Mathematical Modeling Transfers to Football

Dr. Roger Kaufmann

May 2014

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 2014 2

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 2014 3

Wanted: World Champion

May 2014 4

Probabilities

Brazil Argentina Germany Spain Colombia Uruguay Chile Netherlands Ecuador Portugal France England Italy Russia USA Belgium Switzerland Others

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%

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 – Switzerland vs. Ecuador

• Up-to-date figures for the first match of Switzerland

Part 4 – backtesting and further applications

• Backtesting • Outlook

May 2014 5

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 2014 6

Elo Rating

• Both friendly and qualifying matches considered

• Daily update

May 2014 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

May 2014 8

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]

May 2014 9

Dynamic Sports Analysis – Original Output

May 2014 10

Dynamic Sports Analysis – iPhone App

May 2014 11

Link:

www.rogerkaufmann.ch/apps

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 2014 12

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 2014 13

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 2014 14 0% 100% 200% 300% 400% 500% 600%

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 2014 15

Group E – First Round

Switzerland – Ecuador

30.7% Switzerland wins

31.1% draw

38.2% Ecuador wins

May 2014 16

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%

France – Honduras

43.5% France wins

30.4% draw

26.2% Honduras wins

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 2014 17

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

May 2014 18

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

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May 2014 20

Assumed results CZE – POR 2:1 CZE – POR 1:1 CZE – 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 EURO 2008, Qualification for Quarter Finals

Assumed results CZE – POR 2:1 CZE – POR 1:1 CZE – 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 the FIFA World Cup 2014!

May 2014 21