Transcript Footballers` fallacies - staff.city.ac.uk

Footballers' fallacies
Peter Ayton & Anna Braennberg
(City University London)
Footballers' fallacies
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
A Survey of Professional premier league footballers
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
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)
Probability (%) of result for team winning 1-0 at half-time
65.35
67.24
70
63.39
60
50
25.98
40
24.14
28.57
30
8.66
% probability
31 to 45
8.62
20
16 to 30
10
8.04
0
1 to 15
Minute when 1st half goal was
scored
Win (%)
Draw (%)
Result of game
Lose (%)
355 Premier League games that were poised 1-0 at half time
Probability of result for a team winning 1-0 at halftime.
140
100
80
60
Lose by 3
Lose by 2
Lose by 1
Draw
Win by 1
Win by 3
Win by 2
Result of game
1 to 15
0
16 to 30
20
Total
40
31 to 45
Number of games
120
Time in the first
half w hen the 1st
goal w as scored
Number of games
Probability of result for a team winning 1-0 at half-time.
140
130
120
110
100
90
80
70
60
50
40
30
20
10
0
Total
41-45
31-35
21-25
11*15
1*5
Win by Win by Win by
3
2
1
Draw Lose by Lose by Lose by
1
2
3
Result of game.
Minute in the first half
when the 1st goal was
scored
Are teams really vulnerable after scoring?
Percentage of goals scored in each
quartile of time since the first goal.
31.5%
30
26.8%
25.2%
25
20
16.5%
1
2
3
4
Quartile
Across two Premier League seasons 127 games ended 1-1.
Are teams really vulnerable after scoring?
Percentage of goals scored in each
quartile of time since the first goal.
31.5%
30
26.8%
25.2%
25
20
16.5%
1
2
3
Quartile
4
Footballers' fallacies
•
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.