The role of randomness
Its quite hard to accept the role that randomness plays in the outcome of world cup matches. Every nation when they get kicked out or fail to even qualify probably believes their teams were "unlucky" and that their teams are better than they actually are. So what is the relative importance of luck v skill when it come to winning the world cup?
Unlike the premiership where there are 38 games over which time the performance of the teams is largely correlated to the quality of the squads (take a read of the Number Game* by Chris Anderson and David Sally) performance of a world cup squad cannot be calculated by the aggregated skill value of the squad there is a lot more randomness involved. Imagine if the premiership only lasted 3 games: in two out of the last four seasons the team that one the premiership might have been relegated.
*a must read if you are a market researcher and like football!
There is another factor too, in the premiership the best players get sucked up into the best teams hence the much higher win ratios between the top and bottom performing sides compared to the world cup where the best players are distributed more randomly and is proportional to the size of each footballing nation. This in tern makes the outcome of international matches even more random.
Who influences the outcome of a match?
If you look at who has goal scoring influence across a team you will notice that the negative effects of causing goals a pretty well distributed across a team but the positive effects of scoring goals are a lot more clustered amongst some individuals. See chart below showing statistics from an imaginary team based on typical performance data taken from the premier league.
The performance of defence is more a case of luck. You might have one or two unreliable defenders who you may not want in your premier league squad because you know over the course of a season they may cost you a match or two, but at the individual game level and a world cup is based on the outcome of three or four key individual games, the chances are a poor defender might well run their luck. The other two important factors defenders have to contend with are the extra stress and lack of team playing experience of a world cup team compared to a premiership squad. Without doubt stress plays a big part, players are really hyped up and there is probably an order of magnitude increase in tension which is the root cause of many errors in world cup matches. If you look at the defensive mistakes that cost us goals in recent world cups some of the biggest mistakes were caused by effectively our most reliable players, John Terry and Steven Gerrard and Phil Neville. There is also a lack of formation practice to contend which is particularly critical for defence. How many hours of playing together does it take for a defence to gel? Most world cup squads have days rather than months to prepare.
A team like England might well have a higher aggregated skill performance average compared to other teams, but this does not result in the same reliable performance ratios that you see in the premiership. This is because over half the value is based on their defensive skill which can be completely undermined by bad luck and we don’t have a cluster of super-skilled players to elevate the team out of bad luck matches by scoring more goals than we let in.
The influence of the Ref
To win world cup matches you are much more reliant on the manager’s structural approach, the contributions from clusters of individuals who might form good attacking combinations and one other person – the REF! Or rather, the ref in conjunction with the crowd and the linesmen.
*That is a wisdom of the crowd estimate by asking a collection of football fans how many goal-affecting decisions are made in the match by the referee and linesmen, six was the median average estimate.
Now in nine times out of ten these decisions balance themselves out but refs are only human and so it’s no wonder why there is such a big home team advantage – with 50,000 fans screaming penalty it must be extremely difficult for refs not to be influenced by the crowd. In fact you can almost put a figure on the influence of the crowd by comparing home and away goal scoring averages the home side gains an average 0.35 of a goal per game net advantage if you examine premiership games, which can only be really down to the net contribution of the crowd/ref decision effects.
It’s no wonder as a result that there is such a disproportionate home nation advantage. Effectively every home nation team is starting with a 0.35 goal lead, this advantage aggregated up over the course of a tournament has means that nearly 30% of all world cups have been won by the home nation that is 10 times higher than chance.
Am I likely to ever see England win another world cup in my lifetime?
Is probably a question most England fans ask themselves. What does it take to win a world cup – how good do you have to be to override luck? We have taken a look at this and run some calculations.
The chart below take a little explaining but it maps out a team’s skill level v the number of times it’s likely to win a world cup over the course of someone’s average football supporter’s lifetime of 72 years = 18 world cups. If there are 32 teams in a word cup and you are an average team and your team qualifies for every world cup final the chances are you will win 1.1 world cups over your lifetime. If in you are England and only qualify roughly 80% of the time the changes will drop to 0.96. If your team is twice as good as average, you are likely to win roughly 2 world cups and 4 times better 6 world cups.
England have one one world cup, Germany three and Brazil five so does that mean we are average team and Germany are three times better than us and Brazil four times better than us?
Well essentially yes, if you look at the average game-win ratios of all the teams that have played the most regularly in World Cups v the number of World Cups they have won its pretty closely correlated at 0.91. Germany has a three times higher win ratio than us and Brazil four times higher.
Now I appreciate there is some self-selection involved here – this chart should really be based on first round matches only for a totally fair comparison, but we don’t have that data. I think it’s reasonable to say though that England has not really been done out of its fair share of World Cups. I think we have won as many as our teams aggregated performance deserves. You might argue that some teams have been luckier than most: Italy certainly and others unlucky, Mexico should have won it twice by now based on their aggregated performance.
Roughly speaking that means for me there is only about a 40% chance I will witness England lift a world cup in my remaining lifetime but almost certainly I will have to endure another series of victories for Germany and Brazil. Oh well better come to terms with it but I live in hope.
But lets fantasise for a minute, how many world Cups could we have won?
Imagine we lived in an infinite number of universes where for the last 70 years we had been playing an infinite series of world cups with a team with the same skill level.
Well on average 32% of the time we would not have won a single world cup by now, in 21% of cases we might have picked up two and in 7% of case the same number as Germany. There is one universe in 5,000 where Germany would not have won a single world up and England would have won 4! Anyone fancy moving there?