A little more tyranny
To shoot or not too shoot ...
Introduction
In the last article I had a first look at some of the shooting data from the Olympics and ended up posing some questions about the decisions players are making particularly when deciding whether to shoot or make another action. That article was based on a small area of the circle (a section in the top right) because the analysis was in part prompted by a talk Fede Tanuscio recently gave on the Hockey Site.
There is a lot to do with the in-circle data from the Olympics not just from the shooting end, but I do think it’s worth continuing to flesh out the shooting data from the last article a little more and really discussing the implications that arise from the analysis. To do this I’ll use all the shot data from the women’s tournament rather than continuing to restrict the analysis to a particular area of the circle.
The shot data
Here then is the spatial distribution of all the shots taken with those that became goals highlighted in white.
You can see from the summaries in the top left hand corner that overall the median expected goals value (for more on xG see here and here) is 0.089 - in general shots taken across all teams and all 38 games during the 2024 Olympics1 had an 8.9% chance of scoring. When we group the shots into those that scored (white circles) and those that didn’t (orange circles) we find (unsurprisingly or the model wouldn’t be much good) that goal scoring shots had a much higher expected median value (0.32). The total number of shots taken was 458 and the overall scoring prediction from this data (i.e. summing all the xG values for each shot) is 76 goals. The actual number of field goals scored was 72 so the teams were pretty much meeting model expectations based on the number and quality of shots they generated.
It is also worth having a little look at some summary data for each team.
Note here that some of the lower ranked teams had relatively high xG values (France and the United States) and this is in part due to the fact that teams who find themselves defending regularly often generate their own shots from counter attacks and breaks where defender numbers in the circle are low and shot position can be close to the goal. But, high xG values have to be coupled with the total number of shots taken for the overall expected goal estimate and because these teams usually generate far fewer shots than the higher ranked teams (just 9 and 18 for France and the United States respectively) ‘Total xG’ will be low.
Do teams put differing values on shooting?
It is definitely worth asking whether any team, deliberately or through an accident of playing style, generates higher value chances than the other teams.
And the answer is none of them do. The key bit of Figure 2 is at the top where the Kruskall-Wallis statistic is reported (9.95 with 11 degrees of freedom) along with the significance level. The probability that all these teams have a similar distribution of xG values is p = 0.53, which in analytics parlance, means they are pretty much all the same.
And that itself is interesting. It could be that teams don’t seem to think about maximising shooting opportunities - which is hard to believe - or they do but it is very difficult to execute under most situations in the circle and so players take any opportunity to shoot that is presented. Either way half of all shot values are at or below a 9% (229 shots) probability of scoring, and 71% (325 shots) have less than a 15% chance of scoring, a conversion efficiency that is often met or exceeded by the probability of scoring a penalty corner.
The penalty corner data
Talking of penalty corners it would also be good to know how the teams fared with their corners at the Olympics.
Now with this information we can build from the last article and look at what happens over the whole circle instead of just one corner. In that last article, I noted that if shot probabilities are generally so low, the question must be why are players shooting rather than looking for another action that will maximise the probability of scoring? A pass to a more dangerous part of the circle (an area easily identifiable in Figure 1) would do it as would winning a corner. I’ll deal with how well passing to score works in a later article but here the easiest adjustment is to tell attackers that if they are in a situation where the xG value is low, win a corner instead.
Decision making - all together now.
That’s simple enough to say, but what is low? Well, if half the shots taken have a probability of scoring of less than nine percent, that would seem low. So we can take the median value as a cut-off and highlight all those shots that had an xG value less than 0.089.
Here in Figure 3 are half the 456 shots taken during the Olympics highlighted in yellow all having an xG value less than 8.9%. Note also it leaves the high value shooting opportunities (the orange circles) intact and their median value is now 0.18. The total number of goals expected to be scored is 63, the teams only lose thirteen goals if half of the shots taken are removed.
What do the teams gain though by resisting the impulse to shoot and instead carry out the perhaps more mundane action of winning a corner.
Now in Figure 4 the yellow circles have been assigned to the penalty corner conversion rate specific to the team taking the original shot. Remember that the actual number of field goals was 72 and the estimated number from the xG model was 76. Having swapped the low value shots for corners the expected goal total jumps to 106. Thirty extra goals ‘simply’ from a more judicial combination of winning corners and taking shots.
That’s an interesting start but it all may be a little heavy handed. Teams not only have a different penalty corner conversion rate (Table 2) but also a different median xG (Table 1). So we can refine this approach a little more and instead of a blanket application of the overall median value, we can use each team’s specific median xG value to determine whether a player should shoot or try and win a corner. Applying this would see the Dutch, for example, trying to win corners as soon as the shot a player might take has a value less than 27%. By contrast Spain would only try and win a corner when their xG values are less than about 4.4%, the teams penalty corner conversion rate being so poor it makes little sense to switch from shooting to winning corners at the overall median xG value.
Decision making - team by team
Showing these team specific transitions gets very messy if put all on one figure so here are the outputs for all the teams that reached the knockout stages. Below are Argentina, Australia, Belgium and China.
Figure 5 shows the distribution of the shot position and as usual the size of the circle is scaled to the xG estimate. In the top panel for each team is the actual shots taken during the tournament and the panel below what that looks like when shots lower than their penalty corner conversion rate are swapped out for the actual penalty corner rate. The difference in median xG and the total number of goals scored for each scenario is on the bottom left of each panel.
Here are the other four: Germany, Great Britain, the Netherlands and Spain.
Let’s take the Dutch. Of the eighty shots they took, only 11 have an xG value higher than their corner conversion rate. But the benefit of converting those shots to corners can be seen in a doubling of their expected goal total (12.5 to 24.2). That’s nearly a goal a game difference (as if this team need another boost to win games). With Yibbi Jansen at the helm and Frédérique Matla as backup, the Dutch team should be confirmed penalty corner seekers, shooting removed to a distant second choice when they get into the circle.
At the opposite end of the scale, at least for these Olympics2, is Spain. With a penalty corner conversion rate of just 0.044, only five of the 27 shots they took had a lower xG value than their penalty corner rate. As a consequence there is very little difference between the original number of goals they expected to score and when those five shots were converted to corners. Spain should be looking to shoot as much as possible in the circle and eschewing even the vaguest thought of trying to win a corner.
Finally, the tailored approach here - each team’s decision making is based on its corner efficiency - results in the total expected goal count at the end of the tournament jumping again, to 115. A goal a game increase in return for exchanging low value shots for corners.
A complimentary way of looking at the last analysis is to ask how many corners would be needed to replace the low value shots we’ve removed and still keep the same goal estimate (a total xG of 76 from Table 1). It’s forty-one. Forty-one corners leads to the same number of goals as 229 low value shots. The breakdown for each team looks like this.
If we take China as an example they took thirty-nine shots that had xG values lower than their corner conversion rate. These shots would be expected to score nearly five goals. But if the Chinese players decided not to take on those thirty-nine shots they would need instead to win fourteen corners to score the same number of goals. That’s between one and two corners a game against five shots a game. It’s an interesting conundrum.
There is of course much more to look at and discuss around this topic. What cut-off value to use to decide whether to shoot or not. Are team specific values too precise and is there a general maxim that can be used to help educate players in their decision making? And so on and so on. But, the point about the generally low value of shots and whether that can be improved is, I think, worth discussing in a little more detail.
Hockey is not like other sports?
Hockey is a goal-oriented invasion game of course but hockey has a unique and, I think, fundamentally important aspect that the others don’t. Of the invasion games I can think of (rugby, football, lacrosse, netball, basketball, handball, water polo, hurling, ice hockey, Gaelic football, Aussie rules….), all score their goals in two ways: one from open play and the other from some form of formal one-against-one penalty3. Only hockey has a third way - the penalty corner.
Hockey seems to be unique in this aspect then. But hockey doesn’t seem to exploit the option in a way commensurate with its goal scoring value. The game certainly spends time improving the execution of the corner but it doesn’t seem to take as much time ensuring lots of corners are won so they can be executed. If I go down to the club where I coach and watch other teams training, junior or senior, I will see a great deal of effort spent on shooting. This effort is either within specialised shooting exercises or as an end product, a reward, for an exercise designed, primarily at least, to practice some other aspect of the game. This may seem a self-evident approach. In hockey players shoot to score goals. Therefore, coaches practice shooting. A lot. But it is only self-evident from a historical or traditional basis, from a within hockey viewpoint4. Standing outside hockey and using a data lead approach to decide whether a player should come out of a circle entry with a corner or a shot would strongly (at the higher levels at least) favour the corner. There are of course nuances to this but the value of a corner, in general, is more than twice as high as the usual outcome of a shot.
In other sports it’s possible to see players trying to maximise goal scoring values. Take football for example. All the theatrics that occur when players throw themselves to the ground and roll around clutching their ankle trying to con the referee, is driven by the knowledge that the probability of scoring a penalty (about 78% in football) is a lot higher than probability of scoring from a shot. In fact, only 0.8% of shots in football have a higher xG than the probability of scoring from a spot kick. No wonder football takes the increase in scoring probability seriously, even if it often results in less than edifying scenes5.
An overarching impression when citing football as an example is the feeling that an analytic based assessment will see hockey flirt with the less appealing side of other sports. Taking a shot, any shot, is easy, and fun, and exciting. Winning a corner on the other hand, well, it takes real skill but is perhaps slightly dull, has slightly too much the whiff of cold, calculating professionalism. Alyson Annan in her Masterclass on Circle Behaviour on the Hockey Site answered a question about the future of goalscoring. Annan’s answer was revealing:
“I think that too many goals are being scored by penalty corners. I don’t know what the answer is, I like seeing goals being scored, maybe make the goal bigger, .. I do hope the game in the future is not going to be a game of penalty corners. That’s not exciting.”
It’s an interesting perspective, field goals good, penalty corner goals bad sort of thing to paraphrase a well known work. The penalty corner seems to squat there as some sort of gargoyle scoring technique, a traditional but unloved necessity. And yet there is little doubt from the data that placing more emphasis on corners might be a good thing from a quantitative goal scoring perspective if not, as Alyson Annan suggests, a game appreciation aesthetic. Indeed, such a good thing that one might argue we should spend less time trying to add small improvements to shot value when there could be more to be gained if that time was spent learning how to win corners more efficiently.
Following that through requires a better understanding of what happens in the circle. There is clearly theoretical space for improving goal scoring simply by increasing the value of the lowest scoring attempts. If that is to be done by winning corners it would be good to have a grasp on how often players actually try and win corners currently and what the balance of winning corners is versus them being awarded through some accidental mistake in the defence. Getting that information would tell us not only about the decision making priorities players are making in the circle but also whether there is any room for improvement. And then what about all those non-shooting, non-corner-winning actions? Did they result in a better goal scoring opportunities?
“Data, data, data”, as some fictional character once said, “I can’t make bricks without clay.” So back to the analysis and this discussion will continue in future articles.
I am very much focused on the women’s game here and it may be different for the men’s completely or in part. I just don’t pay much analytic attention to the men’s game at the moment.
Spain’s long term conversion rate is around 16% and at their last major tournament (EuroHockey 2023) it was 25% (they didn’t compete in the 2023-24 ProLeague).
I might just be showing my ignorance here and I am very happy to be corrected. But, I really can’t think of an equivalent from other sports. Rugby has a drop goal but that is not, except for occasionally towards the end of very close games, a competing strategy for try scoring and it is worth fewer points.
And, arguably, being a traditional way of scoring, has been and still is influenced by those other sports that don’t have a third way.
A small analysis on the number of penalties awarded per game in football over the last thirty years strongly indicates that more penalties are being awarded now. The increase has been ascribed to the introduction of VAR and also to the increased weight analysis has on shaping game tactics. Perhaps not a compliment for analysis in this regard but there you go.