## A primer: qualcompTSR

This is something I’ve been playing with for a while, but I don’t have the patience to go back and check whether it’s actually more useful than TSR, and it takes an extra step to calculate, so I’ve yet to use it publicly.

The concept is simple, and somewhat similar to 11tegen11’s relative shot rate (link). At only two points during the season, after 19 and 38 games, has each team faced the same opposition. Playing the best possession teams early in the season will adversely affect a teams TSR, and vice versa. Ideally we’d have a way to compensate for this, and my method has been to simply divide TSR by the quality of opposition faced. Here’s the formula.

Step one. Calculate a teams TSR:

TSR = Total shots for / (Total shots for + Total shots against)

Step two. Calculate the TSR of the teams they’ve faced:

This is basically a simple matrix calculation whereby the TSR is worked out as follows.

TSRopponents = (sum of total shots taken by opponents weighted by number of matches vs. opponent) / (sum of total shots taken and conceded by opponents weighted by number of matches vs. opponent)

i.e. Arsenal have faced Villa once and Chelsea twice, so Villa’s TSR only counts once in this calculation, whereas Chelsea’s counts twice.

Step three. Divide by the league average TSR: *

Which, by definition, is 0.500.

Combine the three:

qualcompTSR = TSR X TSRopponents / leagueaverageTSR

Let’s take the two extreme examples to show how this works. Manchester United have faced the toughest competition so far this year, and their calculation looks as follows:

qualcompTSR = 0.525 X 0.513 / 0.500 = 0.539

So because they’ve faced difficult opponents their qualcompTSR is 2.6% higher (and 60% further from the mean) than their basic TSR.

At the other end of the spectrum Spurs have faced the easiest schedule so far:

qualcompTSR = 0.656 X 0.485 / 0.500 = 0.636

Their qualcompTSR is 3.0% lower (and dragged 13% of the way back towards the mean) because they’ve faced an easier group of opponents. So how many points would TSR and qualcompTSR expect these two teams to score over the remainder of the season.

Earlier in the season there’ll be more divergence but by this point even the most extreme cases only have a 1 point discrepancy in their predicted totals.

And there you have it, next time I’ll be putting it to use and looking at the rest of the Premiership season.

*I’d considered changing the third step to be as follows.

Step three. Calculate how average TSR of the league in games that don’t feature team ‘x’:

TSRnonteamxgames = (total shots in league – shots conceded by team ‘x’) / ((2 X total shots in league) – (shots taken by team ‘x’ + shots conceded by team ‘x’)

but this feels like I’m just repeating step 2 and giving a double helping of credit so it feels like a redundant step. I’m more than willing to have a discussion about this.