???, ???, FRA, ??? CZE, GER, ITA, SPAGER, ITAGER University Vienna POR, GER, ITA, SPA, CZE, CRO, FRA, GRI POR, GER, ITA, SPAGER, SPAGER Roger Kaufmann CZE, GER, ITA, SPA, POR, CRO, FRA, GRI CZE, GER, ITA, SPAGER, ITAITA 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.

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 June 17, 200819

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 June 17, 200820

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 June 17, 200821

June 11, 200822 Assumed results CZE – POR 2:1CZE – POR 1:1CZE – POR 1:2 SUI – TUR 2:1 CZE 100.0% POR 72.5% SUI 27.5% TUR 0.0% CZE 96.6% POR 78.4% SUI 25.0% TUR 0.0% CZE 75.1% POR 95.6% SUI 22.6% TUR 6.7% SUI – TUR 1:1 CZE 100.0% POR 76.5% SUI 23.0% TUR 0.5% CZE 83.8% POR 81.9% SUI 19.8% TUR 14.5% CZE 80.7% POR 100.0% SUI 2.8% TUR 16.5% SUI – TUR 1:2 CZE 97.1% POR 81.1% SUI 4.5% TUR 17.3% CZE 79.7% POR 99.6% SUI 0.0% TUR 20.6% CZE 76.8% POR 100.0% SUI 0.0% TUR 23.2% Example of a Manager Decision Qualification for Quarter Finals Assumed results CZE – POR 2:1CZE – POR 1:1CZE – POR 1:3 SUI – TUR 2:1 CZE 100.0% POR 72.5% SUI 27.5% TUR 0.0% CZE 96.6% POR 78.4% SUI 25.0% TUR 0.0% CZE 64.9% POR 99.8% SUI 28.1% TUR 7.3% SUI – TUR 1:1 CZE 100.0% POR 76.5% SUI 23.0% TUR 0.5% CZE 83.8% POR 81.9% SUI 19.8% TUR 14.5% CZE 79.9% POR 100.0% SUI 2.8% TUR 17.3% SUI – TUR 1:2 CZE 97.1% POR 81.1% SUI 4.5% TUR 17.3% CZE 79.7% POR 99.6% SUI 0.0% TUR 20.6% CZE 61.9% POR 100.0% SUI 0.0% TUR 38.1%

Thank you… …for your attention! Questions? Enjoy tonights match! June 17, 200823

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