Following up from Dan’s (@DanKennett) piece yesterday and expanding on my previous article, I decided to look a bit more closely to the Liverpool performance in 2012/13 through the lens the Goal Expectation (ExpG) metric and its associated efficiency. As mentioned in my previous piece, it estimates the probability of a shot being scored by taking into account a number of shot characteristics. The easier the chance, the more likely it is for the striker to score the goal, and therefore the higher the ExpG value. On the other hand, shots from difficult positions (as well as other factors), which are less likely to end at the back of the net, are associated with smaller ExpG values.

Excluding own goals, Liverpool during the 2012/13 season scored a total of 67 goals. To achieve that, they needed 739 shots, which translates to an overall conversion rate of 9.1%. Of those 67 goals, 23 were scored by Luis Suarez (a conversion rate of 12.3%), 10 from Sturridge (conversion rate of 16.4%) and 9 from Gerrard (conversion rate of 9.7%) with the rest of the players scoring 5 goals or fewer. The following table shows the raw conversion rates of all Liverpool players who had at least 10 shots.


Note that Gerrard’s 4 out of those 9 goals were in fact penalties, and one of Sturridge’s goals came from the penalty spot. Had we removed all penalty shots (Gerrard had one saved against West Brom) from the data, the captain’s conversion rate would fall to 5.7% and Sturridge’s to 15%.

It becomes immediately obvious that including penalty data in total shots/goals statistics creates a problem, as conversion rates do not provide a platform to compare players on. Taking this a step further, the same would apply when trying to compare a predominantly long-range shooter to a 6-yard-box goal poacher; conversion rates alone would not make much sense.

It’s here that the metric ExpG we devised with Colin Trainor (@colinttrainor), and have introduced during the past week or so in a series of articles, can provide the additional information and the platform to compare players or teams on. Our calculation of goal expectancy, given the chance a player is presented with, is based on a number of factors. The higher this number, the better the quality of the chance. If a player has many such chances (or in general a higher average ExpG per shot) you would expect their conversion rate to be relatively higher too.

We also devised a metric to measure a player’s ExpG efficiency (ExpG Eff). As described in previous pieces, if a player is expected to score 10 goals given the type of his chances, yet he manages to get on the scoresheet 12 times, his ExpG Eff is 12/10 = 1.2 therefore he is 20% more efficient than how an average player would fare from that particular combination of chances. In a sense, this removes (to the model’s best ability) the explainable factors affecting conversion rates (such as a shot’s location) and leaves whatever factors are unaccounted for. The better the model, the fewer the significant unaccounted factors.

To visualize all this information, I’ve tried to include these metrics for those Liverpool players who had more than 10 shots during 2012/13 in the following plot:


[As you will notice, both Liverpool’s summer transfer Iago Aspas, and transfer target Diego Costa have been included in the analysis for comparison purposes.]

The horizontal axis shows a measure of the average chance quality for each player, according to our calculations. The vertical axis illustrates the efficiency based on ExpG. The size of each point indicates the traditional raw conversion rate while the colour of each point highlights the number of shots each player took. In addition, Liverpool’s average chance quality and overall efficiency are shown as well as what the benchmark efficiency is (1.00).

What can we gather from this? As mentioned in a previous piece as well as a tweet discussion a few days ago, Liverpool’s overall efficiency has been below average, and by our figures lies at around 0.86. This simply means that Liverpool did not score as many goals as their chances should have expected them to do. Liverpool scored 67 goals, but had they been average in terms of efficiency they would have scored approximately 78 goals. As an aside, here is the same chart on a team-level, for the 20 Premier League teams in 2012/13:


Back to Liverpool, the shooting inefficiency was widespread across the team. Only 4 Liverpool players managed to have an above average efficiency: two strikers (Suarez with 1.08 and Sturridge with 1.02), a midfielder (Henderson with 1.30), and a defender (Sktrel with 1.83). The rest of the players posted marginally or grossly inefficient figures, irrespective of their position on the pitch.

It’s also interesting to note that both Sturridge and Borini come out on top of the chance quality measure, as one would expect given the fact that they are strikers, but the same does not apply to Suarez. The average quality of his numerous (red dot!) chances is lower down, evidently affected by his choice of difficult-to-score shots from acute angles or long-range efforts. However – and this is something that the efficiency picks up on – due to the difficulty of his chances he is “only” expected to score 21.2 goals from those 187 shots, whereas Sturridge was expected to chip in with 9.8 goals from his 61 efforts. So in effect, Sturridge may have registered a higher conversion rate, but given the type of chances he had, he was expected to do so. It’s for this reason that looking at the 16.4% raw conversion rate for Sturridge against the Uruguayan’s 12.3% is not directly comparable.

The ExpG efficiency measure is also more robust against the inclusion or lack of penalty shots in the data. Gerrard’s ExpG Eff is at 0.93 but “only” falls to 0.83 once penalty shots have been removed instead of a 9.7% to 5.7% move in the raw conversion rates. Other players with a significant number of shots include Johnson and Downing, both of whom have contributed less than expected. While in the case of Johnson, that may be excusable given that he is in fact a defender, Downing has consistently failed to live up to expectations in terms of scoring (and in terms of assists, but that’s another matter!), so it may indeed be the final curtain for him. On the other hand, Henderson’s impressive 1.30 ExpG Eff, as well as his shooting from favourable positions, may necessitate keeping a closer eye on him in the future. As for Skrtel, he has performed way above scoring expectations, but that is only based on 15 shots, so I would not jump into conclusions just now.

As mentioned above, data from the 2012/2013 Celta Vigo season for Iago Aspas have also been included in the char,t as well as Diego Costa’s metrics. Aspas performed very similarly to Suarez, scoring 12 goals while expected to score 10.9 out of 102 shots. That gives him an ExpG Eff of 1.11 and if he can replicate his performance for Liverpool, he may prove an excellent addition (or should I say replacement?) to Suarez, especially given the relatively low fee. Talk of Diego Costa has somewhat quietened, but perhaps his raw conversion rate of 20% was misleading given that his shots came from chances of extremely high quality. More relevant would be his efficiency, which is not much different to either Suarez or Aspas and lies at 1.09.

It’s reasonable that such analysis, both in terms of methodology and with respect to its usefulness, is open for debate. The main question, associated with sample size, is whether a single season’s results can be repeated or whether they are down to chance. Unfortunately, we don’t have access to previous seasons’ data and cannot answer this question. With the new Premier League season starting soon, perhaps additional data will either reinforce or contradict our findings. One thing is for certain though: metrics such as these help to better understand and compare the more traditional statistics, and perhaps occasionally unearth information hidden under the large volume of noise.

  • sid

    Could you give the expG Eff figures for Cavani, Zlatan, and Falcao ?

    • sid

      And fantastic work as usual!!!

      • Constantinos Chappas

        Thanks for the kind comments sid. For what it’s worth, for the players you mentioned we have:

        Cavani – 0.96
        Falcao – 1.01
        Ibrahimovic – 1.28

        • sid


  • Toshack


    Yes very, very, interesting post. And agree that penalties need to be excluded in your new metric.

    How much data do you think you need to be able to say that you metric is a true and fair picture of reality (seeing that is contains a bit of subjectivity – at least as far as I understand it)?


    • Constantinos Chappas

      Thanks Peter for your interest.

      I may not have explained myself properly but I wasn’t suggesting that penalties were to be excluded from ExpG. I was simply illustrating how the traditional raw conversion rate of Goals / Shots can be skewed due to the presence of penalties. In similar fashion, raw conversion rates will be skewed if a player has many shots from “easy” positions which ended up as goals. It’s for this reason that I postulate that traditional conversion rates are not comparable between players or teams exactly because they fail to take into account the quality of the chance, however this is measured.

      Our ExpG measure overcomes this problem, (and that’s the reason that removing penalties or “easy” chances in general is NOT necessary) by assigning different ExpG values to an “easy” chance, like a penalty shot, compared to a more difficult shot e.g. from way outside the box. If our expectations calculations are correct then, on average, you would expect the total ExpG for a player/team to mirror the actual number of goals scored. See for example my previous article on this at

      Regarding the sample size it’s a bit difficult to say at present. Obviously looking at the team level is much more reliable than comparing players whose figures may change by 1 goal scored/missed. I guess monitoring these numbers as more data becomes available will also tell us something about their consistency and therefore about the possibility that they indeed paint a picture close to the truth.

      Once again, thanks for your interest.

      • Toshack

        Thanks for your answer Constantinos,

        Sorry for misunderstanding the “penalty thing”. Some backwards brain association… Got it now.

        Also thanks for the clarification on data sample volume. I guess I’m asking because of all these things I’ve been seeing on randomness such as the books The Numbers Game – Why Everything You Know About Soccer Is Wrong (50% of the outcome of a match is down to luck…) and Fooled by Randomness/The Black Swan. (I have The Numbers game but have not read it yet and am in the midst of reading Fooled by Randomness (in which the Black Swan theory is mentioned).

        I guess I don’t know exactly what to think on the various football metrics and the reliability, only that the larger the data volume the more reliable it would be (I hope…).

        Ps. Then of course we have this “bias” on goals and strikers vs. the accomplishments and efforts of the team. So can Sturridge and Coutinho replace Suarez and Liverpool be a better team from it? And does it matter than Torres and Ba have “lousy” metrics as long as Hazard, Oscar and Mata keep creating loads of chances? More questions than answers…

  • Steve


    You said on twitter that I should post a comment here, so I’ll repeat the example I gave which shows my reservations about your ExpG Eff metric:

    If you have player A and player B who had the following stats in a season:

    Player A: took 100 shots, all shots were taken from outside the area. Goals scored = 5.
    Player B: took 100 shots, all shots were taken from inside the 6-yard box. Goals scored = 25.

    Using figures from this average shots/goal model:

    Average # of shots/goal for shots from outside the area = 33, and I’ll assume that it takes 3 shots/goal when shooting from inside the 6-yard box.

    So the ExpG values for the 2 players should be:

    Player A: ExpG: 100 shots / 33 = 3 goals, and player A’s ExpG Eff would be 5 / 3 = 1.67.
    Player B: ExpG: 100 shots / 3 = 33 goals, and player B’s ExpG Eff would be 25 / 33 = 0.76.

    So player A is considered in ExpG terms to be far “better” than player B even though player A is a prolific goal scorer and player A rarely scores due to the fact that he shoots from very poor locations. This is why I say that ExpG makes allowances for strikers who shoot from poor locations whereas it penalises players who’re more selective with their shooting locations.

    Another argument that highlights the limitations of ExpG is in the following article about how to assess the value of strikers who’ve only had 1 season in the main leagues:

    That article makes the point that the only goals that are ‘repeatable’ (unless the striker has a special skill, such as Bale’s ability to score from outside the box etc) are those that came from shots from good areas, i.e. from the middle of the penalty area, and all others, such as penalties and those from poor locations are not ‘repeatable’. And similar to the example I gave above, it’s easy to see that a player with a high ExpG Eff score could have a very low number for ‘repeatable goals’ and vice versa.

    In comparison to ExpG Eff, shot conversion isn’t prone to providing misleading information: with all else being equal, strikers who choose to shoot from poor locations will end up with a lower shot conversion and those who’re more selective will have a higher shot conversion. As such, I think it is wrong to claim that ExpG Eff is superior to raw shot conversion when it comes to comparing strikers’ efficiency.

    • Colin Trainor


      I guess there are a number of points to reply to:

      So player A is considered in ExpG terms to be far “better” than player B even though player A is a prolific goal scorer and player A rarely scores due to the fact that he shoots from very poor locations. This is why I say that ExpG makes allowances for strikers who shoot from poor locations whereas it penalises players who’re more selective with their shooting locations.

      Neither myself nor Constantinos has said that, in your example, Player A is better than Player B. All we are saying is that Player A finished the chances he attempted better than Player B. Period. That’s all we are saying about Player A and B.

      As such, I think it is wrong to claim that ExpG Eff is superior to raw shot conversion when it comes to comparing strikers’ efficiency.

      So if ExpG Eff is not superior to raw shot conversions I guess I can assume that you think raw shot conversion is a superior measure.
      That being the case it’s good to know that Stephen Fletcher is either a “better player” or hell even just a better finisher than Gareth Bale as Fletcher converted at 20% and Bale at 13% last season.

      • Steve

        “So if ExpG Eff is not superior to raw shot conversions I guess I can assume that you think raw shot conversion is a superior measure.”

        Yes, you can assume that.

        “That being the case it’s good to know that Stephen Fletcher is either a “better player” or hell even just a better finisher than Gareth Bale as Fletcher converted at 20% and Bale at 13% last season.”

        But you’re assuming that I totally ignore shot locations, which isn’t the case at all. I think it’s wise to take all measures into consideration. And as I’ve said on twitter, I don’t have a problem with ExpG Eff in itself, so long as its limitations are accepted. My only issue with it is the claim that it’s superior to shot conversion, which I consider to be false because of its inherent limitations. At least with shot conversion for Bale and Stephen Fletcher you know that both were inefficient.

        Btw, I think a more useful measure of a striker’s worth is the ‘marginal points contributed’ metric calculated in The Numbers Game (pages 101 – 105) based on the marginal points produced by goals given how many have already been scored. Points are ultimately what counts, and you don’t get any extra points for scoring from distance or with a bicycle kick.

        • tknutso

          No, apparently you get points by scoring at a convenient time though. Planning is everything…

          • Steve

            I was going to say that rather than calculating the marginal points based on only the number of goals a team’s scored (as they do in The Numbers Game) it would be better to calculate the marginal points based on the actual score when a goal is scored, because e.g. a goal to go 3-2 up is obviously more valuable than one to go 3-0 up.

          • Steve

            … or more simply base the marginal points based on game state, e.g. goals scored when at -2, -1, 0, +1, +2 etc.

    • Constantinos Chappas

      Hi Steve.

      I see that Colin has beaten me to it. Regarding efficiency, prolificity and other measures, I would only add that different metrics measure different things. If you want to know who is the more prolific striker, use the number of goals to compare them. If you want to know whose shots are more likely to end in the back of the net, use the conversion rate. And if you want to know who is more efficient at finishing his chances given the factors affecting the difficulty of each chance (estimated by our measure, rightly or wrongly) then use ExpG Efficiency.

      Regarding the repeatability issue, as I did mention in my post, it’s something which needs monitoring. I have read the post that you linked to, but I have not been convinced (either way, by the way) whether some shots are repeatable and some aren’t. And to add to that I would question on what grounds one could say/prove that a player has a “skill” to shoot from long range positions therefore his shots are repeatable whereas someone else is just lucky scoring from those long-range positions. My belief here is that time will tell if these results are consistent or not. As I mentioned in a previous comment, perhaps the team figures are more reliable and thus more likely to be repeatable, due to the sheer number of shots.

      Thanks for leaving a comment here as it’s much better to discuss this here for two reasons: (a) explanations are not fragmented due to the Twitter character limit and (b) the discussion could potentially help other readers of the piece.

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