The next step in football analytics: Game States

One of the most appreciated posts last year on 11tegen11 did not contain any numbers, nor did it contain any tactical analysis. It did contain a picture of a flying pig (really…) to help making the point that analysis without context is pointless, or at least dangerous.

Or, quoted from Nate Silver’s inspring book ‘The Signal and the Noise’, “a failure to think carefully about causality will lead us up blind alleys”.


Football analytics

Too many people think that football analytics revolves around fancy individual player analysis, multivariate scouting models or complex GPS tracking data of on field events. While it may be true that these ‘holy grails’ get most attention, it’s the simplest of questions that yet remain unanswered. With this tendency to run before we can walk, we run the risk of falling and hurting ourselves over and over again.

Think about this very simple question: why do better teams win football matches?

Obviously because they score more goals than weaker teams.

This bears down to two factors involved in goal scoring: creating shots and converting shots. And, of course, to the defensive equivalent: preventing shots and saving shots. This post will focus on shot creation, and a quick follow-up post will take on shot conversion later.


Total Shot Rate

In order to assess shot creation and prevention in a single number, we’ve become familiar with the concept of shot rates: Total Shot Rate (TSR) and Shots on Target Rate (SOTR). I’ve made no secret of my preference for TSR over SOTR, simply because it has three times more shots to work with and variation in offensive and defensive shooting accuracy between teams is mainly noise. For this analysis, however, I will also include SOTR to serve the audience of people who still believe certain teams to be substantially better at hitting the target than others.

Let’s look at shot creation and prevention by way of TSR for different game states (GS). With GS, I mean score differentials while the shot is taken. Each match starts with both teams at GS 0, until one team scores a goal and moves to GS +1, with the opposing team moving to GS -1.

This is a very interesting graph, containing a wealth of information in a single line. Broadly, the line moves from the lower left hand corner to the upper right, indicating that either leading teams create more chances, or the reverse causation, teams that create more chances end up leading games.

But there’s much more to this graph than just that. Let’s start with GS 0. This point of the graph will always be 0.500. Football is a closed model, meaning that one team’s created shot is another team’s conceded shot, and at GS 0, both teams are at that same state. So each created shot is automatically a conceded shot in that same category. Likewise, shots created by teams at GS +1 are conceded by teams at GS -1 and vice versa. In short, the graph will always be a point symmetrical around GS 0 and 0.500.

Now, while it’s true that the line roughly indicates that there is a positive correlation between TSR and GS, the catch is that over 80% of shots take place at GS -1, GS 0 or GS +1, the so called close game states (CGS).

And in these CGS, there is a negative correlation between TSR and GS. In simple words: teams that go a goal up create over 10% less chances, and allow over 10% more chances at the same time. The shift in TSR is over 25% in favour of the team trailing the goal.


Shots on Target Rate

We can’t really judge this trend without taking the accuracy of shots into account. Therefore, I’ve also included the same graph for SOTR and GS.

To cut a long story short, both graphs are virtually identical. So, the hypothesis that teams at GS -1 take overly hopeful pot-shots does not gain ground from these data. At least, the shot accuracy between GS -1 and GS +1 is virtually identical. This does not mean that the quality of the shots is comparable too, but we’ll go into that when we look at conversion rates.

First, I want to stress the implications of the fact that TSR is negatively correlated with GS for over 80% of the match. This means that teams that spend a lot of time trailing a single goal, will have an inflated TSR, while teams that spend a lot of time defending a single goal lead will be underestimated in terms of TSR.


In early September, only four matches into the season, we’ve gone bold by publishing a predicted final standing of the Eredivisie based on TSR. There are some interesting over- and underestimations in this prediction to learn from.

Willem II, now bottom last and near-certain relegation candidates, had been predicted 14th with 37 points. Of their shots created and conceded, 25% took place at GS -1, compared to a league average of 17%, and only 7.3% at GS +1. This has significantly overestimated their qualities.

Another overestimation is RKC. Top-half in terms of TSR, they are now 14th in the actual league table and are battling to avoid the relegation playoffs. Needless to say they won’t make their predicted 7th spot. Of RKC’s shots, 23.5% took place at GS -1, and a somewhat substandard 15.5% at GS +1.

There are also some interesting underestimations in the model. Feyenoord do better than their TSR would suggest, as they spent over 40% less time at GS -1 than the average team and nearly 30% more at GS +1. Vitesse are another example, with nearly 20% less time at GS -1 and over 25% more time at GS +1.

PSV and Ajax are less affected, because they also spent quite some time at GS +2 and higher, where leading teams create a dominant TSR.


In the end

In short, TSR depends on Game State. Over 80% of all shots are contested at Close Game States (GS -1, GS 0 or GS +1), where TSR and GS are negatively correlated. Teams that spend a lot of time trailing single goals are overestimated in terms of TSR, while teams that spend a lot of time defending single goal leads are underestimated.

10 thoughts on “The next step in football analytics: Game States

  1. bart

    I agree with your conclusion that Team TSR is most probably linked to GS for the average team … but there’s something niggling in the back of my mind here and I cannot quite put my finger on it … here are my thoughts …

    What you are showing here is GSTSR … now let us imagine Team A is playing Team B … The game starts and GS is obviously 0 … the first goal falls after Team A has taken 4 shots and Team B 6 … at this point GSTSR is 0.500, whilst Team A has a TSR of 0.400 and Team B 0.600.
    It was Team A that scored thus for Team A GS is now +1 and Team B -1 … Team B was slightly dominating at equal score and they start putting on even more pressure … a second goal falls after Team A has taken 2 more shots and Team B 8 more … GSTSR +1 is 0.200, GSTSR -1 is 0.800 … Team A TSR has become 0.300 and Team B TSR 0.700.
    etc. etc.

    It is interesting to see that the team in GS+1 concedes more shots than it takes, but that does not say much about the quality of a team … no I’m not saying it right … this is my issue, I cannot word it properly.

    Also, what about teams like AZ, AS Roma (under Zeman), Athletic Bilbao … these are gungho teams that go for it no matter what the score is (or so it seems). It would be interesting to see their TSRs and how they relate to GS.

    Finally, I’m sure 80% of the shots take place during CGS because probably 80% of the time a team finds itself in one of those states, I would say that GS outside of the CGS are quite rare … I’m sure that a GS of +4/-4 is rare in total minutes when compared with the total minutes played at the end of a season (I would guess only a couple of % at most).

    And finally food for thought (something for the tactical philosophers) … (in general and not specifically at what was written above) … if a team finds itself in GS+1 would the team not try to defend their lead by making sure that the opponent gets as few shots on goal as possible … we know that in general TSR shows the quality of a team, thus wouldn’t outshouting an opponent be the best form of defence, even in GS+1? … yes, I follow the gungho school … “always go for more, no matter what”. 🙂 … look at the advantage one gains when they positively increase the GS! A team would want to be in GS+1 for a little time as possible and try to make it GS+2 to get back on even terms.


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