How would you create a PER for defense?

[Alfred]

PER is a very interesting statistic, because it is able to take the metrics associated with production on the basketball court, and condenses them into a single number. While it's not the end-all-be-all of statistical measurements, it's certainly very useful when evaluating a player.

What I want to know is how to create something similar to that, but for defense. Defense is obviously a much trickier thing to calculate, and evaluate statistically than offensive production, or rebounding production, etc.

However, I think it would be a pretty interesting project to try and create something similar to PER but on the defensive side of the ball. My question to people reading this, however, is what statistics are the most valuable statistics to consider when creating this formula? Here are some ideas:

-DRB%
-STL%
-BLK%
-DRTG
-ON court - OFF court defense points differential (82games.com)
-ON court - OFF court defensive eFG% differential

Some of these are a little subjective, because the ON/OFF court differentials can be skewed by who comes in to replace that player on defense, but I think it's a bit better than nothing.

Anyway, what other statistics would be useful to look at?

[Miller4ever]

on court - off court turnover differential?

Some players just manage to play passing lanes incredibly well and don't always get credited with the steal, or drawing the offensive charge, pulling the chair, etc.

[chsh22]

Rather than looking at the differential, why not just look at how opponents are doing when the player is on the court through things like OPP eFG%. Defense is really about your opponent's offense getting worse.

The big downside I see to trying to approach creating a PER for defense is that quite a bit of defense depends on what position you play. For instance, wing players guarding close shots, bigs guarding the perimeter, and so on.

[rrravenred]

You'd have to make some fairly broad assumptions on what you value for each particular position. Perimeter defenders would have to be disproportionately credited for steals and unsuccessful long-range shots, wheras post players would have to be disproportionately credited for defensive rebounds and blocks. Offensive post players are inherently going to have higher FG% and FTA drawn than perimeter players (for mine), and you have to make your system fine-grained enough not to unduly penalise interior defenders for this.

[Alfred]

You'd have to make some fairly broad assumptions on what you value for each particular position. Perimeter defenders would have to be disproportionately credited for steals and unsuccessful long-range shots, wheras post players would have to be disproportionately credited for defensive rebounds and blocks. Offensive post players are inherently going to have higher FG% and FTA drawn than perimeter players (for mine), and you have to make your system fine-grained enough not to unduly penalise interior defenders for this.

Well, I don't think you would have to be disproportionately rewarded for either of those two categories (steals/blocks), if you weighted them the same.

Offensive post players are inherently going to have higher FG% and FTA drawn than perimeter players (for mine), and you have to make your system fine-grained enough not to unduly penalise interior defenders for this.

If I use anything, it will probably be OPP counterpart PER. PER being equally fair to both perimeter and interior players.

The big downside I see to trying to approach creating a PER for defense is that quite a bit of defense depends on what position you play. For instance, wing players guarding close shots, bigs guarding the perimeter, and so on.

I'm not exactly sure what you mean by this. I think generally bigs have a larger impact on the defensive end anyway, because they do most of the defensive rebounding, and they guard the paint, so it may be unfair to guards, but I'm sort of interested in how different players perform anyway.

Okay, here are the stats that I've narrowed it down to:

-eFG% ON/OFF differential
-DRB%
-D Rating (Player)
-D Rating differential (Team DRating - Player DRating)
-Opp Counterpart PER
-STL%
-BLK%

Here's basically how I think we should weight them:


1. eFG% ON/OFF differential
2. D Rating (player)
3. DRB%
4. Opp Counterpart PER
5. D Rating differential
6 & 7. STL% & BLK%

Opponent counterpart PER might need a bit of explaination, so here goes. Basically, I'm using 82games.com's counterpart PER, which you can find under the "Production by position" section, and then taking the amount they play at each position and adjusting that position's opponent PER to the amount of their own minutes played at that position.

So basically, if we're talking about LeBron James, they say he plays 62% of the team's minutes at SF, and 16% of the team's minutes at PF. So for his opponent PER at SF, I go ((62/(16+62))*Opp. SF PER), which happens to equal 11.05. I then add that with ((16/(62+16))*Opp PF PER), which happens to be 3.69. The sum is 14.74, or the standardized PER of his PF and SF opponents. The percentages played at each position isn't an exact science, so I think that we should not rely on this statistic all that much when formulating an opinion.

Anyone disagree? Anyone have any ideas on how to standardize these different numbers so that they make sense in regards to one another? I'm working on a spreadsheet right now, so I'll inform you guys how much progress I've made.

[Alfred]

Also, to those that haven't seen these sites, I'm getting all of my information from these two sites:

www.82games.com
www.basketball-reference.com

And if you need any help with any of the stats we are discussing, here are some explanations:

http://www.basketball-reference.com/about/glossary.html

[rrravenred]

Alfred.... my understanding of PER is that it disproportionately (in comparison to other available metrics) rewards players for taking shots. Wing players take a lot of shots, wheras post players take proportionately fewer. Do you believe that PER (and correspondingly, opposint PER) adequately captures that difference between the offensive functions of inside vs outside players?

If there's functionally (in terms of this formula) no difference between a long contested jumper and a short hook shot five feet from the basket, do you believe that the benefits and penalties of defending that shot can be considered equivalent?

[Alfred]

PER also rewards you for getting rebounds, which bigs usually get. I do not know the exact PER distribution among guards, forwards or bigs in the NBA, however.

I doubt it would be all that massive anyway.

[Bernman]

This chart should disprove the assumption that PER is a stat biased toward wing players and accordingly to an extent those who shoot more frequently: http://www.82games.com/0809/BYPOS10.HTM

The centers for the top 15 teams in the NBA at that position averaged a 20.9 PER, power forwards 19.3, small forwards 17.8, shooting guards 18.1, and point guards 18.3.

Which relatively accurately represents how post players and point guards, have the most potential to make their impact on a basketball game. Point guards don't only effect their own shooting percentage but those of their teammates. Post players too, to a lesser extent when they can draw double teams and kick out to open shooters as a result. However, in addition they also impact how many extra shots you receive over the course of a game to increase a teams own points per possession number. Of course point guards and posts players are also your first and last line of defense, respectively, giving them more steal (for pgs), block, and charge drawing (for post players, I believe 82games includes the charge stat) opportunities.

That all said, while PER accurately places more importance on the center, power forward, and point guard positions as a whole; those are the positions it least accurately measures on an individual basis. Especially point guards and centers. In no way does PER encapsulate the penetration of a point guard wreaking havoc on a defense leading to passes which lead to passes which lead to scores, disallowing the same effect on the defensive end, proper shot clock usage, etc.; which are major responsibilities of a point guard. Also, in no way does it factor in the shot altering of a post player, kick outs for ball rotation, blocking out to not force his teammate to rebound 1-on-2 on D, etc.; which are not statistically quantified responsibilities of their position.

The positions that PER, or more inclusively, own/opponent PER, most accurately measures are shooting guard and small forward. Their role is primarily about scoring, and doing so efficiently, while preventing their individual opponent from doing likewise. That's mostly what PER measures. So opponent PER is probably the best statistic currently available for measuring defensive prowess and own/opponent PER combined with on/off +/- (Roland Rating) for overall individual ability, at least at the 2 and 3 positions.

Even though I previously stated that PER measures pg, pf, and c the worst of all positions, own/opponent PER is still a VERY GOOD statistic to measure players at those positions in general relative to other stats, because at least it neutralizes the pace factor (by comparing them to the opponents they play it can quantify many of the ways they benefit as well), chucking, and lack of individual defensive responsibility which makes so many players who put up volume stats look better than they actually are to the general public.

[JoeyMorgan619]

Alfred,

I have been interested in seeing a defensive PER for a little while now. Please let us know if you have gotten anything else worked out on that.

Thanks

[charrua]

You can't create a really good Defensive PER, simply because the information isn't there.
The main feature of PER is that, despite his flaws, it incorporates only things that the player himself did. So, even if we disagree about the value of a field goal attempt, we agree on the fact that player X took that shot, that player X did those things and that those things have positive or negative value.
And there's no way to create a useful defensive PER with that criteria, unless we only count steals, blocks and defensive rebounds as defense.
You HAVE to incorporate things like +/-, counterpart PER (maybe counterpart Offensive PER instead) for the number to make sense and those things are NOT things that we know that the player himself did.
Maybe counterpart PER is low because the guy is a great defender or maybe because he plays next to a great defender who takes all the tough covers. Maybe his +/- is good because he's good or maybe because his replacement is awful. There's no good way to remove the team from defense. Even if you decide to watch the game, chart every single play and rate players on their defense, you'll find that most of the time, defensive credit is shared among several players. Someone forces the guy to drive left instead of right, someone else helps and double teams him, a third guy rotates to help the helper, etc. ¿Who defended that shot? Everybody.
Defense is much more of a team thing than offense, which makes individual defensive ratings much less reliaable.

[jsmith]

I tried to come up with one for the raptors starters and a few other players known as defensive studs in the league:

DeAdjRTG = DEF Counterpart PpP + (DEF Counterpart PER - 15)/15 - (STL% * LMW) - (BLK% * BMW) - (DEF Counterpart T/O / OPP Team Possessions Per Game) - (DRB% * BMW)

Where BMW is a big man weight and LMW is a little man weight:

PG BMW = 1, LMW = 0.2
SG BMW = 0.8, LMW = 0.4
SF BMW = 0.6, LMW = 0.6
PF BMW = 0.4, LMW = 0.8
C BMW = 0.2, LMW = 1

This way, steals, rebounds and blocks are weighted more evenly for big men versus little men.

Then, I also added a team weighting element that could be in play which helps forgive players for having bad teammates around them:

DeAdjExcused= DeAdjRTG- (MIN/48) * (Team PPPos - Personal PPPos) * 0.2

This weights the defensive PER based on minutes, and assuming that you are playing 1/5 of the defense on the floor for your minutes out of a possible 48 minutes.



Obviously the lower the better.

Comments/Suggestions?

oh and AVG_PER is just the differential from what their counterpart is playing vs the league avg.

[Alfred]

Wow, excellent work there. My computer went crap and died, and so I haven't been able to do the things I have wanted to IRT stats.

[THROWBACK_91]

This is good as topic im not good with numbers but im going to keep coming back to this thread

[TheSecretWeapon]

Okay, here are the stats that I've narrowed it down to:

-eFG% ON/OFF differential
-DRB%
-D Rating (Player)
-D Rating differential (Team DRating - Player DRating)
-Opp Counterpart PER
-STL%
-BLK%

Here's basically how I think we should weight them:


1. eFG% ON/OFF differential
2. D Rating (player)
3. DRB%
4. Opp Counterpart PER
5. D Rating differential
6 & 7. STL% & BLK%

Defensive rating is already sort of a defensive PER. It incorporates defensive rebounding, steals, blocks, and fouls. Including drtg means that you're double counting the box score stats (by also including drb%, stl% and blk%).

Opponent counterpart PER might need a bit of explaination, so here goes. Basically, I'm using 82games.com's counterpart PER, which you can find under the "Production by position" section, and then taking the amount they play at each position and adjusting that position's opponent PER to the amount of their own minutes played at that position.

So basically, if we're talking about LeBron James, they say he plays 62% of the team's minutes at SF, and 16% of the team's minutes at PF. So for his opponent PER at SF, I go ((62/(16+62))*Opp. SF PER), which happens to equal 11.05. I then add that with ((16/(62+16))*Opp PF PER), which happens to be 3.69. The sum is 14.74, or the standardized PER of his PF and SF opponents. The percentages played at each position isn't an exact science, so I think that we should not rely on this statistic all that much when formulating an opinion.

Anyone disagree? Anyone have any ideas on how to standardize these different numbers so that they make sense in regards to one another? I'm working on a spreadsheet right now, so I'll inform you guys how much progress I've made.

I'd be leery of using counterpart data extracted from the play by play. The numbers at 82games are generated based on assigning each player a position. One position assignment error and 40% of the data is wrong.

In addition, there's no accounting for switches, help defense, zones, or anything else involved in playing good defense. Help defense is EXTREMELY important -- especially for big men.

The underlying assumption in counterpart data is that one defender is responsible for one offensive player. But that's simply not accurate. In hand tracking games, it becomes apparent very quickly that "matchups" -- which are the basis for sooooooo much NBA analysis -- aren't what we think they are.

For example, back in the 05 playoffs, the Wizards played the Bulls. Hinrich and Arenas were both designated PGs. I tracked game 4 of that series for an article that's still at SI.com.

The defensive stats collection also highlights the uselessness of a common method for rating individual defenders: studying counterpart box-score stats. In theory it makes sense -- Arenas and Chicago's Kirk Hinrich are both point guards, so looking at what each does offensively should offer insight into what the other does defensively. Except in practice, it doesn't.

Such analysis ignores that NBA teams use an array of defenses, including various zones (the Wizards use at least three in the half-court), and an astonishing array of nuanced man-to-man schemes. Defenders switch constantly and every NBA team expects every man on the floor to help.

For example, in Game 4, eight different Bulls were responsible for the outcome of at least one of Arenas' offensive possessions, not counting three possessions which couldn't be assigned to any particular players. Hinrich did most of the work, accounting for seven possessions -- but that was less than a third of Arenas' possessions.

[Pogue Mahone]

My beef with using counterpart PER as a measure of individual defense is that 1. PER is intrinsically tied to USG-R (roughly 1 point of USG-R is equal to .61 points of PER) and 2. as mentioned previously, it doesn't count for switches or a poor rotation by a teammate.

Here is an example.

While many around the league, including many Boston fans, think Brian Scalabrine is a terrible defender, I find him to be well above average. I think his help defense is great. I think his man defense is slightly above average, on the whole. If Brian Scalabrine hedges the pick on a pick-and-roll and help doesn't come when his man rolls (or even if his man registers a USG-R related event), Scalabrine is penalized for doing his job as far as counterpart PER is concerned. That makes no sense to me.

Another thing that should be taken into account is that not all PER is created equal. Certain events are easier to accomplish against starters than against reserves and vice versa. In fact, scoring against reserves is more about getting to and making foul shots, on the whole, than about getting easy shots. A higher eFG% against starters than against reserves, believe it or not, is how it shakes out. There are other box score recordable events that tend to hold constant when measuring starters vs reserves.

In my studies, I have used a defensive disruption factor along with a regression of on-court/off-court data and a starters faced adjustment. While not perfect, it certainly tends to jibe with who many considered defensive dogs and really separates the help defenders of the league.

Now if we could just get the league to start recording tipped balls, we would really be making some headway.