Monday 3 August 2020

On Football Managers and Randomness of Success

Football managers are a strange bunch. No matter how successful they are, many seem to spend a lot of their time bitterly fuming about bad decisions, conspiracies against them and referee biases and generally brooding on many dark thoughts even about their own players.

Which is quite odd really, when you think that these are extremely successful professionals in a very competitive field. These are the best in the world. And usually the best people in the world in any sphere have a positive attitude. They would forget past setbacks, except insomuch as you can learn from them, and look to the future. Not football managers. They can look back and name every single time they were hard done by.

I have a theory as to why this is. It's because in football managership, more than almost any other profession, success is largely determined by luck. That is not to say that there are not very good (and bad) managers. But that the 'error' between input and outcome is one of the largest of any job.

Supposing you are a solicitor with 100 cases a year. Maybe if you are good at your job you will win on average 60, and if you are bad you will win 40. Over the course of 1 year, 5 years or 10 years, it will become pretty clear if you are good at your job or not. Yes, your promotions and success will depend on other factors like office politics and luck with job openings. But these are the same in every career. As a salesman, as a doctor, as an accountant, as a bus driver. Short of some catastophic bad luck that ends your career, you have a pretty good chance that your success is very closely related to your ability and your effort (assumiong no prejudices against you for whatever reason).

As a football manager, firstly you get relatively few job opportunities in your career. Unless you make a success reasonably early on you are more-or-less on the scrapheap. Similarly, a succesful manager who has failed in their last few jobs is assigned to a similar pile of people looking for TV punditry work or coaching in China. So each opportunity you get is very important and you are judged heavily on this.

Even then, your success potentially is heavily affected and limited by the situation you are in and the people around you. A shambolic set-up, a few unhelpful characters in the dressing room, injuries etc can all have a large impact, but the manager gets the blame. A manager who would otherwise have been hugely successful can come to an organisation unwilling to change, and end up as a failure. And no-one would have known the potential.

And then even with all of this going well, a manager is pretty much always a few bad results away from the sack at any time. The pressure at the top of the game is so high and as soon as it looks like some sort of malaise has set in, the manager is at great risk of the boot.

With relatively few chances to prove yourself, even fewer with a good opportunity to succeed, success measured over very short time periods, and a few failures meaning the end of a career, you would hope at least that in the time you get to prove yourself you get to give a fair reflection of your abilities.

No, again.

There are countless examples. To pick one almost at random from this season. When Manchester City played away at Tottenham in February. Despite being down to 10 men after an hour (something very difficult for the manager to affect), City had 19 shots at goal with an expected goals of 3.25. Tottenham had just 3 with an expected goals of 0.42. With these statistics, Spurs had just a 2% chance of winning (putting it through a Poisson process). But 2% chances happen, and when they do the narrative is not 'City totally dominated and put themselves with a 90% chance of winning away from home at a top rival'.

Instead it is "this was a story of City misadventure, of a team that looks like it needs a mid-season refresh more than most" and "They were not unlucky. No, they were careless." Even though the manager created a 90% chance of winning, the result means that City manager Guardiola's old rival Mourinho is considered to have executed a managerial masterclass over his tired team.

This is the typical narrative when an upset occurs. Plucky X had the luck of the green at times, but deserved their win for hanging in there and taking their one chance. But if the match were replayed with exactly the same circumstances, team talks, everything, then team Y would have won nine times out of ten (with plucky X being equally plucky).

Then there is the path dependency. As an example, take Manchester United's 4-0 victory over Chelsea on the opening day of the season. United managed to score early, but Chelsea hit the woodwork twice in the first half and the probability is that had Chelsea scored first, United would have found it hard to break down Chelsea's defence.  In the event, United produced an excellent counter-attacking display to score 3 more goals as Chelsea pushed for an equaliser. It looks like a big deal. Lampard, Chelsea's new manager, given a lesson in footballing reality. But the teams were quite evenly matched and were the game replayed 10 times, I suspect Chelsea would have won three or four times. What determines that Chelsea take a chance in one match but miss the same chance in another? Luck mainly.

What I am saying is nothing new, but in football the narrative is so driven by the result and not the process. Whoever wins usually 'deserves' it for being more clinical or good tactics or good performances by certain defenders or goalkeeper. If a team manages to score an equaliser they deserved the draw but if it hits the post, they just weren't good enough and maybe are in crisis.

And a referee's decision can often be the crucial difference between winning and losing. So for all we can say they even out in the end, for the manager "Just saying to your colleague: the referee's got me the sack".

Arteta's FA Cup win

This was what inspired me to write this article. I would like to say first that I think Arteta is a very talented young manager and I have a lot of respect for him. Winning the FA cup with Arsenal in his first season was a very impressive achievement.

But what did he actually achieve in terms of process? Under the previous manager, Unai Emery, maybe Arsenal had a 10-15% chance of winning the FA cup. There are, after all, 64 teams involved and a few are significantly better than his team. 

What sort of improvement could Arteta have made? At absolute best, he could have made it 20-25% probability that Arsenal win. Even that is extremely high, given the number and quality of other teams involved. 

Assuming this is the case, and bearing in mind that this is a spectacular achievement, what we are saying is that Arteta increased Arsenal's chances of winning the FA cup from about 12% to about 24% and then still had to have huge good luck to win it.

And he might not even have done that. We ascribe the probability as higher than the original estimated probability because the result actually happened. But maybe he still had a 12% chance of winning. Maybe he actually even reduced their probability of winning but they still won despite that. We don't know.

Arteta, at best, moved the probability from 12% to 24%. Which, as I said, would be spectacular. Luck moved it from 24% to 100%. So really if we are assigning the glory we should really credit luck with the major part. However, in real life (not my fantasy world where good work gets fairly rewarded) the one with the luck gets all the glory and the plaudits. The manager that moves the probability from 12% to 36% but still loses gets nothing.

But what about the League? The best team wins that surely?

Here again I'm not sure. The league is a series of 38 matches. Each of these contains a huge amount of luck. A few pieces of bad luck can mean 10 points lost easily. Very few leagues are won by more than 10 points. This is without the compound effect caused by loss of confidence after bad luck. 

Liverpool this season won 99 points. This is one point off the all-time record. The 18 point gap to Manchester City (with 81 points) is one of the most dominating performances ever. Only the most hardened, bitter, opposition fan would argue that it was anything other than a thoroughly deserved trophy for a team of winners. It is hard to imagine any other scenario for this season other than this happening. It was huge.

And yet, even then. Even then...

Liverpool scored 2.24 goals per game and conceded 0.87. On the basis that the chances they score and goals they concede are equally likely in all matches, this equates to an expected points total of about 85 points. Which is a great total and would win the league many seasons. 

Manchester City, though, scored 2.68 and conceded 0.92 goals per game. If their goalscoring and conceding were evenly spread  they would have 91 points with average +1.76 goal difference per match. And what is City's average over Guardiola's 4 seasons? 89 with average +1.70 goal difference per match. Some seasons they have more than 89 points, some seasons they have fewer. But it's difficult for me to escape the conclusion that the quality is the same but the difference is luck.

One could argue that City's superiority on this measure is from often taking apart opposition that were already beaten, and scoring a lot of unnecessary goals. The expected goals (xG) table has Manchester City expected to get only 87 points for this reason. But for Liverpool, their expected points was only 74. Part of the difference is made up for by their superior goalkeeper Allison who conceded 7 fewer goals than expected. And partly it is their superior front line scoring 10 more than expected. But still this is 25 points fewer than they actually got.

Undoubtedly, Liverpool are a team of winners. The winning mentality got them to hold on to victories in tough circumstances and their belief in themselves got them to eke out late goals when matches were going against them. But how much of this is us giving the credit to the process that was actually just from the result?

One way of telling is looking at the betting odds for next season. Manchester City are still given 50% probability with Liverpool only having 38% probability. If the performances were that dominating then Liverpool would surely be favourites.

Once again, I am not trying to say anything other than Liverpool have been formidable this season and last. Over two years of incredible consistency they deserved a title. A 40% chance for 2 years means 0.8 titles on average, which rounds to 1. So this is really not to begrudge.

But if this particular season were more luck than not, would we know? 

So what's the point?

What is my point? Even the second largest points margin in history has elements of luck. In football there is so much luck involved. 

Has Solskjaer been a successful manager at Manchester United? At the moment most would say yes. Had Jamie Vardy's header dropped under the crossbar on the final day of the season at 0-0 and United lost to Leicester (and been eliminated from next season's Champion's League)? We all know that then the commentary would have been that "he has done well but in the end lacked the experience and winning mentality". And "they need to find a proven winner to replace him". Maybe he would have had a future relatively successful managerial career at West Ham. Fine margins.

Luck is great, and part of the fun. The best teams win enough as it is; can you imagine if there were even less luck involved? But really spare a thought for the managers that were failures - they may not have been as bad as you think. And consider that maybe the winners may not have been quite as good as we give them credit for.