Footballers' fallacies

Peter Ayton & Anna Braennberg (City University London)

1) Vulnerable just after scoring?

2) Goal just before half-time has more impact?

3) Form: Are players who scored in preceding games more likely to score in their next game (the “hot foot”)?

Footballers' fallacies

Do you think teams are temporarily more vulnerable just after scoring a goal?11/15

Do you think teams are more likely to concede a goal just after scoring than at other times during a game?

6/15

Imagine you go in at half-time from a game 1-0 ahead. Do you think it is better if the goal was scored just before half-time rather than earlier in the game?

9/15

Do you think it gives you a better chance of winning the game if the goal was scored just before half-time rather than earlier in the game?

5/15

Do you think players go on and off form even when fully match fit?14/15

Imagine one of your players had scored in each of his last two games. Do you think he would be more or less likely than usual to score in the next game?

‘More likely’: 13/15

Footballers' fallacies A Survey of Professional premier league footballers

The hot foot?Alan Shearer

Shearer scores in 50/86=58% of his games but in 24/36=66% of games where he had not scored previously and 26/50=52% of games where he previously had scored.

The hot foot?Alan Shearer

Shearer scores in 50/86=58% of his games but in 24/36=66% of games where he had not scored previously and 26/50=52% of games where he previously had scored.

But: Alternation problem – home games alternate with away games and players score more at home than away…

The hot foot?Alan Shearer (Home games only)

At home Shearer scores in 34/43=79% of games. If he failed to score in his previous game then his hit-rate is 17/20=85%. If he scored in his last game then his hit-rate is lower at 17/23=74%.

Alan Shearer (Away games only)

Shearer scored in 16 away games and failed to score in 27 - a rate of 16/43=37%. If he had previously not scored his hit rate was 7/16=44%. But if he had scored last game then his rate 9/27=33%.

The hot foot?Top 12 Premier League scorers (Home games only)

Just looking at home games, our sample of players score in 196/451=43% of the games. If they had been previously unsuccessful (including ocasions when the previous game was away) then the rate was 125/298=42%; if they were previously successful then the rate was 71/153=46%. χ2 (1 df) = .88 (p=0.366)

The hot foot?Top 12 Premier League scorers (Home games only)

Just looking at home games, our sample of players score in 196/451=43% of the games. If they had been previously unsuccessful (including ocasions when the previous game was away) then the rate was 125/298=42%; if they were previously successful then the rate was 71/153=46%. χ2 (1 df) = .88 (p=0.366)

Top 12 Premier League scorers (All games)

χ2 (1 df) = .190 (p=0.663)

Win (%)Draw (%)

Lose (%)

1 to 15

16 to 30

31 to 45

65.35

25.98

8.66

67.24

24.14

8.62

63.39

28.57

8.04

0

10

20

30

40

50

60

70

% probability

Result of game

Minute when 1st half goal wasscored

Probability (%) of result for team winning 1-0 at half-time

355 Premier League games that were poised 1-0 at half time

Win

by

3

Win

by

2

Win

by

1

Draw

Lose

by

1

Lose

by

2

Lose

by

3

1 to 15

16 to 30

31 to 45

Total

0

20

40

60

80

100

120

140

Num

ber o

f gam

es

Win

by

3

Win

by

2

Win

by

1

Draw

Lose

by

1

Lose

by

2

Lose

by

3

1 to 15

16 to 30

31 to 45

Total

Result of game

Time in the first half when the 1st goal was scored

Probability of result for a team winning 1-0 at half-time.

Win by3

Win by2

Win by1

Draw Lose by1

Lose by2

Lose by3

Result of game.

1*5

11*15

21-25

31-35

41-45

Total

Minute in the first halfwhen the 1st goal wasscored

0102030405060708090

100110120130140

Num

ber

of g

ames

Win by3

Win by2

Win by1

Draw Lose by1

Lose by2

Lose by3

Result of game.

1*5

11*15

21-25

31-35

41-45

Total

Minute in the first halfwhen the 1st goal wasscored

Probability of result for a team winning 1-0 at half-time.

1 2 3 4

20

25

30

Quartile

16.5%

26.8%

25.2%

31.5%P

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ent

ag

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als

sco

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qua

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of t

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rst g

oa

l.

Are teams really vulnerable after scoring?

Across two Premier League seasons 127 games ended 1-1.

1 2 3 4

20

25

30

Quartile

16.5%

26.8%

25.2%

31.5%P

erc

ent

ag

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f go

als

sco

red

in e

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Are teams really vulnerable after scoring?

• Despite the increasing use of statistics in football coverage, these often have a "trainspotter" uselessness about them. Perhaps the last time a goalkeeper whose mother-in-law's maiden name began with a "Q" saved a penalty in the 2nd half of an FA cup semi-final was in 1897, but….?

• Maybe the pundits would be embarrassed by more rigorous analyses. Wagenaar (1989) analysed all world cup final tournaments from 1930-86 and found 172 triads of matches (A played B; A played C; B played C) and 30 intransitivities. This indicates that only 5 per cent of the variance could be atrributed to due to team strength—95% of the outcome of each game is due to non-stable factors - chance if you will.

• Wagenaar argues that it is this uncertainty that makes games exciting. If it were possible to predict the result, they would be boring.

• Perhaps dispensing with proper analysis in sport gives more room for the endless "debate" which inevitably accompanies sport. I suspect it is largely froth and about as insightful as a the TV commentary on the numbers drawn in the Lottery.

Footballers' fallacies