Possession adjusted defensive numbers argue in a circle

Dividing tackles by opponent possession corrects one bias and installs another, and the correction is rarely examined.

Here is a fix that created a new problem.

Raw defensive counts obviously favour teams that defend a lot. A player in a side with thirty per cent possession will make more interceptions than an equivalent player in a side with seventy, and comparing them straight is nonsense. So the field adopted possession adjustment: scale defensive actions by opponent possession, and now the two are comparable.

Except they are not, quite. Possession adjustment assumes defensive opportunities are proportional to opponent possession, and they are not, because opponents choose where to have the ball. A side sitting in a low block can concede seventy per cent of the ball while conceding almost no possession in dangerous areas, which is the entire point of the arrangement. Their defenders get few chances to act, not because the opponent had the ball briefly, but because the opponent had it harmlessly in front of them.

Adjust for possession and you scale up the actions of players who were deliberately not acting. The metric rewards a defence for the emptiness it created, then rewards it again for whatever tackles it did make. It flatters the well organised low block for reasons unrelated to the individuals in it.

Turn it around and the same adjustment punishes defenders in high pressing sides. They have less opponent possession to divide by, so their raw counts get deflated, even though the actions they made were harder ones taken high up the pitch against players facing forward.

I am not saying the adjustment is worse than nothing. Comparing raw counts across teams with wildly different styles is plainly worse. I am saying the adjustment is a model with an assumption baked in, and the assumption, that opportunity scales linearly with opponent possession, is false in the specific cases people most want to compare.

The way out is to define the denominator by opportunity rather than possession. Count the number of times an opponent carried or passed into the zone a defender was responsible for. That is available from tracking data and it is what the adjustment was trying to approximate all along.

There is a general lesson here that I keep running into. Every normalisation is a claim about what causes the thing you are normalising by.

Nobody states the claim. They just divide, and the assumption travels along inside the ratio, invisible, into whatever argument comes next.