PER formula question - how do you figure out lg_APR?

[funkdoc1112]

I've got the formula for PER down pat, but this part is where I run into some trouble:

"The final step is to standardize aPER. First, calculate league average aPER (lg_aPER) using player minutes played as the weights. Then, do the following:

PER = aPER * (15 / lg_aPER)

"

It's possible I'm just an idiot, but I don't quite understand what's being said here. At first I assumed that lg_aPER was just identical to lg_uPER since the pace adjustment would be moot, but doing that leads to incorrect results - for example, LeBron's 2008-09 PER comes out to 32.05 instead of 31.67. So how exactly is this minutes weight done? I tried thinking of it as a per 48 adjustment like how you adjust possessions per game to pace (league MP/240) but while that got me closer it still wasn't right. Feels like a weird thing to not expound on at the very end. But like I said, I could be an idiot

[Mike G]

The idea is to force league PER to be 15, which will then be average.
So you add up every player's (min*aPER) and divide by total league minutes to get league avg aPER.
It will be close to 15 but not exactly.

Multiply every player's aPER by (15/lg_aPER). Now when you sum everyone's (PER*min) and divide by league min, you get 15.00

League total minutes will not be just 30*82*240, but a bit more due to overtimes. It was about 241.4 this year; but just total the player minutes since you have them.

[funkdoc1112]

The idea is to force league PER to be 15, which will then be average.
So you add up every player's (min*aPER) and divide by total league minutes to get league avg aPER.
It will be close to 15 but not exactly.

Multiply every player's aPER by (15/lg_aPER). Now when you sum everyone's (PER*min) and divide by league min, you get 15.00

League total minutes will not be just 30*82*240, but a bit more due to overtimes. It was about 241.4 this year; but just total the player minutes since you have them.

Ahh, I see. I thought you could figure out league PER simply by inputting the league average stats into the formula (which did work at achieving the 15 number, but the LeBron number was slightly off), but it's not as simple of a one size fits all thing as I thought. And what do you know, that worked. Kinda similar to how the the BPM listed on the site is an average of single-game BPMs rather than the number calculated off their season averages which leads to similar small discrepancies. Thanks!

[Mike G]

...Kinda similar to how the the BPM listed on the site is an average of single-game BPMs rather than the number calculated off their season averages ...

What site does this?

Over here --
https://www.basketball-reference.com/te ... /2024.html
-- we see Kawhi Leonard was in 2 playoff games this year: 34.9 min @ 7.6 BPM, and 24.5 min @ -4.6 BPM.
The avg is 1.5. But minutes-weighted it comes to 2.6 -- which agrees with his listed playoff BPM.

[DSMok1]

...Kinda similar to how the the BPM listed on the site is an average of single-game BPMs rather than the number calculated off their season averages ...

What site does this?

Over here --
https://www.basketball-reference.com/te ... /2024.html
-- we see Kawhi Leonard was in 2 playoff games this year: 34.9 min @ 7.6 BPM, and 24.5 min @ -4.6 BPM.
The avg is 1.5. But minutes-weighted it comes to 2.6 -- which agrees with his listed playoff BPM.

Yes, BPM is the minutes-weighted average of the single game calculations.

The original version of BPM was calculated only at the season level, which missed game-to-game variations in strength of schedule.