Transcript 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
Part 3 – today's matches
• Up-to-date figures for tonight
Part 4 – backtesting and further applications
• Backtesting
• Outlook
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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
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Wanted: European Champion
Probabilities
The favorites:
Spain
24.6%
Netherlands 18.9%
Germany 15.6%
Croatia
14.3%
Portugal
9.9%
Turkey
5.1%
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Italy
Sweden
Romania
France
Russia
4.5%
2.3%
2.2%
1.3%
1.3%
Spain
Netherlands
Germany
Croatia
Portugal
Turkey
Italy
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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
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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
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FIFA World Ranking
• Both friendly and qualifying matches considered
• Monthly update
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Mathematical Ingredients (cont.)
General football statistics
• Goals scored by home teams
• Goals scored by away teams
• Frequency of draws
• Frequency of favorites underestimating
outsiders
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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]
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Dynamic Sports Analysis – the Output
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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
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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
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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%
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0.0%
100.0%
200.0%
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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
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Today's Matches
Netherlands – Romania
49.1% Netherlands wins
28.2% draw
22.7% Romania wins
France – Italy
27.0% France wins
29.0% draw
44.0% Italy wins
Quarter Finals Semi Finals
Final
Champion
Netherlands
100.0%
68.4%
33.8%
18.9%
Italy
44.8%
17.7%
8.8%
4.5%
Romania
34.4%
10.8%
5.0%
2.2%
France
20.8%
6.7%
2.9%
1.3%
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European Champion
evolution of probabilities over time
Group A
17 June
Portugal
9.9%
Turkey
5.1%
Czech Rep.
--Switzerland
---
15 June
15.4%
1.8%
7.3%
---
11 June
9.7%
0.5%
14.9%
0.8%
6 June
6.8%
2.6%
12.2%
2.7%
Group B
Germany
Croatia
Austria
Poland
15 June
11.5%
10.7%
0.2%
0.03%
11 June
17.7%
6.3%
0.1%
0.6%
6 June
14.2%
5.4%
0.7%
2.1%
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17 June
15.6%
14.3%
-----
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European Champion
evolution of probabilities over time
Group C
17 June
Netherlands 18.9%
Italy
4.5%
Romania
2.2%
France
1.3%
15 June
18.3%
4.3%
2.1%
1.2%
11 June
11.1%
5.7%
3.0%
4.3%
6 June
4.5%
15.6%
3.6%
5.9%
Group D
Spain
Sweden
Russia
Greece
15 June
23.9%
2.1%
1.3%
---
11 June
19.5%
3.5%
0.5%
1.6%
6 June
13.2%
1.3%
1.7%
7.5%
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17 June
24.6%
2.3%
1.3%
---
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Comparison with UBS, DeKaBank and
University of Vienna
Quarter Finals
Semi Finals
Final
Champion
UBS
CZE, GER, ITA, SPA,
SUI, CRO, NED, GRI
CZE, SUI, ITA, NED
CZE, ITA
CZE
DeKaBank
CZE, GER, ITA, SPA,
???, ???, FRA, ???
CZE, GER, ITA, SPA
GER, ITA
GER
University Vienna
POR, GER, ITA, SPA,
CZE, CRO, FRA, GRI
POR, GER, ITA, SPA
GER, SPA
GER
Roger Kaufmann
CZE, GER, ITA, SPA,
POR, CRO, FRA, GRI
CZE, GER, ITA, SPA
GER, ITA
ITA
• 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.
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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
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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
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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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Example of a Manager Decision
Qualification for Quarter Finals
Assumed results
CZE – POR 2:1
CZE – POR 1:1
CZE – POR 1:3
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 64.9%
75.1%
POR 99.8%
95.6%
SUI 28.1%
22.6%
TUR 7.3%
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 79.9%
80.7%
POR 100.0%
SUI 2.8%
TUR 17.3%
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 61.9%
76.8%
POR 100.0%
SUI 0.0%
TUR 38.1%
23.2%
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Thank you…
…for your attention!
• Questions?
Enjoy tonight’s match!
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