Quarters, Halves and Hydration breaks

A comment on hockey going back in time

Yesterday Joris texted with a link to this article and asked whether it was worth a bit of research given the claims made by the two coaches being interviewed. The article was a consideration on the benefits of the current hockey model, four quarters and sixty minutes, compared to the old seventy minute and two halves game.

On a first read through I thought, oh, this is just a bit of clickbait in time for the forthcoming World Cup prompted, no doubt, by the ‘hydration break’ going on in the current football World Cup (effectively making that sport a four quarter game too) and all the various commentaries (mainly negative) associated with the change.

But as I read it a second time there were a couple of points made by Rick Mathijssen (head coach of the Amsterdam men) and Paul van Ass (former head coach of both the Dutch men and women) that I thought, hold the phone, that’s not quite right is it?

The first one was from van Ass who is quoted as saying:

‘Yes, we used to wear teams down a bit in two 35-minute halves. That you keep the tempo so high that your opponent can no longer keep up by the end, giving you a better chance to turn the tide and score goals at the end of the match. That is now outdated. I actually liked that periodization weapon. Now it is four 15-minute halves going all out. Simply being fit and being able to run as hard as you can gets you a long way. I wouldn’t mind if two 35-minute halves came back.’

Apparently then, the old format allows a team to build pressure and that leads to more goals later in the game. Presumably that’s later in each half but van Ass doesn’t specify. Whatever it is, this is certainly a testable claim. Is the distribution of goal scoring in a 70 minute game skewed towards the end of each half?

To check van Ass’s assumption I put together a small dataset for both the men and women from before the switch in game duration (Olympic Games 2012 and World Cup 2014 - when van Ass was in charge of the men for both competitions) and after the switch (Olympic Games 2020 and World Cup 2022/23). If there is an effect we’d expect to see an increase in goals as the 70 minute game progresses but no increase in the 60 minute game because the quarter time breaks homogenise goal scoring.

Figure 1: Frequency distributions of the number of goals scored per minute from Olympic Games 2012 and World Cup 2014. The solid line is the kernel density estimate showing a smoothed version of the frequency distribution

Well, there may be a little lift in goals for the women’s game in a two half game but certainly not enough to be compelling from an analytic point of view. And maybe there is also a little increase in the men’s game though again, by eye, that looks like a lack of goals in the first ten minutes rather than a big increase later.

In fact, across all these combinations the analysis says that the timing of goal scoring is completely uninteresting. There are differences between the men and the women (men score more p < 0.01, a fact already well known), but there is no effect of game minute on goal scoring, whether we examine every minute or pool them into two or five minute chunks (p = 0.54 or higher).

It’s possible that examining the number of goals at these smaller scales might miss some larger effect. Since the idea is that goal scoring increases later in the game we can pool the goals into two distinct match segments. One section is the first time period of each half (minutes 1 to 17.5 and again from minutes 36 to 52.5) and then the second section is simply the second time period of each half (minutes 18 to 35 and 53 to 70). Rather ironically this is now dividing the game into four quarters but it is an attempt to clarify the more detailed summaries shown above.

Figure 2: Average number of goals scored in the first and second time period of each half for each tournament.

But no, there is really no difference in goal scoring between the first 17.5 minutes of each half and the second, neither for the men (χ² = 0.0387, df = 1, p = 0.87) nor the women (χ² = 0.04, df = 1, p = 0.85). Indeed, Figure 1 and 2 are exactly what one would expect to see given what we already know about goal scoring both in hockey and other sports. So there is no signal overall that there is an effect of “wearing teams down”¹.

But perhaps van Ass only meant that the Dutch team (and the men’s at that) created this kind of pressure and reaped the subsequent reward.

Figure 3: As for Figure 1 except the data shown is only for the Netherlands women’s and men’s teams during the above tournaments.

Again, there is no hint here that the Dutch were scoring more goals towards the end of each half in these two tournaments. In fact, for both the men and the women the impression one gets from Figure 3 is that there is a decline in goal scoring as one approaches the half time break and again as they approach the end of each match. If there is any reward for building momentum, for the gradual application of pressure, for wearing teams down, the Netherland hockey teams don’t appear to have been rewarded for their attempts to do so in these competitions.

The second point that I thought was a little much was made by Mathijssen who said:

“During those breaks, defensive errors are more easily corrected,’ Mathijssen believes. ‘As a result, the chance of many goals is smaller. That is a shame, because surely you would much rather see a match end 7-6 than 1-0?”

He was talking about the quarter time breaks and how that can decrease goal scoring. Given what we know about the pattern of goal scoring over the last two to three decades this didn’t really ring true. Luckily the claim is also eminently testable but comparing the two game formats leads to a problem, the very issue that is being debated in the article: match length is not the same and teams had more time to score goals in the seventy minute game. We can correct for this very simply by taking goals per minute which avoids any bias from the longer game format.

Figure 4: Average goals per minute in matches of seventy minutes and two halves compared to matches of sixty minutes and four quarters

There is no evidence that goal scoring is higher in the old format than in the new. Far from it, a formal analysis indicates that both both the men (marginal mean = 4.57 goals per game in a seventy minute game and 5.57 in a sixty minute game: p < 0.001) and the women (mean is 3.44 for a seventy minute and 3.55 for a sixty minute game: p = 0.032) score more goals in a four quarter, sixty minute game than in the old format.

Possibly Mathijssen doesn’t care about the niceties of statistical fairness and his point is just that more goals are scored in a seventy minute game because games are longer and they don’t have the interruption in the middle of each half. We can do that too.

Figure 5: As in Figure 4 but the metric is now goals per game

And it makes very little difference. More goals are still scored in the sixty minute game for the men (p = 0.0046). True, there is no difference in the women’s game now (p = 0.73) but equally there are clearly not more goals being scored in the seventy minute game.

The number of goals has been increasing year on year in international hockey, both for the men’s game and for the women’s. I can’t point you to the evidence because I’ve just realised I haven’t put up a piece here (something I should redress) but I think I mentioned it in this talk on Ernst Baart’s Hockey Site. The idea that the old seventy minute game resulted in more goals than the current format is simply not correct. If hockey were to go back to the 70 minute game now, well, perhaps there would be a difference. But, it would be because the factors that cause an increase in goal scoring are associated with a mix of rule changes over the years and the increased professionalisation of the sport, not with game length or the number of breaks.

Patterns of goal scoring during a game are a little more nebulous. Momentum, the actual measure of game momentum via models that look at the probability of ball progression (like VAEP and expected Threat models) is a commonly used metric in sport (though I think The Secret Analyst is the only one I have seen using it for hockey). Momentum seems to hold the promise of goal prediction. But in football the relationship between momentum and goal prediction is weak at best² and I imagine it is similar for hockey. Claims like wearing a team down over a 35 minute period (or even 70 if that was van Ass’s meaning) does sound like a plausible outcome. But the data above, limited though it is to just two tournaments, doesn’t support the idea. In fact there seems to be some better evidence for increased goal scoring through a match quarter than there is here over a 35 minute half. It is possible that the nature of pressure, of momentum is played out over much shorter time scales in modern hockey. That is, of course, until someone throws a big aerial over the top and a forward latches onto it and scores against the run of play.

I’m sure Paul van Ass and Rick Mathijssen were responding in a fairly light-hearted manner, the article itself prompted by the obvious footballing comparison rather than a serious disquisition into the nature of how we play hockey. Yet comments like this do suggest how much the sport is still very much at the behest of personal opinion, at gut feeling. Nothing wrong with that to a certain extent of course but, given the evidence of a simple analysis, perhaps not what major changes in a sport should be based on.

1. I realise I said I would compare the pattern of goals scoring in the 70 minute game to the 60 but I’ve already done too much. This is what I would have discussed. Enjoy.

2. I wonder if it is a better measure for predicting a try in Rugby … Joris?