Do bigger squads lead to bigger results?

In football, you can only have 11 players on the pitch at any one time. You can make substitutions during the game and you need to have players on the bench in case of injury. So you need a squad of more than 11 players. But of course, players cost money and players want to play and not sit on the bench. These factors, and league rules, put a cap on squad size.

I decided to see if there was any correlation between squad size and goals. To cut to the chase, the answer is no.

(Google Gemini)

The data

I've taken the data for this blog post from TransferMarket.com (https://www.transfermarkt.com/) that has data on the squad size of English football clubs at the start of each season. Obviously, transfers etc. change the size, but it's a reasonable place to start.

The charts

Here are charts showing total goals for, against, and goal difference per season per club per league against squad size at the start of the season. I've added a linear fit to the data so you can see the trends. I've added a 95% confidence band around the fit. The r² value is in the chart title, as is the p-value.

The charts are interactive, you can:

Zoom in and out of the data using the menu on the left.
Save the charts to disk using the menu on the left.
See the data points values by hovering your mouse over the data points.
Select the league tier using the buttons.
Select the season using the slider.