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Thinking About NBA Statistics: A Proposal

Great job, and I really like it.

It's funny, you look at the quarter and it was one of those times where watching the game, it seems like Evans has such a huge impact (If I'm remembering correctly), but the numbers in the micro pretty much tell you exactly what numbers in the macro tell you. Even when he's on, he does just as much harm as good. Look at all the offensive boards his man got. That's the tradeoff of playing that crazy defense where he was doubling the ball 30 feet away from the hoop.

Compared to baseball, basketball is really like the wild west in terms of using statistics to understand the game. The box score stats tell you so little about what happened in the game. Part of me loves that, but a bigger part of me wants to look closer and figure out why certain things work, why certain players are so much better than their stats. What affect coaches and systems really have on the outcome of a game. Really great work here.

The most amazing thing, though, is that you still have that Lakers game on your DVR. If I don't watch a game in a day or two it's gone forever, replaced by Sesame Street.

The most amazing thing, though, is that you still have that Lakers game on your DVR. If I don't watch a game in a day or two it's gone forever, replaced by Sesame Street.

Ha ha, it helps that (a) I'm the only in the house that knows how to record with the DVR and (b) I only have one kid. It also helped to figure out that cartoons look almost as good in Standard-Def as High-Def (HD is what really takes up the storage space, about 5% per hour for me).

Anyhow, this Lakers game was recorded in Standard-Def (before I got an HD TV) and takes up almost no space. I also have the Bulls last Spectrum game and the Magic Game 1 playoff game still on my DVR.

Great stuff. You're right that it can get a little subjective when evaluating defense, but if common sense is used, it shouldn't have a huge impact (as long as the same person does the evaluation each game). For instance, if the offensive player dribbles by his man and is challenged by a defensive big but scores anyway, how would this be marked? It seems that the original defender would receive a -1, but help defense from interior defenders is very important in evaluating their worth. Perhaps a sub-score could be added for help-defense effectiveness?

Anyway, this is a minor detail. Again, great work.

Jesse reply to Jesse on Jun 2 at 1:55

In particular, I'd like to see how Speights performs in this category. Watching the games, it seems that he is a very poor help defender, but I'd like to see some stats to back that up.

This is a good point about help defense. The question for me would be: did the help defender do his job? If he didn't, there's a good case that the initial defender and help defender would split the -1. Another example would be the Elton Brand play where a defender doesn't show on a pick-and-roll and the dribbler goes in for a basket. Blame could be divided between the initial defender and the help defender, depending on how good the pick was and how good the help was.

09-10 76ers games would have been interesting to score this way, but I deleted most of them right after I watched them!

I think the main problem with basketball analysis is that unlike baseball, you can't just plug in a number. There needs to be some type of evaluation and common sense. That's why I like what you are trying to do here. Statheads sometimes aren't willing to look at the play and see what happened because they want a number. In basketball, that's not possible. It's too much of a team game, which is dependent on circumstance. A couple of things that I saw:

1. It's hard to determine how much a pass in worth. Personally I feel a dump off for a dunk or an alley-oop should be waited more heavily than passing it to an open three point shooter. The guy still has to make a shot, and it does get hazy. I think Rajon Rondo is great, but when Ray Allen starts hitting absurd contested jumpers off screens that Rondo passes to him, Rondo's numbers are inflated. Giving him +0.5 for some of those shots seems like too much. I'd rather give the shooter closer to full credit.

2. Defensive credit to the guy nearest the shot might be unfair as well, especially for Eddie Jordan coached teams. Take a play where Willie would get beat off the dribble and the defense would scramble (Thad would undoubtedly be a part of this) and cover up 2 more passes until someone was left wide open from three. Iguodala would contest it very late by coming from out of his rotation and they'd hit a three. I'm not sure this would be Iguodala's place to get a -1.

3. I think this system would be awesome for stuff like offensive boards. Sam does have games where he gets a bunch of offensive boards and misses shots right after, which really inflates his value. Let's say he gets an offensive board and goes back up with a bad shot and misses. He does get an 0-1, but the offensive boards may take precedence if he piles them up. In this system, while he's getting a +0.5 for the rebound, he gets a -1 for the miss. That takes away what I feel are "hollow" offensive boards.

Alright, that's all I have for now. Great post.

Your method's strength and weakness is it's subjectivity. Rich's post convinces me to suggest changing one thing: all misses should be -1 and offensive rebounds +1. I acknowledge that jacking up a shot with no one underneath is less likely to result in an offensive rebound, but in general there's no reason the shooter should get half the credit for an offensive board. There's no magical way to shoot to make it clank off the rim and into a teammate's hands.

Rich reply to Bob on Jun 2 at 13:17

That's definitely a fair point Bob. There could be some good misses like if Jameer Nelson drives the lane and draws a couple of guys and his shot is cleaned up easily by Dwight Howard. That's a pretty good miss. In most cases as you say, why would more credit be given to the shooter if someone cleans up his mess. I can only guess Statman's thinking, but if you make it -1 and +1 on a miss and rebound, then a guy like Sam won't really be held accountable for what he does after a rebound. This way, even if he keeps the possession alive but then misses, it's still a -0.5 net for him instead of 0 if we made all missed shots one. That's a matter of opinion on how valuable the offensive rebound is. Should it be +1 because you are creating a possession that wasn't there without the rebound or 0.5 because you are simply keeping it alive?

Could an offensive rebound be +0.5 with the miss still being -1 without the math and system being compromised?

I'm actually leaning the other way, an o-board should be +1.

Essentially, what we're talking about here is relative team production. So with the baseline of 1 point per possession, Dalembert is salvaging that point by extending the possession with the offensive rebound. He's penalized if he misses the put-back or turns it over from that point.

This is what I mean...

- Possession is worth one point.
- When the shot is missed, that possession is worth zero points.
- When Dalembert gets the offensive rebound, it's worth one point again (a gain of one point).
- When Dalembert misses the shot it's back to zero, or the exact same as if he hadn't grabbed the offensive rebound.

So it's a zero sum in that case, +1 for the board, -1 for the shot. It's not logical to me for Dalembert to get a -.5 for grabbing a board and then missing a shot/turning the ball over.

I could see splitting the credit on a tap out offensive board, that would make sense. But when we're talking about value, if you think about it, an offensive rebound and put back is really worth just as much as a made three, relatively speaking. The three is 2 more points than expected (1 is expected on a typical possession). The o-board put-back is worth 2 points (0 is expected on a missed shot).

This is exactly the point I was making but expressed more fully and clearly.

Okay, so here was my thinking on the -0.5 for misses that result in an offensive rebound. I began by assigning -1 for a miss and +1 for an offensive rebound. As Brian noted, there is something elegant about -1 for losing a possession and +1 for re-establishing possession. But here was the problem: on defense, I assign a +1 for a defensive stop, and I divide it into +0.5 for the defender on the ball and +0.5 for the rebounder (or -0.5 for someone who gives up an offensive rebound to the other team). So if on offense I give -1 for a missed shot and +1 for an offensive rebound, I would be weighting misses and rebounds differently on offense and defense.

As it turns out, there is a good way to think about the system as is: every shot has two components, whether it goes in or not and who gets the rebound. I assign equal weighting to those two components (0.5 each). For a missed shot/defensive rebound, both components get assigned to the shooter (-1); for a missed shot/offensive rebound, the rebounder negates the missed shot (-0.5/+0.5). The only problem, as you note, is that missed shots are weighted differently depending on who gets the rebound. But is this really a problem? It's true, as you note, that the shooter has no idea who is getting the rebound when he misses. But it's not the intention of the shooter I'm scoring, it's the result of the play. And I would argue that a miss that results in an offensive rebound is not as "harmful" as a miss that results in a defensive rebound. In fact, possession isn't truly lost if someone gets an offensive rebound (I'm pretty sure in offensive/defensive efficiency ratings, a shot+offensive rebound+follow shot counts as one possession, not two).

So, guys (Rich, Bob, Brian), think it over and let me know what you think about the above reasoning. I think giving +1 for an offensive rebound and -1 for all misses could work, but it would weight offensive and defensive rebounds (and offensive/defensive misses) differently. Thanks.

I regret that i don't have the time right now to fully think this through. but i will suggest a case for why defensive rebounds might count less than offensive rebounds: the expectation is that a miss will be rebounded by the defending team. (what's the ratio? 65/35?) so, an offensive rebound results in a whole new possession for free. A defensive rebound is only expected. The numbers get screwy because it isn't reasonable or fair to expect 100% defensive rebounds.

I made a case but haven't convinced myself. Still, I don't see the point of penalizing someone for a misses put back.

Regarding defensive rebounding: would it make sense to penalize a defender for allowing an offensive rebound? the net result is something like 65% of a turnover.

Hmmn, this is really interesting.

So here's the question I'm left with. Are offensive and defensive rebounds equal in terms of ppp? I'm not sure it really matters, in the grand scheme of things. The important part is that defensive rebounds are worth the same on both ends of the floor, same with offensive rebounds. Both methodologies accomplish that.

I think I still lean toward +1 for o-boards and -1 for all missed shots, simply because that keeps the shooting portion of the equation in line. Since it's a zero-sum in terms of PPP, I don't think it's fair for a guy to wind up -0.5 if he grabs and o-board and misses the putback. Essentially, his missed shot + o-board is worth the same as the guy who missed the first shot and did nothing else to further the possession, if that makes sense.

Rich reply to Statman on Jun 2 at 16:06

The more I think about it, I like the -1 and +1 values being distributed. I know that you are scoring the result and in that case -0.5 makes sense, but it can misrepresent a shooter's game. Let's say Kapono goes 0-5 and has none of his shots go for offensive boards. His total is -5. Let's say four of them get rebounded between Sammy and Brand. Then his total is -3. I still think he's just as useless, but the team did a better job cleaning up his mess. I think they should be rewarded.

The one problem I see with this system is that it may place too high of a premium of guys who grab offensive rebounds. Reggie Evans may have scored a little too well if you go at it this way.

Evans would probably wind up being a zero anyway:

Lou misses jumper (-1), Reggie Evans o-board (+1), Reggie Evans misses layup (-1), Reggie Evans o-board (+1), Reggie Evans misses layup (-1).

Defensive rebound Gasol, Reggie Evans fouls Gasol (-1) :)

Hey guys, thanks for the feedback. Looks like it's unanimous that offensive rebounds should be scored +1 and all misses -1. In my example quarter, the changes would have been minimal: Iguodala down from +6.5 to +6, Lou from +1 o +0.5, Sam up from +0.5 to +1, and Evans up from +2 to +2.5 (only two Sixer offensive rebounds).

There's still a problem in my mind with this revision, because offense and defense lose symmetry. For example, say Kobe plays good defense on Iguodala and forces a missed jumper, then Sam rebounds it over Gasol and puts it back in. Defensively, Kobe gets +0.5 and Gasol -1.5 (-0.5 for the rebound allowed, -1 for the basket allowed). Under the original scoring, Iguodala would have gotten -0.5 and Sam +1.5 (symmetrically the opposite of Kobe and Gasol). Under the revision, Iguodala would get -1 and Sam +2. That doesn't seem right on the face of it. On the other hand, a miss/defensive rebound is never symmetrical, so maybe it doesn't matter.

I guess there's no perfect solution. I'll try it out both ways when the season starts and see which one seems to be working better.

I see what you're saying about the defensive end, I think. Does the math still work? If you give Kobe a +0.5 for causing the miss, then does Gasol get a -0.5 for not getting the defensive board?

Right, that's how it was originally designed. And that in turn was based on a +1 for a defensive stop being divided into +0.5 for the on-ball defender and +0.5 for the defensive rebounder. So a guy giving up an o-board would get a -0.5, instead. In turn, that scoring dictated how I originally thought of scoring a miss/o-board on the offensive end. But there's something to be said for the idea that all misses are scored the same; I can see both points of view ...

(The team math still works for both methods, to answer your question. As long as the net for a possession is correct, the team math works out. There are more points assigned on offense, both positive and negative, in the revision.)

What if a guy like Chauncey makes a 3 pointer 5 feet away from the 3-point line? Wouldn't it be irresponsible to contest that shot?

Rich, thanks for the thoughts. Here are some responses ...

Personally I feel a dump off for a dunk or an alley-oop should be waited more heavily than passing it to an open three point shooter.

That's true, and 82games' Passing Rating takes into account the type of basket in weighting their assists. In the case of my system, I do take into account (somewhat subjectively) how much the pass helps the shot. On one play early in the quarter, Miller passed cross-court to Iguodala, who dribbled in from 25 feet pass two defenders to lay it in. Miller was credited with an assist officially, but I gave full credit (+1) to Iguodala. On a couple of Marshall's 3's, Lou made a decent pass but I gave Marshall +1.5 and Lou +0.5. On the third one, Lou did a good job of drawing two defenders, and his pass set up a wide-open shot for Marshall, so I split it, +1/+1. Really, there should be greater precision involved, but that would also allow for more subjectivity.

Defensive credit to the guy nearest the shot might be unfair as well

Yes, and I did try to take this into account. There was one play when Evans overplayed Gasol, Gasol drove, Marshall helped, and Gasol passed to Josh Powell (Marshall's man) for a lay-up. I assigned Evans the full -1 for that play because Marshall did his job and Evans was the one who "caused" the basket. On the switch play you described, I would think about who deserved the most blame for the play and try to assign "blame" accordingly.

In this system, while he's getting a +0.5 for the rebound, he gets a -1 for the miss. That takes away what I feel are "hollow" offensive boards.

Well, actually a miss that results in an offensive rebound is scored at -0.5. There's a reason for that, although the reason may not hold water after examination. I'll give the reasoning in my response to Bob's post (which will be later because I've got to go).

Sorry, a bit O.T., but I wrote part 2 in my open letter to the Sixers.

Pt 2:

The First post basically says the team needs to go back to trying to win with a captivating Franchise player and stop with all of the quick fix band-aid moves.

art 2 is basically a simple 3 year plan:

Draft Turner and try and win ASAP, but without selling low on the current young players or committing to new long term contracts for vets. Then decide if in 3 years to either try and contend (using Brand's expiring + a young player to add the final star piece) or be in great position to make wholesale changes without being under the burden of bad longterm contracts.

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