As Liverpool fan I’m of course disappointed about the current run of own goal matches.
26 Dec 2011 LFC – Blackburn 1-1 (Own goal by Charlie Adam)
30 Dec 2011 LFC – Newcastle 3-1 (Own goal by Daniel Agger)
But despite suffering from own goals in two consecutive matches, LFC gained 4 points, so is it really that bad to concede an own goal?
The purpose of this blog is not to fully give an answer to questions like this, but to state facts which will indicate an answer, and when possible pose an imperfect case study which should be investigated further to give a more trustful answer.
So here we go…
Looking at (only) Liverpool’s premier league matches from ongoing season and the two previous seasons, counts 95 matches, of which Liverpool have suffered an own goal in 7 matches.
In my study design, I have looked at the goal differences of all 95 matches, and asked the question: “Does the sample of 7 goal differences from the 7 own goal matches come from the same underlying probability distribution as the 88 goal differences coming from the rest of the matches?”
The analysis is performed in R and the data has following appearance
> data
Type Gdiff
1 OGMatch 2
2 OGMatch 0
3 OGMatch -1
4 OGMatch 1
5 OGMatch 0
6 OGMatch -1
7 OGMatch -2
8 Match 0
9 Match 2
10 Match 1
11 Match -1
12 Match 0
.
.
95 Match -1
With the most recent matches with lowest indices. That is, observation 1 is the Newcastle match, observation 2 is the Blackburn match, observation 3 is last season’s away game against Tottenham of November 28th, and so on. Observation 8 is the Wigan match of December 21th, observation 9 is the Villa match of December 18th, and so on. Source http://www.liverpoolfc.tv/match/fixtures.
Here is the box-plot of the samples.
> boxplot(Gdiff~Type)
Because of the sample size and the lack of normality (not proved here - the bigger sample actually looks normal in a histogram, but for most clubs I believe goal difference data can’t be normally distributed), my analysis is based on the non-parametric Wilcoxon Rank Sum test also known as Mann-Whitney test.
Because we don’t expect it to be an advantage to score an own goal, and because the mean goal difference of own goal matches is lower than the mean of the other matches, we choose the one-sided alternative: “Is the goal difference higher for own goal matches?”
> mean(Gdiff[Type=='Match'])
[1] 0.5795455
> mean(Gdiff[Type=='OGMatch'])
[1] -0.1428571
And the test is performed as outlined
> wilcox.test(Gdiff[Type=='Match'],Gdiff[Type=='OGMatch'], alternative="greater", paired=FALSE)
Wilcoxon rank sum test with continuity correction
data: Gdiff[Type == "Match"] and Gdiff[Type == "OGMatch"]
W = 381, p-value = 0.1474
alternative hypothesis: true location shift is greater than 0
The null hypothesis is that own goal matches produce a higher or equal goal difference than other matches. Since the p-value = 0.1474 > 0.05, we can’t reject that hypothesis, that is, own goals does not have a significant negative effect on the goal difference of the game, when we (only) consider premier league matches played by Liverpool FC in the previous two and a half seasons.
Comment on the imperfect analysis: Above analysis should under no circumstances be regarded as a proof that own goals doesn’t influence soccer matches. The analysis is as most proving that Liverpool FC has done respectively well in their last 7 own goal matches (or not significantly worse than in the surrounding 88 matches since the beginning of the season 2009-10).
26 Dec 2011 LFC – Blackburn 1-1 (Own goal by Charlie Adam)
30 Dec 2011 LFC – Newcastle 3-1 (Own goal by Daniel Agger)
But despite suffering from own goals in two consecutive matches, LFC gained 4 points, so is it really that bad to concede an own goal?
The purpose of this blog is not to fully give an answer to questions like this, but to state facts which will indicate an answer, and when possible pose an imperfect case study which should be investigated further to give a more trustful answer.
So here we go…
Looking at (only) Liverpool’s premier league matches from ongoing season and the two previous seasons, counts 95 matches, of which Liverpool have suffered an own goal in 7 matches.
In my study design, I have looked at the goal differences of all 95 matches, and asked the question: “Does the sample of 7 goal differences from the 7 own goal matches come from the same underlying probability distribution as the 88 goal differences coming from the rest of the matches?”
The analysis is performed in R and the data has following appearance
> data
Type Gdiff
1 OGMatch 2
2 OGMatch 0
3 OGMatch -1
4 OGMatch 1
5 OGMatch 0
6 OGMatch -1
7 OGMatch -2
8 Match 0
9 Match 2
10 Match 1
11 Match -1
12 Match 0
.
.
95 Match -1
With the most recent matches with lowest indices. That is, observation 1 is the Newcastle match, observation 2 is the Blackburn match, observation 3 is last season’s away game against Tottenham of November 28th, and so on. Observation 8 is the Wigan match of December 21th, observation 9 is the Villa match of December 18th, and so on. Source http://www.liverpoolfc.tv/match/fixtures.
Here is the box-plot of the samples.
> boxplot(Gdiff~Type)
Because of the sample size and the lack of normality (not proved here - the bigger sample actually looks normal in a histogram, but for most clubs I believe goal difference data can’t be normally distributed), my analysis is based on the non-parametric Wilcoxon Rank Sum test also known as Mann-Whitney test.
Because we don’t expect it to be an advantage to score an own goal, and because the mean goal difference of own goal matches is lower than the mean of the other matches, we choose the one-sided alternative: “Is the goal difference higher for own goal matches?”
> mean(Gdiff[Type=='Match'])
[1] 0.5795455
> mean(Gdiff[Type=='OGMatch'])
[1] -0.1428571
And the test is performed as outlined
> wilcox.test(Gdiff[Type=='Match'],Gdiff[Type=='OGMatch'], alternative="greater", paired=FALSE)
Wilcoxon rank sum test with continuity correction
data: Gdiff[Type == "Match"] and Gdiff[Type == "OGMatch"]
W = 381, p-value = 0.1474
alternative hypothesis: true location shift is greater than 0
The null hypothesis is that own goal matches produce a higher or equal goal difference than other matches. Since the p-value = 0.1474 > 0.05, we can’t reject that hypothesis, that is, own goals does not have a significant negative effect on the goal difference of the game, when we (only) consider premier league matches played by Liverpool FC in the previous two and a half seasons.
Comment on the imperfect analysis: Above analysis should under no circumstances be regarded as a proof that own goals doesn’t influence soccer matches. The analysis is as most proving that Liverpool FC has done respectively well in their last 7 own goal matches (or not significantly worse than in the surrounding 88 matches since the beginning of the season 2009-10).
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