How often does a cup final go to penalties?

Yesterday Liverpool won the English League Cup and took home their first trophy since the FA Cup triumph in 2006 and the following FA Community Shield win. As Liverpool supporter I’m of course very happy, but I wasn’t impressed by the performance, especially not the performance by Captain fantastic (Gerrard). His performance was miles away from the outstanding show he pulled off in the 2005 Champions League final and the 2006 FA Cup final. He can’t run away from his age, and I’m sad to say, that one of my absolute favorites of all time doesn’t have many seasons left as a top player.

Liverpool excels in giving their supporters nail-biting and nerve-wracking finals. Yesterday’s performance was no exception, and an exciting penalty shoot-out should decide it all at last. A total of 5 missed penalties, tells the story: Liverpool didn’t earn it, but Cardiff couldn’t close it.

Enough about Liverpool. Lately I watched another final, the African Cup of Nations final between Ivory Coast and Zambia. Ivory Coast were big favorites before the match, and didn’t concede a single goal during the entire tournament. The final was a goalles draw, and in the penalty shoot-out, Zambia won the lottery.

After watching two consecutive finals go in to penalties, and thinking about Liverpool’s 2005 and 2006 wins (also penalties), I find myself browsing for different kind of statistics on penalties in finals.

A hypothesis is that finals and semifinals (and perhaps quarterfinals) more often go into penalties than preliminary round knock-out matches, because the teams are more evenly matched at that stage of the tournament. But collecting the information below, I have already spend my weekly blog hour, so it will have to do for now.

It’s hard to find information on when (for the first time) finals in specific tournament was scheduled to be decided on shoot-outs after full time and 30 minutes extra time. It has been introduced in different years in different tournaments. And often penalties are introduced several years before in earlier knock-out rounds than in the final.

I’m surprised that the two English Cups have introduced penalties in finals so late compared to the other tournaments I have investigated. Take a look at the stats. It certainly looks like the African teams should practice penalties before the final!

Tournament	Shoot-out scheduled in final first time	Finals since first scheduled	Shoot-out finals %
African Cup Of Nations	1980*	16	43,75
Fifa World Cup	1986	7	28,57
Uefa Champions League	1980**	32	28,13
English League Cup	1998	15	20,00
Uefa European Championship	1976	9	11,11***
English FA Cup	1993	19	10,53

*My best guess. In 1974 the drawn final triggered a replay. In 1976 the final stage of the tournament didn’t involve knock-out matches. In 1978 a qualification match was decided on shoot-out, but shoot-outs were also used in the qualification in 1974. In 1980 the first ever match of the knock-out stage of the finals was decided on penalties.

**My best guess. In 1974 the drawn final triggered a replay. In 1980 the drawn final of the Uefa Cup Winners Cup is decided on penalties after the 30 minutes extra time. In 1984 the first Uefa Champions League final is decided on penalties.

***Two finals which possibly could have gone to penalties were decided on golden goal.

A bunch of wiki-sources was used to gather above information. Here are the links which gives the critical years:
http://en.wikipedia.org/wiki/Penalty_shoot-out_%28association_football%29
http://en.wikipedia.org/wiki/Africa_Cup_of_Nations
http://en.wikipedia.org/wiki/List_of_European_Cup_and_UEFA_Champions_League_winners
http://en.wikipedia.org/wiki/FA_Cup_Final
http://en.wikipedia.org/wiki/List_of_Football_League_Cup_winner

And here is a really interesting one on penalties. By Karel Stokkermans and Carles Lozano, enjoy:
http://www.rsssf.com/miscellaneous/penalties.html

Does Howard Webb favour Manchester United?

Howard Webb is one of the highest ranked referees in the English Premier League. Since 2005 he has been FIFA-listed, and in 2010 he refereed the FIFA World Cup Final between Spain and the Netherlands. There is a lot of great facts on Howard Webb on the wiki site http://en.wikipedia.org/wiki/Howard_Webb, including a criticisms section, where three incidents where Manchester United seems to be favoured.

But what does three incidents say about a referees overall appearance? Let’s instead look at some stats.

Now, I will consider penalties given. You could look at yellow cards or sending offs, but the criticism is mostly about penalties.  

Looking at the top teams of the last five seasons of the Premier League (2007-08 up until now, todays matches not included) we get following summary statistics (source http://www.statbunker.com/):

Team	M	PF	PA	PF/M	PA/M	(PF-PA)/M
Arsenal	16	1	3	0,0625	0,1875	-0,1250
Chelsea	14	1	2	0,0714	0,1429	-0,0714
Liverpool	18	2	2	0,1111	0,1111	0,0000
Manchester City	14	2	1	0,1429	0,0714	0,0714
Manchester United	23	7	2	0,3043	0,0870	0,2174
Tottenham Hotspur	16	1	3	0,0625	0,1875	-0,1250

Where M=Matches refereed, PF=penalties for and PA=penalties against.

So is 0.2174 significantly higher than the rest of the (PF-PA)/M sample?

If we assume normality of data (I know the sample size actually is too small, but I think that for a bigger sample, data would approach normality), the 95 percent confidence interval for the sample without the Man U=MU (funny!) observation is [-0.1556,  0.0556], and the t-test gives a p-value of 0.002159, strongly indicating that the MU observation has no chance of being the real mean value of Howard Webb’s (PF-PA)/M-population. That is, this short analysis suggests that Howard Webb do favour Manchester United, though it’s a hard accusation. An approved analysis would of course compare above results with results of other referees, to decide if Howard Webb really does favour United.

Now I will enjoy Manchester United-Liverpool with Phil Dowd as referee, and I hope he will favour Liverpool.