APBRmetrics

[Joe]

I've developed a modified version of PER that accurately estimates assisted vs unassisted field goals as opposed to just using the crude estimates that don't account for the fact that %ast rates vary wildly throughout the league (and more importantly for these purposes, throughout teams). The article on the methodology is here:

http://www.hoopdata.com/recent.aspx?aid=39

I also added charges into the formula with the same weight as steals, which makes sense given they have the same exact effect in regards to possessions, and there's no reason not to account for them since they are now recorded.

Past four seasons of APER (alongside normal PER) are here:

http://hoopdata.com/advancedstats.aspx

Interestingly enough, things don't change as much as you might expect (I'd use the 08-09 numbers as a reference point before the small sample 09-10). I detail specifics in the article, but PG's obviously now rank out the highest, but they are basically less favored relative to other positions with this new formula than PF/C's were relative to other positions with the old formula. All in all, PG/PF/C rank out pretty high on average, with SG/SF falling a bit lower, but 6 of the top 10 last season were SG/SF, so take it for what it's worth. No one at the top takes a big hit, but a few guys up top to get a big jump, with pretty much all adjustments in the rankings being due almost solely to whether the player is above or below the league average %Ast.

I have some other ideas for ways to modify PER with some other statistics as we add new stuff to our database, but these were the two most obvious additions for now.

I looked into modifying the accounting of positive possessions used (changing how PER doesn't deduct for possessions used on makes after accounting for the added value in points), but the results were wildly out of whack with reality, and I now understand why Hollinger weighed the formula the way he did. I'm sure this has been discussed ad nauseam here, but due to the accuracy of offensive box score statistics relative to defensive box score statistics in measuring performance, it's necessary for the offensive statistics to be weighted more highly than the defensive statistics in the formula, otherwise the results are just ridiculous. Hollinger's modification for positive possessions and not debiting them appears to be the most obvious solution. Just wanted to cover that issue before someone suggested I make that modification, though I'd definitely be curious if other modifications could be made to better measure efficiency while still maintaining the offensive to defensive weight.

Curious to hear feedback/suggestions as always. Hope you guys find this useful. In browsing the forums and past discussions on PER, I know this is something that has been asked for pretty much every time it's been brought up.
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[Mike G]

What could you do to PER such that a team's PER is commensurate with it's point differential?

I see that of GSW players, filtered to 15+ mpg and 40+ G, 9 of 10 have a PER >14.2, 4 are >16. Your adjustments don't really change the overall picture of a well-above-average team. Yet they were 29-53 last year.

Their offense may have been above league average, independent of the context of their opponents. And you could argue that on a given team, PER ranks players about right. But between defensive and defenseless teams, there's no correction.
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36% of all statistics are wrong

[supersub15]

[kjb]

A couple years back, in the privacy of my own spreadsheet, I did a simple defensive adjustment to team PER that I then applied to the players on that team. Players on good defensive teams got a bonus; players on bad defensive teams got a penalty.

The process is so simple, it's almost embarrassing -- lg. avg. drtg/team drtg. Then multiply that percentage by the individual player PER and voila -- defense adjusted PER.

Gilbert Arenas has a PER of 19.2, the Wiz have a drtg of 107.2 and league average efficiency is 105.5.

So, it's 105.5/107.2 * 19.2 = 18.9.

At the team level, the results end up correlating extremely well with winning percentage.

Smart people here can probably come up with something much better. This was something simple I did for myself a couple years back.

[Joe]

PER already correlates at about an 85% level with wins, higher than AWS, WS, and EFF (based on some quick excel work I did on the 2009 season). Hollinger has written in these forums before he doesn't believe assigning team credit for defense to players is a good idea because it's going to unfairly distribute credit based on the performance of teammates. Ironically, that's exactly what I got away from by fixing the assist adjustment, but that's only because it's actually possible to do now, while it wasn't before.

To answer the other questions, to get PER to correlate with team efficiency, you'd need to make it based on actual possessions and apply equal weights to offense and defense in the formula, two things that would basically ruin the formula because it's not possible to accurately measure defense through box score statistics.

And Mike G, we have Team PER listed on our advanced team page, which calculates PER at a team level. And of course the adjustments to the player PER won't change anything at a team level, because all it's doing is redistributing the credit for scoring and passing, while the ultimate output on a team level is still the same.
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[Mike G]

So you aren't looking to 'fix' PER, but just to 'tweak' it a bit?
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36% of all statistics are wrong

[Joe]

Until someone reinvents the way basic box score statistics are tracked, specifically to make the accuracy and complexity of defensive stats on the same level as offensive stats, it's impossible to 'fix' PER in the way you want it to be fixed. Giving equal weight to defensive stats that are far less accurate in explanatory power is not a solution that would 'fix' PER. Likewise, neither is distributing credit for team defense to individual players regardless of if they deserve it.

All I'm looking to do is modify PER to account for things that are trackable, in addition to the things it already tracks well. One idea is distinguishing between free throws that account for possessions and ones that don't, rather than using the 0.44 estimator, a percentage which varies from player to player (though not on the same level as the %Assist rate was varying). If you want me to modify PER to make it some kind of end-all, be-all stat that matches up to efficiency differential, it's not happening, because it's not possible to do it accurately with the data at public disposal.
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[Mike G]

One stat that is tracked is Opponent Pts/G (or Pts/Poss). Just as a player can have a Reb% that is scaled to Tm and Opp Reb (not necessarily in equal measure), we can scale a player's Scoring to Tm and/or Opp Scoring.

In other words, 20 points in a 115 PPG environment is not equal to 20 points in 90. This seems pretty obvious; just as getting 10 Reb out of 50 is not as good as 10 of 35.

You wouldn't have to scale a player's whole PER to the available points, just his points. There is a 'scoring' component, isn't there?
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36% of all statistics are wrong

[Crow]

If you don't think you can fix PER to weight defense equally and accurately then I'd vote for an adjusted, strictly offensive PER.

The slightly adjusted for assisted rate and charges is an improvement over the classic version but I'd probably be much more regular in using an offensive PER.

I'd mainly use defensive Adjusted +/- for the other half of the game.

[Joe]

[deepak]

Any plans to factor in charges into your APER, since you are tracking them?

[Joe]

From first post in this thread:

[deepak]

Don't know how I missed that.

I wonder, though, if a steal is really the same value as a charge. It's true that they both result in a defensive stop, but steals also typically lead to transition opportunities (hence, better offensive possessions). On the other hand, one could argue that players who collect a lot of steals also tend to to gamble more, so maybe that cancels out the offensive benefits on average.

Should such things be taken into account in these linear weights ratings?

[Joe]

One of our plans is to eventually make a stat that accounts for steals that lead to made baskets within 5 seconds or so, something we could possibly modify the APER formula with when we do it. Another thing is distinguishing from blocks recovered by offense and blocks recovered by defense, which could also be modified in the APER.

The problem with changing the value of steals based on what they lead to, however, is technically, if you're going to give a player more than the value of a possession for stealing a ball, you really should be subtracting that extra value from scorers on the team, because you're suggesting that the credit for the scores steals lead to belong in part to the thief. It doesn't make sense to distribute the credit twice, such as statistics like Win Score over-counting assists by not deducting them from scorers. Then again, PER doesn't follow a strict possession formula, so it is something that can be considered.
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