Game states and conversion

Sometimes the easy questions can be the hardest ones to answer correctly. This is true in statistics, and since we apply numbers to football, this is true in football analytics as well. Take the never ending debate around shot conversion. Why are better teams able to convert a higher percentage of their shots into goals?

Providing an answer is not the hard part here. Providing a correct answer is.

Let try this, often heard answer. It’s simple. Better teams have the better players. Better players hit more difficult shots, leading to more goals per shot.

Game states

The problem with this answer is not that it isn’t correct. Because it is. Better teams have better players, and these players turn more shots into goals than weaker players.

The problem with this answer is that it stops most people from looking beyond it and consider other factors that come into play here. And you’d probably guessed from the title of this article already, that it’s game states and conversion that I would like to link today. It turns out that game states may well explain more of the variation in shot conversion between better and weaker teams than player quality will ever do.

Two weeks ago I wrote about Total Shot Rate (TSR) and Game States. Let’s recall the graph that was central in that piece.

Let repeat this exercise for shot conversion. So, here’s the same graph, linking shot conversion and game state. Please note that this graph contains all shots from all Eredivisie teams in the present season until match day 27. This time I’ve concentrated on GS -2 to GS +2, to prevent the low numbers at more extreme Game States from disturbing the picture. The shot numbers at different Game States are 371 shots at GS -2, 1160 shots at GS -1, 2885 shots at GS 0, 922 shots at GS +1 and 363 shots at GS +2.

It turns out that, like TSR, shot conversion is also related to Game State. TSR had a complicated shape, with an inverse correlation at close GS, but shot conversion is a lot easier to digest.

In general, the more favorable the Game State, the better shot conversion is. The only exception is at GS 0, where shot conversion is lower than at GS -1 and GS +1. Overall shot conversion for the league is 11.7%. Shot conversion at favorable Game States is significantly better, with GS +1 at 14.1% and GS +2  at 17.1%. The most interesting observation is that shot conversion at GS 0 (10.4%) is lower than at GS -1 (11.6%).

Things become more interesting when we combine the conclusions from TSR and shot conversion at different game states.


GS 0

At GS 0, both teams are by definition balanced in terms of TSR, as both team are at the same game state and each team’s shot created is a shot conceded by the other team. In terms of conversion, this is not a fruitful game state. This may well be due to the fact that teams are inclined to be more cautious at this score, since they have a point to lose, particularly near the end of games. A further explanation may be that this Game State, by definition, occurs more in the opening stages of matches, and teams may well be more conservative at the start of a match than they are at the end.


GS +1

At GS +1, there is an interesting trade off. The TSR declines over 10% to 0.443, while the shot conversion rises to 14.1%. The tricky situation with TSR is that it works two ways. The leading team creates 44.3% of shots, but it concedes 55.7% at this game state. So, overall, the TSR of a chasing team is 26% higher (0.557/0.443) than the TSR of a team defending a single goal lead. Despite the fact that the conversion at GS -1 is better than at GS 0, teams at GS +1 convert 22% (0.141/0.116) better than teams at GS -1.

If we combine the shift in TSR and shot conversion for teams at GS -1 and GS +1, we find that a team at GS +1 pays 26% of TSR to gain 22% in shot conversion.

So, generally speaking, teams have a slightly worse chance of scoring when leading by a single goal than when chasing a single goal.


GS +2

At GS +2, there is a whole new world. Teams at GS +2 have restored their TSR to 0.495, while their conversion rises further to 17.1%. Teams at GS -2 fall back in terms of TSR (to 0.505), while their conversion drops to 8.6%. Overall, both teams create a roughly equal amount of chances, but the team leading by two goals converts nearly twice as much.


In the end

Let’s turn to the opening question once more. Why are better teams able to convert a higher percentage of their shots into goals? They take a much higher proportion of their shots at favorable game states.

Who are the conversion kings of the Eredivisie? Right, PSV at 16.9%. They took 20.6% of their shots at GS +2 or higher, compared to 8.3% on average for the other Eredivisie teams…

18 thoughts on “Game states and conversion

    1. 11tegen11 Post author

      No, I don’t have that graph yet, but the required information is definitely in the data…
      It’s on my ‘to-do list’ as of now…

  1. bart

    back to being that irritating flea …

    In the past you (and others) have used TSR as a possible indicator of a team’s quality (i.e. higher TSR would indicate a higher quality team) and to go along with that PDO is often used to give an indication if a team is “lucky” or not (I’ll get back to PDO in a second) … you’ve tried to refine TSR to reflect quality of opposition etc.
    However, (and herein lies my main issue) the TSR that you are using above (and in the previous post) does NOT indicate the quality of a team, but the ratio of shots during a certain GS. Thus you are using the same acronym to indicate two different types of qualifications. This is why I suggested using a different acronym … I wrote GSTSR last time, maybe GSSR is actually better.

    … sorry, just got a phone call, have to go to lunch … will continue later with my thoughts …

    1. bart

      back …

      1. TSR
      Anyway, the casual reader could thus make the mistake of thinking that the quality of a team goes down as it rises up in game states until it reaches GS+3 when TSR is above 0.500 again. This would clearly be the wrong conclusion.
      Hence the advice to use a different acronym to not run into problems of this type.

      2. Shot Conversion
      Running through the numbers you provide above (conversion rate, number of shots etc.) I come to a league average of 12.072% in shot conversion during GS-2 to GS+2 … you state the overall league shot conversion rate (11.7%) and this is once again slightly misleading … as you’ve just stated above that that you would limit your view to GS-2 to GS+2 as at other times conversion numbers are misleading … to then include them in to show that conversion rates are “significantly better” is unfair as you are using data that is outside of the sample range that you are showing. I, for example, cannot find out what conversion rates, or shot numbers are in states outside those that you are showing … meaning I have to take your word for it …
      So, either show it all or limit yourself at all times.

      3. PSV/Conclusion
      It is a pity that you had to add that paragraph at the end of the post … it deserves its own post really. I would say the conclusion is tentative and not definite … a follow-up post comparing PSV conversion rates and shot per GS totals (why not throw in TSR per game GS too) would highlight any possible conclusion.
      Also, you state that PSV “took 20.6% of their shots at GS +2 of(sic) higher” … whereas all the above information you have given stops at GS+2, once again alluding to information that I, as a reader, have no access to.
      I’ll take your word for it that, for example, during GS+1 there have been 922 shots, but when you reference data that you have previously excluded (for whatever reasons) then doubt creeps in …

      Now on to non-niggly stuff …

      Have you thought of how these numbers may affect the view on PDO?
      – As you’ve used conversion rates, it naturally also shows save% … thus Team A is a GS+1, where the average shot% is 14.1 and their opponent is at GS-1 (naturally) with a shot% of 11.6 … which implies a Team A save% of 88.4 … which implies a Team A PDO at GS+1 of 1025 (thus a Team B PDO at GS-1 of 975) … if Team A moves to GS+2 then their PDO becomes 1085 …

      Now, naturally both teams cannot score at the same time so one will have a save% of 100% (thus shooting 0% for the other team) … I’m not a maths/stats etc. whiz but maybe there is something interesting that can be taken from that with regards to talent/luck and related to GSSR. As Team A at GS+1 will have a lower GSSR than average (0.443).
      Also, how often goes GS move from GS+1 to GS+2 or GS0 from a single team’s perspective … is this because they cannot convert or is it because they are lucky to be up by one goal etc. etc.

      That’s all for now, cheers for the interesting post!

      1. Maurice

        Very interesting post.
        I have some practical questions (for myself):
        Are statistics on TSR per GameState per team available somewhere?
        I mean not only for the dutch Eredivisie, but also for the English Premier League, Bundesliga, etc? Or do you have to pay for it at Infostrada or Opta?

        Bart raises some good questions. Would like to hear more about this topic of GameStates.

        1. 11tegen11 Post author

          Unfortunately these stats are not available (yet)…

          If smart stats in football keep on rising like they do at present, it might not be long though before you can find Game State stats in your local newspaper…

      2. 11tegen11 Post author


        Thanks for your extensive comment.
        Let’s go over your points…

        1. This is just the second post on Game States on 11tegen11. I think the term TSR holds true, as that’s just what it is: Total Shot Rate. The fact that TSR is lower at GS +1 does not indicate a decline in quality, but a shift in the type of play. Less chances, but of higher quality. Hence the trade-off.
        I’ll keep on referring to TSR for now.

        2. I merely meant to focus the graph on GS -2 to +2, as the edge would disturb the picture otherwise, while the edge have way too little shots to be of significance. For now, just take my word on the numbers.

        3. A PSV focused post will come any time soon anyway. Their behavior is different from rivals Ajax in a way that caused the TSR prediction model to overestimate PSV and underestimate Ajax. That thought will get it’s own post for sure. And team specific TSR and conversion per Game State will follow soon.

        4. Extending this information to PDO is definitely important, it was just too much for one post. You’re line of thought is completely correct, at more favorable Game Sates, team have a higher PDO. This may lead to wrong conclusions about luck and skill, which is very important.
        On top of that, there are completely different patterns in different team, which, for all I know now, may be part of lower numbers and random variation, but may also be indicative of different approaches to leading and chasing Game States.

        1. bart

          hi 11v11,

          Cheers for the reply … understand your arguments for 1 & 2, but just wanted to put mine down, again thanks for the reply.

          3. looking forward to an in depth analysis … I recently stumbled upon another blog, that I’m sure you read, by someone called B. Pugsley … he does some interesting team v team analysis using GS, TSR etc.

          4. also looking forward to posts going deeper into the PDO thing.

          Keep ’em coming and I’ll continue being the “luis in de pels”, as they say in Dutch. 🙂


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    1. 11tegen11 Post author


      There’s work to do there.
      It seems plausible that teams are more cautious in the opening stages of games (when the Game State is often level, or GS 0) and in the end stages of games that are GS 0. In contrast, at GS -1, teams will take more risks, and are rewarded with more chances and a slightly higher conversion, but pay a price with a high conversion on chances conceded. Sacrificing defense in order to try and create an equalizing goal.

  3. Amir

    There might be a selection bias here.
    Better teams are more likely to be at GS +1, so it might be this fact that explain the difference in conversion rate, and not the GS itself.
    An in-match analysis might answer that.


    1. 11tegen11 Post author

      This is definitely a good point and I haven’t explained this clearly in the text.

      If we take each team’s TSR at GS 0 and set this as 100%, we can calculate relative TSR’s for each team at GS -1 and GS +1.
      On average, teams experience a 15% increase in TSR when going from GS 0 to GS -1, and a 15% decrease in TSR when going from GS 0 to GS +1.
      The variation between teams is bigger at GS -1 than at GS +1, indicating that this effect is more homogenenous at GS +1 and more heterogenous at GS -1.

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