shot ratios

Prediction versus Explanation by Drew Olsen

There is a subtle, yet very important, distinction between explanation and prediction in most sports, and Major League Soccer is no different. I don’t intend to make this long or particularly math heavy, so hang on. Here’s a simple example of what I’m talking about when I refer to explanation. In its first six games of the season, the Portland Timbers recorded 89 attempts and allowed just 57 to their opponents. During that same time, Portland scored ten goals while allowing eight. I might explain that the Timbers’ +2 goal differential was due—at least in part—to earning more offensive opportunities than their opponents.

Here’s another example, but this time in regards to prediction. In their first six games, the New England Revolution scored two goals while allowing six to its opponents. During its next six games, New England scored eight goals while allowing just three to its opponents. Using just New England as an example, it would seem as though goal scoring in the past (-4) poorly predicted goal scoring in the future (+5).

Of course, we have nineteen teams, not two, so I sorted through all nineteen teams looking for patterns. Here is what I found.

A team’s goal differential during its first six games explained its total points over that same time period extremely well (R2 was 77%). This is not surprising. Teams that tend to score more goals than their opponents also tend to win more games. Nothing shocking there.

However, a team’s goal differential in the first six games of the season provided no help in predicting its total points over the next six games. Here’s the plot on that one:

GD vs. Future Points - 6 weeks 2013

There is virtually no relationship between how well a team scored before, and then how many points it earned later. In other words, goal differentials are not predictive over six games.

But if you’re convinced the lack of predictive ability is completely due to a small sample size of twelve total games, check this out. A team’s attempts differential in its first six games shows a statistically significant correlation to both its future goal differential and points earned:

AD vs. GD and AD vs. Pts


Because it’s sports, prediction is never going to be precise, and these aren't perfect correlations at all. But I find it particularly impressive that over just twelve total games, the attempts data from a team’s first six games shows statistically significant predictive ability of the team’s results in the next six games.

If you’ve listened to our Game-of-the-Week section during our podcasts, you hear us talking a lot about shot ratios. This post hopefully clarified why we do that. Past shot ratios are better than past results at predicting future results.

Montreal's Paradox by Drew Olsen

If you have listened to our podcasts or read through our stuff, you will have heard us talk about shot ratios a lot. That's how many shots a team gets divided by how many shots its allows its opponents. A shot ratio of 1.5, for example, means that a team gets one-and-a-half times as many shots as its opponents. When soccer teams create extra opportunities for themselves, it generally leads to more goals and more points in the standings. And then there’s Montreal. The Montreal Impact has been something of a Cinderella story this season, at least statistically. Leading up to its matchup with the Chicago Fire on Saturday, the Impact had recorded the second-worst shot attempt ratio in the entire league. Montreal had earned just 61 shot attempts with 28 on target to its opponents’ 95 shot attempts with 32 on target.  Yet somehow, the Impact had maintained a positive goal differential (+2) and the second-most points per match right behind FC Dallas.

Against Chicago, Montreal not only won on the scoreboard two-nil, it also won the shooting and possession battles. But that is a rare feat this year for the Impact, and it’s worth posing the question: Has Montreal been lucky this season, or does it do things that shot ratios and possession just can’t explain?

Using just shots on goal for now, I regressed goal scoring ratios against shot ratios to see how teams “should do,” as if shots on goal were the only thing that matter. Even this early in the season, the regression was not all that bad (R2 = 0.4). It also said that Montreal’s 0.94 shot ratio should lead to about the same goal ratio.* Well that makes sense. If you generate roughly the same number of shots on target as your opponents, you should score about the same number of goals. The Impact, however, have scored nine goals to its opponents’ five—a 1.8 ratio, or +4 differential, if you prefer.

An obvious thing to consider is finishing rate. Despite being outshot, the Impact players finish their attempts with goals more than twice as efficiently as opponents do. That ratio is the best in the league. My first instinct is that the Impact has been somewhat lucky, and that opponents will start to finish with more frequency. But there are two possible explanations I want to explore first before waving the cliché luck flag: the quality of opportunities for Montreal and the quality of opportunities for its opponents.

Harrison talked a little bit about Montreal’s counter-attacking style during a recent podcast, and there’s a possibility that the Impact’s style allows low-quality opportunities to its opponents, leading to higher-percentage opportunities for itself on the counter attack. (Before we investigate, it should be noted that Montreal’s schedule has featured teams that average out to be, well, league-average when it comes to finishing.)

Let’s take Saturday’s match against the Fire as an example of the tools I’m using. Check out the Opta chalkboard for yourself here, and you can see from where teams are shooting and scoring by clicking the appropriate boxes for team and statistic of interest. During this particular game, I have Montreal down for 16 scoring attempts, nine from outside the box, six inside, and one from right on the edge. Both its goals were scored from inside the box (though you could argue one was one the edge). Chicago, on the other hand, earned 11 attempts, ripping seven of those from outside the box, just two from inside, and two from the edge of the box. Chicago did not score. I did this for each of Montreal's seven games this season.

Obviously things like angle matter, too, but I’m not going to pull out my protractor for this one. Here’s the breakdown for Montreal and its opponents on the season:

Attempts Goals Finishing
Stat Montreal Opponents Montreal Opponents Montreal Opponents
Inside Box







Outside Box







On Edge















Montreal earns more shots inside the box than outside, and that might very well be a product of its system and players, rather than just dumb luck. While the Impact is being outshot in total, perhaps that stat is skewed slightly by shot selection. Montreal's system seems to create a greater proportion of opportunities in the box. I would still expect some regression from Montreal this season back toward the middle of the standings—as its shot ratios are not favorable even after adjusting for quality—but perhaps not as far as a simple shot model would suggest.

*One might note that Montreal’s attempts ratio is quite a bit worse than its shots-on-goal ratio, which isn’t even that good to begin with. It is apparently too early in the season for attempts ratios to explain much of anything with certainty, but shots models from past seasons suggests Montreal’s goal scoring ratio should probably be even worse than even-ish. That is, if shots aren't broken down by quality.