One of the great things about soccer is that there are many ways to score goals and win games. I’ve been thinking a lot about why teams choose different tactics, and I decided to test some of my ideas with data. The results offer food for thought.

Let’s start with two assumptions, which we’ll check against the data later:

1. There is a tradeoff between shot quality and shot quantity.

This implies that shot quality isn’t fixed, and there’s a cost to improving it. Teams have at least two ways of creating high-quality shots. One is to keep passing the ball until the opponent makes a mistake or an opening appears; we can call this the Wenger way. The other is to break quickly and overrun the opponent’s defense with pure speed; we can call this the Mourinho way (though we could arguably have called it the Ferguson way, too, as both managers have used the tactic with speedy squads).

Both of these ways are costly in terms of shot quality. The Wenger way takes time; each shot is the result of a long possession, meaning there will be less time for additional shots. The Mourinho way requires a lot of energy, since players have to sprint as soon as their teammates win the ball. Players tire, and fast-break opportunities are limited. So doing things the Mourinho way will limit the number of shots, too.

2. The more shots a team takes, the more shots it will have to defend.

Most shots result in a loss of possession. The exception is when the ball comes back to the shooting team off the post, the goalkeeper, or a defender. These offensive rebounds, to borrow a basketball term, are rare. Usually the shooting team surrenders the ball, giving the opposition a new possession.

A team that tries to win by taking a lot of shots – let’s call it the Villas-Boas way – will generate more changes of possession and more opportunities for the opposition to shoot, too. Naturally, a team that works hard to regain control of the ball will be able to limit this effect somewhat, but the baseline effect must be to give the opponent more chances.

Now, with just these two assumptions in mind, how should a team try to win games? It can wait for opportunities to break, like Mourinho; pick opponents apart with passing, like Wenger; or hit dozens of shots, many from outside the box, in the shotgun approach taken by Villas-Boas. The choice could simply come down to the players’ attributes or the manager’s preference. But let’s go back to the first assumption, the tradeoff.

Here’s a different way to state the assumption: a given team in a given match will have a fixed total of expected goals. Expected goals are simply the probabilities, based on historical averages, that shots will turn into goals. But really, we don’t have to talk only about shots; every situation in soccer has some chance of turning into a goal. So for the purposes of this thought experiment, we can say that a given team in a given match can create different combinations of situations that will all, on average, lead to the same total number of goals.

Of course, that average is just one number that doesn’t say anything about the situations themselves. One tactic may offer a team four 25% chances of scoring, and another may yield ten 10% chances of scoring; for both combinations, the expected number of goals scored will be one. And this is where things get interesting.

If a team chooses to take a small number of high-quality shots, its chances of scoring one goal will increase, all other things equal. But if it decides to take a larger number of low-quality shots – again, with the same total of expected goals – its chances of scoring a single goal might fall, but its chances of scoring multiple goals will increase. The simplest example is to consider a team choosing between one 100% chance of scoring and two 50% chances of scoring. The first tactic yields one goal for sure; the second offers a 50% chance of one goal and a 25% chance of two goals.

So, is it more important for a team to score one goal for sure, or does it need to try for more? A team with a porous defense will have a hard time winning if it scores only once, so it should probably take the Villas-Boas approach. But our second assumption suggests that the Villas-Boas approach will put even more pressure on the team’s defense, so this might be a losing recipe. A team that takes the Wenger approach doesn’t give itself many chances to score, but it doesn’t give the opponent many chances, either; it needs a defense that’s reliable, if not particularly durable. The Mourinho approach probably requires a defense that can soak up long stretches in its own half, but each shot by the opponent may lead to a counterattack. The key is to force the opponent into bad shots.

All of this sounds reasonable enough to me, but let’s see whether it jibes with the data. One way to test the first assumption is to look at the coefficients of variation for shots, expected goals per shot, and total expected goals across matches for individual teams. If total expected goals vary less than both shots or expected goals per shot, then the tradeoff in the first assumption may be present. For the 2012-13 English Premier League, this was indeed the case for every single team:

I’m not sure if this tradeoff comes from the sources I suggested. In open play, for any given number of passes leading to a shot, the speed at which the ball travels is positively (if rather weakly) correlated with expected goals. And within any narrow speed range, the number of passes leading to a shot if also positively (if even more weakly) correlated with expected goals. Still, the tradeoff seems to be there.

Now, what about the second assumption? Of the roughly 10,500 shots tracked by Opta in 2012-13, about 1,000 resulted in goals; about 3,500 were misses that went out of bounds; and about 2,100 were saved and retained by the opposing team. So at least 63% of shots resulted in losses of possession. However, it’s not easy to see whether taking more shots leads to more shots by the opposition. This is because a lopsided contest will probably result in an unusually high number of shots for the good team and an unusually low number for the bad one. We’d want to see the same teams play each other multiple times in the same stadium to see whether differences in shot volumes were correlated.

Finally, let’s look at how teams fared depending on the tactics they appeared to use. In the graph below, each dot represents the goal difference (excluding penalties and own goals) in a game in the 2012-13 season. The dot’s location is determined by the number of shots and the average expected goals (ExpG) per shot for the team in question. The iso-ExpG curves show groups of points that represent the same total expected goals (shots times ExpG per shot).

The pattern here isn’t completely obvious, but it looks like moving to the right along the higher iso-ExpG curves leads to worse results. In other words, the Villas-Boas approach – choosing quantity over quality – may be inferior to the Wenger and Mourinho ways of playing for teams that already have a high expectation of success. This insight may be particularly pertinent for teams that sometimes seem torn between the various tactics, like Liverpool:

Liverpool had quite a few losses and draws in matches with high total ExpG, and in all of these matches it took more than 20 shots. This phenomenon – if it is real – could come from the effects I suggested on defending, or from the influence on play of scoring the first goal, or from other factors. But it does suggest that in a tradeoff between quantity and quality, good teams should choose quality.