How Much Risk Should a Football Manager Take?
Introduction
How much risk should a football manager take if their team is the underdog in a match? Should they take on the opposing team to try and win the game or sit back and just try not to lose? The decision made is inherently linked to how risk averse the club’s manager is, but is there actually an optimal strategy to use in when in this position?
Exploring tactics using the EI Index
My EI Index considers a team’s performance to be normally distributed around their true skill level so for any given match we can predict the probabilities that a team will perform above or below their average rating. By looking at how different tactics change these performance curves we can see how they affect each team’s chance of winning.
The average EI rating is 2000, with better teams having higher ratings. The larger the difference in EI between two teams then the greater the chance the higher rated team will outscore the lower team. However, since team’s performances vary from match-to-match it is possible for the lower rated team to out-perform the higher rated team and win the match.
The Underdog
Looking at Figure 1 as an example, the underdog (orange) on average plays with an EI rating of 1800 and the favourite (blue) plays with an EI rating of 2000. Overall the favourite is expected to out-perform the underdog and win the match, yet in around 15% of matches the underdog will actually play above the favourite’s EI rating of 2000.
All Out Attack
So what happens if the underdog decides to play the more high risk strategy of attacking the match and going all out for the win? We would expect the more risk a team takes then the more variance we will see in their performances as they have more chance of scoring and yet more chance of conceding too.
Figure 2 shows what happens when the underdog’s variance doubles. Notice how there is now much more of the orange curve exceeding the favourite’s average EI rating of 2000. In fact, in this example the underdog now has around a 31% chance of playing above the favourite’s average and so is much more likely to win the match than before.
There is a down side though as there is also more orange distributed towards lower EI ratings meaning that although they have a greater chance of winning, the underdog has also seriously increased their chances of a humiliatingly large defeat.
Playing Safe
Let’s compare this to Figure 3 where the underdog sits back and plays conservatively hoping they will not get beaten. This low risk strategy reduces their performance variance meaning they are much less likely to out-perform their opponents and win the match. In fact reducing their variance by a half reduces their chance of playing above the favourite’s average down to just 2% at the benefit of maybe grabbing a draw or minimising the risk of an embarrassing defeat.
The Favourite
What about the favourite, how should they respond to a change in risk by their opponents? The optimal choice would appear be to utilise a low risk approach to reduce the variance in their performance and minimize the chance of playing at a level below the underdog’s expected performance (Figure 4). This means there is less chance of a glamorous, high-scoring win for them but importantly less chance of making a mistake and throwing an easy victory away.
The Real World
So what tactics should a manager choose? In the case of the underdog it surely makes sense to take the high risk strategy of attacking the match to increase their chances of winning all three points. The downside is of course that they are at more risk of losing by a heavier score line. But whether a team loses by one goal or by four goals, the net outcome in terms of points is the same – zero.
Over the course of a season it is much more beneficial to gain additional points at the risk of worse goal difference. One extra victory is worth more in league placement than having a superior goal difference to the teams around you. Plus, you need to hold on and scrape three draws to equal the benefit of getting that one extra win.
To counter this high risk approach, the favourite should then play safe to reduce their risk of a poor performance and try to maintain the relative difference in expected performances.
Overall this means we would expect the lower rated team attack the game and take risks while the higher rated team plays safe and waits for the underdog to make an error.
Conclusions
Is this what actually happens in football though?
Personally, I suspect not. It is difficult to quantify the actual risk teams are taking in matches so it is impossible to say for sure but from personal observations it seems much more likely that the underdog will play safe to try and avoid defeat and hopefully grab a lucky draw even though they are then at a much lower chance of winning the match.
There are certainly times when this approach has worked, such as this season’s Champions League match when Celtic beat Barcelona against the odds. But it is perhaps not the best strategy long term over the course of a season to maximize a team’s outcomes.
So why would a team not play to an optimal strategy? There are likely many competing reasons of which one is that football managers are not statisticians and cannot necessarily be expected to view matches from a probability or risk-based viewpoint.
Another explanation also seems to be the public and media’s perception. One victory and three heavy losses are worth more in points and league placements than two draws and two narrow 1-0 defeats yet the manager presiding over the three heavy losses would come under much more criticism even though he had achieved more. A manager’s career is short and unstable – it doesn’t take much for a trigger-happy chairman to wield the managerial axe so rightly or wrongly many managers seem to be focussed on the goal of retaining their job ahead of anything else.
Luck and variation will always play a big role in a team’s results, that’s why football is so exciting, but playing the least risky strategy available may not be the best approach for the smaller teams. Sometimes behind brave is best.
Comments
GoalImpact - March 11, 2013
I came to an equal conclusion here (sorry German)
http://www.goalimpact.com/2013/02/der-sturm-gewinnt-spiele-die-abwehr.html
Jupp Heynkes once said: Attack wins games, defense championships. The opposite is true for the underdog.
Martin Eastwood - March 12, 2013
Thanks for the link, I put it through Google translate and it looks like we came to similar conclusions that the underdog needs to take risks and attack the match rather than sit back and play safe.
Looks like a really interesting site, I look forward to reading more :)
Miguel - March 13, 2013
I disagree with your premise and think there is actually an optimized strategy for the underdog.
There is an assumption that a team that plays it safe does so in order to not get scored on. While this is true, they also play defensively because it increases their chance of scoring. The more defensive they play, the more numbers the favorite must send up to attack, the less numbers the favorite has defending, the more probability of scoring.
So when the underdog plays defensively, it not only decreases the chance to receive a goal but it also increases their chance to score one.
GoalImpact - March 13, 2013
I agree with your assessment. However, I’m not sure it necessarily contradicts Martin’s statement. IF playing defensive increases the goal difference, i.e. increasing the mean of the own distribution and/or decreasing the opponents, it may be worthwhile going for it. Otherwise, seeking their chances may be a better way to optimize the team’s number of points.
Martin Eastwood - March 13, 2013
Yes, it is more about mangers being prepared to take the risks needed to win the match rather being negative and playing to not lose. There may well be cases where that risk lies in playing defensively.
2ndMan - March 13, 2013
Good article, in terms of getting more points I certainly think it’s worth a risk, but agree that when you consider squad harmony and morale then playing it safe may be better for the long term. Allardyce’s “respect the point” comes to mind.
I disagree completely though Miguel, you say defending means the opposing team commit more men to the attack, but that also requires you commit more men to defend. Generally the team in possession is gonna have at least 1 more defender back than attackers you have forward, and the more men you bring back to defender the greater the opposing teams advantage (having 3 attackers v 4 defenders, down to 2 v 3 and 1 v 2).
Miguel - March 15, 2013
2ndMan, the arithmetic that you are using cannot be applied to how the game is realistically played. In other words, 1 defender does not cancel out 1 attacker or, even, 2 defenders cancel out 1 attacker. The game is played at a very fluid pace and when a team is playing very defensively and they are able to get a turnover in the middle of the field, they can exploit the space that is available. And the space, which is the key, is the difference maker.
http://www.youtube.com/watch?v=P2jq2NP2osM
Look at this video, it is a video of a series of counterattack goals by Real Madrid. I know they are one of the best teams in the world, but in almost everyone of those plays, the defenders have the numerical advantage. The huge disadvantage that the defense has is that they are running back to cover the space and it is that space, that is usually not present even when you are attacking with your whole team, that creates the offensive advantage. I would love to see a statistical analisis of success rate of a counterattack, but I can guarantee you a much bigger percentage of goals are scored when the defense is running back to cover the space in front of the box, than when they are positioned there to begin with, regardless of the numbers each team has attack or defense, and this is the offensive advantage that a team has when playing it safe and counterattacking, that they dont have when attacking with numbers.
Nick - March 20, 2013
There is also a mode of thought that the more “possessions” there are in a game, the more likely the better team is to take advantage of those possessions. I believe this came from the NBA.
Therefore an underdog who limits the changes of possession, either by keeping the ball, making the opposition “over-pass”, time wasting, slowing the game down, etc is actually shortening the length of the game and is increasing the chances of an upset.
Does anyone know if there are figures for the average number of team possessions in EPL, for example?
Martin Eastwood - March 21, 2013
Good points Nick.
I don’t think that data for average number of team possessions is currently available. As far as I am aware Opta calculate possession percentages from completed passes rather than the number of actual possessions each team has had during the match.