You win some, you lose some – the value of consistency and randomness

The new buzzword in Dutch football is “ondergrens”, which means something like lower limit. Managers want to raise their team’s lower limit or complain when they “sink below it”. If only their teams would be more stable, more consistent, all their problems would be solved…

Feyenoord’s technical director Martin van Geel was the latest to complain about the club’s inconsistency a few days ago, but does he have more reason to than his colleagues?

Let’s say that we can consider a team inconsistent if their actual performance often (and heavily) differs from their expected performance. To measure this I created a simple model to predict the number of shots created and conceded based on team and league averages. I expect a team to take a number shots equal to their average multiplied by the average number of shots conceded by their opponent, divided by the league average:

Exp. Shots (A) = Avg Shots (A) * (Avg Conc Shots (B) / League Avg Shots)

If I do this for both teams, and apply a correction for the average home advantage (currently a TSR of 0.55 in favor of the home team in the Eredivisie), I get what seems to be a decent prediction of “performance” for each match.

For example: for the match between Groningen (14.2:15.6) and Zwolle (14.0:14.2) last Sunday this gives (in retrospect) a prediction of 15 vs 14 shots. In reality Groningen created 22 shots to Zwolle’s 6.

In this case Zwolle’s TSR was a dreadful 0.26 lower than expected, but looking at their average difference in TSR over the whole season they have been quite consistent:

Team Avg Diff TSR Avg Negative Diff TSR
Roda JC 0,147 -0,124
Cambuur 0,125 -0,127
NAC 0,122 -0,101
Groningen 0,120 -0,117
AZ 0,118 -0,097
Twente 0,118 -0,105
Go Ahead 0,109 -0,070
Vitesse 0,106 -0,110
RKC 0,096 -0,091
Feyenoord 0,095 -0,135
PSV 0,094 -0,095
Zwolle 0,087 -0,061
FC Utrecht 0,085 -0,061
Ajax 0,085 -0,099
Den Haag 0,079 -0,075
Heracles 0,075 -0,076
Heerenveen 0,073 -0,050
NEC 0,058 -0,083

Since managers won’t be quick to complain about the highest highs, but only about the lowest lows, the third column shows the average of only the cases of underperformance. It’s clear that although Feyenoord is not that inconsistent overall, they really phone it in on their bad days and Van Geel is somewhat justified.

The value of consistency

The next question is: does it matter? I would say that in general these managers shouldn’t worry about being inconsistent, but about being bad on average. However, there are some things to consider when it comes to consistency:

  • If you are the best team in the league on paper and you are consistent, won’t you consistently beat other teams?
  • And the other way around, if you are consistently the worst team in the league, will you ever win a match?
  • As a mediocre team playing against similar opponents, won’t being consistent just get you a whole bunch of draws, which is not optimal considering football’s point system?

The answer to all three of these questions is far from obvious thanks to football’s low scoring nature and the large role chance plays in the actual outcome of a match. Experience shows that even the most stable, well-oiled machine will sometimes suffer a shock defeat (and isn’t that what we all love about this sport?).

To simulate this, I created another model based on some binomial distributions with the number of shots and the average conversion rate in the Eredivisie (currently 0.117) as input. It’s all just theory, but it shows for example that with a shot rate of 22:6 you’d have a 79% chance at winning the match, while 15:14 gives you a mere 41% chance. (For Groningen the difference didn’t matter as the match ended 0-0.)

If I use this model to predict a team’s results over a whole season, we can answer the questions above. To answer the third question let’s compare a team that has a shot rate of 13:13 in every single match with a team that has a rate of 16:10 in half of their matches and 10:16 in the other half. The more consistent team has on average a 1.81 percentage point higher chance of drawing a match, and and an expected points total of 46.75, which is marginally lower than the 47.06 of the inconsistent team.

In fact all teams, good or bad, have a higher chance of drawing a match if they’re more consistent, but teams that are well above average also have a higher chance of winning a match if they’re more consistent. The model shows that a team with an average shot rate of 16:13 is still better off being inconsistent, but consistency starts to pay off at a rate of, for example, 17:11.


All in all though, the difference it makes will hardly be more than a point over a full season, and only for the best and worst teams.

Reducing randomness

The points above about a good team wanting to exploit their advantage on paper, and draws not being optimal still stand, but if there’s any way a team can gain advantage from this, it’s not by tinkering with the consistency of performance, but with the randomness of the outcome.

It’s because so few goals are scored in a match that the underdog so often gets a result. For example, let’s say we were playing a game of dice with the following rules:

  • The winner would be the one who most often rolled a six.
  • You would get to throw twice as often as me.
  • In case of a draw, I would be declared the winner.

Now if I had just one throw and you would have two, I’d actually have a 75% chance to win, but if it was ten throws vs twenty, you would win 70% of our games.

Since you can view every shot in a match as a dice throw, it’s obvious that the underdog will benefit from a game with few shots in total, and the favourite will want to open the game up.

As for the other factor, the amount of draws, it’s quite obvious as well. Assume there are two teams who each randomly score nil, one or two goals, three of the nine possible results are a draw. If instead they score up to four goals, only five out of 25 possible results are draws.

I have put it all together by looking at expected points vs TSR and comparing averages of 20 and 40 shots. You can see that the draw factor causes the tipping point to be below average, at a TSR of about 0.475


Of course I don’t really expect any team to able to open a game up or shut it down at will, and averages of 20 or 40 shots a game are not that realistic, but it’s promising nonetheless.

It’s also another reason why TSR doesn’t tell the whole story. Ted Knutson actually touched upon the same issue in this fine article yesterday and showed a fantastic real world example.

If it’s indeed a way to gain an advantage, there’s just one question left: which teams in the Eredivisie are doing this correctly already?

This table shows the average amount shots in matches with a TSR over and under 0.475, and is sorted by the difference between them:

Team >= .475 TSR <.475 TSR Difference
Twente 30.9 17.0 13.9
PSV 31.6 29.0 2.6
NAC 31.2 28.9 2.3
Vitesse 32.0 30.0 2.0
Ajax 27.5 25.5 2.0
Feyenoord 29.4 28.5 0.9
RKC 31.8 31.6 0.2
Heracles 29.3 29.2 0.1
Zwolle 28.0 28.3 -0.3
Heerenveen 29.9 30.3 -0.4
Den Haag 26.9 27.5 -0.6
FC Utrecht 30.0 30.8 -0.8
Groningen 29.4 30.3 -0.9
AZ 26.7 28.2 -1.5
Roda JC 28.3 30.1 -1.8
Go Ahead 27.8 30.9 -3.1
NEC 27.0 30.3 -3.3
Cambuur 21.2 26.6 -5.4

Twente are doing fantastically well. To be fair they only played one match with a low TSR so far, but I couldn’t wish for a more perfect example. Away against Cambuur they had a shot rate of 7:10, showing they performed poorly but managed to keep the randomness high, and in the the end they nicked a 1-0 win.


I’ve realised that the metric for how well a team takes advantage of randomness can be improved.

I calculate a value for each team in each match:

  • If TSR < 0.475: Total Shots (League Average) – Total Shots (Match)
  • If TSR >= 0.475: Total Shots (Match) – Total Shots (League Average)

And take the average over all matches:

Team Total Shots Influence Score
Twente 2.54
PSV 2.10
Vitesse 1.70
NAC 1.09
Feyenoord 0.39
Heerenveen 0.11
Heracles 0.05
Zwolle -0.06
Groningen -0.40
FC Utrecht -0.65
RKC -0.85
AZ -0.86
Ajax -0.90
Roda JC -0.91
Den Haag -0.98
NEC -1.26
Go Ahead -1.55
Cambuur -2.29

Ajax are suddenly looking a whole lot worse. Although their good matches have more shots than their bad matches, total shots are still too often below league average.

Author: Bart Schotten


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