2025-04-22, 04:04 PM - Word count:
Would you rather take 20 shots each with an xG of 0.1 or 5 shots each with an xG of 0.4? If we imagine the number of goals scored in a game as a binomial random variable with the above parameters we would expect on average the same number of goals (2=20*0.1=5*0.4). Of course, there is some variation from game to game with a wider degree of variation for the team taking more shots.
![[Image: image.png]](https://i.ibb.co/RTBr1qXY/image.png)
How should we expect that to affect the game result? Let’s imagine them facing off head to head with independent team performances.
![[Image: image.png]](https://i.ibb.co/1GGVs7Tf/image.png)
The team with the lower variance ends up winning more often. They never blow out the opposition, but they are more likely to win a close fought game. And most importantly across all results they end up winning a higher share of the games.
![[Image: image.png]](https://i.ibb.co/s9kZFrwL/image.png)
So assuming equal xG in total you would tend to prefer taking fewer, higher quality shots. But things aren’t always equal. If you are an underdog, you’d be in pursuit of variance. You would need to get a result near the top of the distribution. Taking more shots gives you that chance to overcome a disadvantage in expected goal scoring capability. Just look at those same overall goal differential results, but netting out an expected xG deficit. If you needed to overcome an expected xG benefit of 4, 5, or 6+ goals the higher shot volume strategy gives you the better chance of winning).
This has all been from the perspective of the shot taker. But of course the same applies from the defender’s perspective. Assuming equal xG conceded from two strategies you might prefer to give up more, lower quality shots. There will be higher variance, but on average you'd expect to come out ahead on that strategy. If instead, you had an advantage you might want to limit your exposure to variance opting to give up fewer, higher quality shots to limit the possibility of an extreme outcome.
These assumptions are pretty limiting. In reality, you don’t exactly get to choose the mix of shots you take or give up. But I think the philosophy stands. You might alter your tactics toward a higher or lower variance strategy depending on the matchup or the broader context of the league.
For fun let’s look at the results achieved by each team last season. Noting again this is a mix, not equivalent to a single binomial random variable, but we can maybe get some read on the sort of strategy different teams chose to apply.
![[Image: image.png]](https://i.ibb.co/pvqcnQnN/image.png)
As always Reykjavik and Black Forest are a fun contrast to observe. On the offensive side Reykjavik seems to have deployed a shoot early shoot often strategy, while Black Forest generated fewer, but higher quality attempts. Defensively Reykjavik were elite in limiting shots, but tended to give up slightly higher quality shots, Black Forest were elite in limiting shot quality while giving up a fair number more shots. And USP was somewhere in the middle on both metrics.
How should we expect that to affect the game result? Let’s imagine them facing off head to head with independent team performances.
The team with the lower variance ends up winning more often. They never blow out the opposition, but they are more likely to win a close fought game. And most importantly across all results they end up winning a higher share of the games.
So assuming equal xG in total you would tend to prefer taking fewer, higher quality shots. But things aren’t always equal. If you are an underdog, you’d be in pursuit of variance. You would need to get a result near the top of the distribution. Taking more shots gives you that chance to overcome a disadvantage in expected goal scoring capability. Just look at those same overall goal differential results, but netting out an expected xG deficit. If you needed to overcome an expected xG benefit of 4, 5, or 6+ goals the higher shot volume strategy gives you the better chance of winning).
This has all been from the perspective of the shot taker. But of course the same applies from the defender’s perspective. Assuming equal xG conceded from two strategies you might prefer to give up more, lower quality shots. There will be higher variance, but on average you'd expect to come out ahead on that strategy. If instead, you had an advantage you might want to limit your exposure to variance opting to give up fewer, higher quality shots to limit the possibility of an extreme outcome.
These assumptions are pretty limiting. In reality, you don’t exactly get to choose the mix of shots you take or give up. But I think the philosophy stands. You might alter your tactics toward a higher or lower variance strategy depending on the matchup or the broader context of the league.
For fun let’s look at the results achieved by each team last season. Noting again this is a mix, not equivalent to a single binomial random variable, but we can maybe get some read on the sort of strategy different teams chose to apply.
As always Reykjavik and Black Forest are a fun contrast to observe. On the offensive side Reykjavik seems to have deployed a shoot early shoot often strategy, while Black Forest generated fewer, but higher quality attempts. Defensively Reykjavik were elite in limiting shots, but tended to give up slightly higher quality shots, Black Forest were elite in limiting shot quality while giving up a fair number more shots. And USP was somewhere in the middle on both metrics.
