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Goalkeeper Resiliency: Measuring Game Difficulty

A statistical approach using xG

One of the most interesting things available in Football Manager 2021 is the ability to track expected Goals, or xG. In combination with Pelham, I think I’ve worked out a useful way to measure what I’m going to call Goalkeeper Resiliency (GR), that is, the degree of difficulty that a goalkeeper is facing, relative to that normally faced by goalkeepers in their league. 

The Theory of Goalkeeper Resiliency

The thinking behind the theory is that a goalkeeper is using up mental and physical energy every time a shot is taken, whether it is on target or not. Seeing a player shape up to shoot, you measure angles, check positioning, get on your toes, get your arms out, and try to judge the shape of the player’s body to help predict the shot. 

The idea comes from a 1986 book on ice hockey statistics that introduced a stat called “Perseverance”, which attempted a similar idea. It was flawed, because shots weren’t differentiated as to where they were taken from, or their general danger level, but the concept was the birthplace of the stat I’m proposing today.

To measure this in football, I’m proposing that we use an existing stat in a different way: xGA, or “expected goals against”. This would be, for a goalkeeper, the cumulative difficulty of shots they faced. It won’t be a perfect measure, but it should give us something we can use to compare. 

But a raw examination of xGA wouldn’t tell us much, because we have nothing to compare it to. The obvious comparison is the other goalkeepers in the same division: average the xGA in every game, and use that to compare to the xGA of the game being examined. 

So what we’ve got so far is (xGA/LgeAvexGA), which will give us a high number if the game was difficult, and a number less than 1 if it was notably easy.

 

Applying the Math of Goalkeeper Resiliency

The key question then is how to use that generated number, that GR (Goalkeeper Resiliency). I believe the best use is to modify a more conventional stat, like Goals Against Average. This is a simple measure, like Conceded/90, that tells you how many goals a keeper gives up per game. As a raw stat, it’s marginally useful, but has no way of coping with the difference in difficulty of a given game.

To show how this would work, I’ll put up three scenarios here. For all three scenarios, the league average expected goals against is 2.8.

Scenario A

In the first scenario, the goalkeeper gave up just one goal, despite the xGA being 4.9. This is an excellent performance.

Scenario B

In this one, the goalkeeper conceded two goals, while the xGA was only 0.4. This is a very poor performance.

Scenario C

In the third, the keeper concedes two goals, while the xGA was also 2.0. 

Doing the Math

So, in order to get the Adjusted GAA (or AGAA), we take the GAA for each scenario. These are respectively 1.00, 2.00, and 2.00 for A, B, and C. We then divide it by the Goalkeeper Resiliency number, which we can derive (as shown above) by xGA/LAxGA. 

In A, we have 4.9/2.8, or 1.75. So the AGAA is 1.00/1.75, or 0.57. 

In B, we have 0.4/2.8, or 0.14. The AGAA is 2.00/0.14, or 14.00.

In C, we have 2/2.8, 0.71. The AGAA is 2.00/0.71, or 2.80. 

So the goalkeepers gave up 1, 2, and 2 goals, but their AGAA is wildly different. For GK A, who faced a plethora of good goalscoring chances, his AGAA is 0.57, considerably better than his GAA of 1.00. GK B is looking quite shockingly bad to have conceded a 14.00 AGAA, which is a lot worse than his GAA of 2.00. And the last goalkeeper has given us a league average sort of AGAA, at 2.80, compared to his GAA of 2.00. 

We can see that the AGAA more accurately reflects the performance of the keepers, given how difficult the game they faced was. While their GAA were fairly similar – ranging from 1.00 to 2.00 – their AGAA show that some of them faced much harder games. 

Conclusion

So that’s my proposed new measure. What do you think? Does it capture what it’s intended to capture? Is there a better way to do it? I’d love to have a discussion about it, if you have any thoughts or comments.

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Written by oldladyplays

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