Defensive Contributions Compared to Average

It‘s been a while since I last did some work around defense, but in my spare time my interest was sparked again – so I started trying to figure ways in which I might be able to advance some of the quantifiable ways players can be judged by defense. This time, instead of merely introducing a new way of judging players defensively via work done at statsbomb, I’d like to expand upon the work already done.

First of all, we should probably revisit the work that’s already been done. Ted Knutson and Marek Kwiatkowski did some work a few years ago in their attempt to account for possession when quantifying defensive metrics. The idea is that players cannot make a defensive contribution while their team is in possession (for obvious reasons), so their numbers will look worse. That doesn’t inherently mean they’re lesser defenders than players on teams that don’t hold substantial amounts of possession – it just means their opportunities are limited. To account for this, Marek introduced a sigmoid function that “gets more extreme in adjustment as you get further away from 50% possession.”

I gathered the data from for the five major leagues in Europe (EPL, Bundesliga, La Liga, Serie A, and Ligue 1) from 2010 to 2015, but I focused on Serie A for the purpose of this exercise. Serie A has built its reputation as being a tactically astute league that focuses on the defensive side of the ball – so it felt right to start the exercise on defensive metrics in the defensive league. The correlation between the adjusted tackles and interceptions and goals conceded was -0.61 – which makes sense. As goal saving contributions go up, goals go down. The data also produced an r^2 value of 0.37.

Team Defense - Italy.png

While the value, at first glance, seems low, it’s actually pretty impressive. As Ted Knutson wrote in his piece, “given how complex football is, I actually think that’s pretty good.” Football has a lot of moving pieces that all function together, so finding a stat that explains 37% of the output is a pretty impressive step forward. But so far none of this is my own – just an updated version of Ted and Marek’s work. To add my own spin, I decided to attempt to take on the task of trying to determine just how much was saved defensively through these measures.

My first step was finding the line of best fit, which in excel is pretty easy to do. Doing this gave me a slope of -15.762, meaning for every drop in adjusted tackles+interceptions there would be an additional goal expected. I applied the absolute value of the slope to the adjusted figures for individuals by dividing the individual totals by the slope – to find an overall figure for goals saved. Here’s the top 20 from that list.

Goals Saved.png

I decided to take it a step further, though. See, this figure doesn’t really give any sort of baseline. While we know that the top 20 are going to be better than everyone else, this figure doesn’t really give us any sort of reference point. I decided that the best point reference point, at this point in time, would league average. I found the league average rate of tackles and interceptions per minute (no need to adjust the average figures – as league average possession is 50). From there, I multiplied the league average per minute by the total number of minutes played for an individual.

This figure shows how many tackles and interceptions the average player would’ve made given the same amount of playing time. From there it was a simple case of subtracting the average player from the individual, and dividing by the slope from the line of best fit. Once more, the top 20:

Goals Saved Above Average.png

There are a few problems with this – obviously. First, and foremost, is that the information assumes that all defensive contributions are created equally. It assumes that a tackle in the final third, made by the last defender, is as valuable as a tackle in the first third by a forward – and that’s almost assuredly not the case. It’s also incredibly prone to being overrun by holding and box-to-box midfielders. Players that spend a large portion of a match in both the middle and final third are going to have more opportunities to make a defensive contribution than a player that only spends the match in the final third.

The stat is by no means perfect. It’s by no means the end-all, be-all of defensive metrics. But it’s progress. It gives people more information to supplement a judgement.


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