I screwed up in the last post. It’s really not the first time and it won’t be the last . But it was the good kind of screw up, the kind that makes me go out and break out some maths and some datasets. So feel free to grab a drink, review the Basics or the Basics walkthru even, because this post? It goes to 11.

The mistake in question has to do with the number 2. When working out opponent adjusted WP48, I double counted all the stats. This is because the ADJP48 includes all the marginal value generated by the team and the opponent. In my defense, I would have realized this if I had not been in a hurry to post in the 15 minute break I had during lunch at work (It was either post or go to the bathroom, and yes I have a problem). But really the margins just didn’t add up.

Let’s do the long winded explanation for this. Try to stay with me, I know it’s math but i’ll throw in some jokes and some pics to keep you entertained and I promise the payoff will rock! Consider this rev #2.1 (powered by NerdNumbers) which is as good as it’ll get until we get play by play data (which Andres is working call it super NerdNumbers powers) .

To recap:

I revisited the idea of adding individual opponent adjustment to the Wins Produced model. The driver for this has been the fact that currently Wins Produced divides defense up at the team level for all stats that are not in the boxscore and I have been trying for a while to get at this. Why? I don’t know call it a pet peeve.

The goal then is WP48 at the player level adjust for what the player does and what his opponent does. To do this I look edat Player data for the last ten games for each team and mapped how each opponent did by position. I’ve also accounted for the effect of altitude,rest and home and away. That looked like so:

Then I worked out WP48 for the last 10 games adjusting for position based opponent production and then use my nifty points equations (last seen here) to work out point margin contributions (for every player). See that here (for the corrected version go here):

But as I said I screwed up. I was re-checking the numbers from my previous post and I realized this fairly quickly. I’ve explained this before but the gist of it is, for the game to game instead of doing:

Sum of ADJP48 for Team * MP/48 – Sum of ADJP48 for Avg Team * MP/48 , We do

Sum of ADJP48 for Team * MP/48 – Sum of ADJP48 for Opponent * MP/48

In layman’s terms instead of being compared to the average team, we compare you to the player on the other side.

So when I worked out the following relationships :

**Point Margin for a game = 0.0377 + 15.5 Wins Produced **

**Expected Avg Point Margin for Team (season) = 31*(Wins Produced (team for the season) -41 )/82**

**Wins Produced (team for the season)**** = ****(Expected Avg Point Margin for Team (season)*82)/31 +41**

**Marginal Wins Produced (team for the season)**** = ****Expected Avg Point Margin for Team (season)*82/31 = PM*2.645**

**Point Margin = 31/82 * Marginal WP = .378 *WP
**

**So:**

** +1 Points = 2.645 wins over .500 (43.645 wins)**

** +10 Points = 26.45 wins over .500 (67.45 wins)**

**+1 WP = +.378 Points**

**+10 WP = +3.78 Points**

Which all tracked at 99.9% correlation.

I noted:** “I had a mistake when I put this up. To convert WP to expected Point Margin (and vice versa) for the team I have to account for the fact that for a single game half the win credit goes to the victor and half get charged to the loser so the equations for conversion become”**

** **

** **

** ** This means that for normal WP we assume Player production vs. average opponent and assign full value to the margin and it works fairly well. When I went to Defense adjusted the point margin equations all got skewed by a factor of two (at the player level). This happens because working out opponent WP48 also lines up with team wins. So classic WP48 and Wins Produced and Opponent WP48 and Opponent Wins Produced get to the same result when you add them up individually by team. If I add the two of them I just get double the wins. How do I know this? Because I just did all the numbers for 2010 and I’m not afraid to post them.

What did I actually do? I worked out

- Classic WP48 for each player.
- Opponent WP48 for each player by game based on time by position (this is Wins Produced by team based on deviation of the opponent from average)
- Added them up into a number I’m calling Combined WP48 (by the simple expedient of taking the average)
- Then I went out and computed the Expected Point Margin Generated by each player

I used game splits for 2009-2010 (you can thank Andres and our pet project which we’ll call SuperNerdNumbers for Now). Now before we get too crazy with some fancy new equation, I wanted to check that the correlations are all still ok:

Cool . Let’s use it to look at players:

Next time well play with this some more :-).

*Uncategorized*

some dude

12/23/2010

This is nice work, Arturo. I like. The list seems to make much more sense, now.

Nice to see David Lee and Troy Murphy be so poor defensively and have it reflected in their measurement. No longer superstars and now just above average players (hurrah!). 😀

And Wade is also negative defensively, which is something I thought was true the last couple years. And Miami was a really good defensive team, too.

Bogut, though, is odd. I would expect him to be one of the best on defense as a C, not a negative producer.

I also don’t get Bargnani. How is he a positive contributor on D when the Center position gives us 121% on Toronto? Even Bosh was a positive producer. That one confuses me.

This is a real good start. Now what we need to do is get correct who guarded who in what game to adjust the likes of Steve Nash properly. Or Matt Bonner (who is not a better defender than Timmy!) Once we do that, then we can try to find a way to figre out if a poor(or average) defensive player is being overrated because he’s playing with other even worse defensive players who are being exploited more.

Love to see these numbers for the playoffs, too. Thanks for the work, I believe this is a good step in a better direction.

some dude

12/23/2010

Whoops, also forgot to ask. Is the average player still .100 in the combined WP48?

arturogalletti

12/23/2010

SD,

.099 (but yes).

I really don’t know if it’s better as of yet, just different.

If you think about it I’ve done WP (and tweaked around with the baselines and scheduling effects as well as edge effects), the Point Margin work (which is really a regression based version of adjusted +/-) and Combined WP (which is really a dyi,open source version of Win Shares with the difference that the adjustment is made based on when the player was on the court and at the position).

I know all three are predictive of team success in the present tense. The first two I know are fairly consistent on a year to year player to player ratio (which would let me as a gm of a hypothetical team avoid making like Pacman Jones with the teams money). The third I need to go out and test. I suspect (at least in this incarnation) it’ll have some of the same issues that the WS model has year to year, my hope is that this is an improvement (and we’ll learn something).

Guy

12/23/2010

This is a substantial improvement, Arturo. Any chance you could show us how that impacts each position? Maybe report average OldWP48 and average ComboWP48 for >400 MP players at each position, or something like that?

Guy

12/23/2010

Let me amend that: it will be more interesting to look at position averages among the top 30 players at each position, or something like that, to see how much their WP drops. If you also include the bad players, whose WP often increases, it will be hard to see the impact of comboWP on the players we most care about.

arturogalletti

12/23/2010

Guy,

It’s a much flatter world. However that’s to be expected given the way it’s constructed. I’m lumping players together and trying to guess at their impact from the size of the hole they make. The standard deviation from the mean should shrink (actually the same would happen if I did this with original WP48). This is the main caveat with this kind of adjustment (see my comment on WS above). That said, it’s an excellent tool for seeing defensive impact (but not in a vacuum you’re much better off if you know the particular set a team plays) and for knowing which position is each teams strength and weakness. The next logical step (and one we’re working on , we already have the data sources) is play by play.

Guy

12/23/2010

Exactly right. But is the world equally flatter at all positions? Just eyeballing your tables, it appears that the standard deviation for big men shrinks much more than for perimeter players. Is that true?

I think you deserve a lot of credit for posting this data. Clearly, you are a fan of the Wins Produced metric. But your data now clearly reveals that WP does an extremely poor job of allocating productivity among players. Big rebounders like Camby, Love, Lee, and Wallace are barely impacting the production of opposing players. But opponent AdjP48 includes those players’ rebounding performance, as well as scoring, STL, etc. So your data proves beyond any doubt that these big rebounders are not having anything close to the impact that WP48 was estimating — it would be impossible to add 5 or 6 rebounds per game while seeing no reduction from your opposing players. This is an important discovery, and I’m sure was not what you were hoping to find. So kudos to Arturo for coming forward with his data, even though it revealed huge flaws in his own favored metric.

arturogalletti

12/23/2010

All the averages have to stay the same actually.

guy

12/23/2010

No, I think almost every good player has a lower comboWP rating than oldWP. The question is whether the decline is uniform by position.

arturogalletti

12/24/2010

Guy,

It’s a function of the construction. By averaging by position (because I lack the play by play), I change the shape of the talent curve. It’s a compromise (and I think it’s the same one Oliver made) that’s not perfect. But it’s a useful mechanism regardless.

Man of Steele

12/23/2010

Guy,

Yes, I agree, but it does the same things to the best guards. Chris Paul is barely even part of the upper echelon of the league in Combined WP. The ranking list, top to bottom, is substantially the same, but with moderate fluctuation within levels. Marcus Camby is still one of the best players in the league. This analysis I think takes us the same distance beyond WP that WP took us beyond simple box score stats in isolation:

The true superstars are still superstars

Players who are efficient offensively but poor defenders are overrated by WP, and are not quite as productive as they appear.

Bad players are bad. Defense does not a transform a turnover machine with a TS% of 45% into a star. Efficiency still matters.

Guy

12/23/2010

MOS: Even if the rankings stayed the same, discovering that the true variance is much smaller would be very important in terms of understanding players’ true value — as you seem to agree. But I’m less sure than you that this data should leave the rankings unchanged. I don’t view the data on opponents’ AdjP48 as being only — or even mainly — “extra” defensive information that was missed by oldWP48. That is how Arturo is incorporating it here, and it does indeed contain some of that information (especially opponent shooting efficiency). But oppAdjP48 also captures many other elements that oldWP48 was supposed to already be measuring, including opponent Reb, Stl, Blks, Tov, FT, and PF. So opponent AdjP48 also gives you a way to evaluate and validate WP48: there should be a very strong correlation between oldWP48 and oppWP48. For high-Reb48 players in particular, it’s a chance to see if their opposing players really do have low rebound totals. Looking at this data, it seems that this is not generally the case: guys like Camby, Lee, Wallace, and Love are clearly not taking large numbers of rebounds from their counterparts on other teams — if they were, they would have very high oppWP48.

This is great analysis by Arturo, but it’s definitely a lump of coal for Dr. Berri’s stocking.

some dude

12/23/2010

Cp3 is still at the top. His totals are low because he missed a lot of games and he played hurt (though his D is overrated).

But guys like Murphy and Lee are now much worse than previously thought. They are no longer close to superstars. Camby is still a good defender, so he won’t be brought down as much.

Then look at Ron Artest. he goes from below average to above average. He even surpasses Ariza. By WP48 it was an incorrect move, with this adjusted WP48 last year’s swap was the right move.

EvanZ

12/23/2010

Obviously, it would be interesting to go back and revise 2010 predictions. It will also be interesting to make these adjustments to the college rankings.

Man of Steele

12/24/2010

some dude, yes Paul is still close to the top of the league, but by WP he’s been one of the top two players in the league the last three years. In this metric, he’s merely in the top dozen. That is a difference of some significance (I think).

some dude

12/24/2010

He’s 6th in this new metric. Sure, Camby shouldn’t be ahead of him, but he’s really close to them and that was when playing hurt.

Crow

12/24/2010

After you get counterpart WP48 from play by play which covers boxscore stats of the local match-up, one can pause, look around and recognize that as useful as that is it still lacks measurement of player impacts on team defense outside their main counterpart match-up and non-boxscore player impacts on team offense (spacing, the team value of drawing extra defensive attention with the ball in the post on drives or maybe on the 3 pt line or being a target in a prime location, picks, passing before the final pass, box-outs, etc) and recognize that these are not necessarily trivial or uniform.

So, to try to incorporate these impacts, one could do a WP-based local / global combination estimate like what the Roland Rating does with PER based data. It doesn’t have to be 50 / 50 though and probably shouldn’t- maybe 2 or 3 to 1 in favor of the local data would be better.

Either counterpart WP by itself or taken further will be more discrete and arguably more discerning than WP or WinShares with their generic equal for all teammates team adjustments for average team defense (when specific players are or are not on the court at all).

And then one can also compare these values to Adjusted +/- which aims at the net sum of these things in one measurement and one can think about the differences in the player data from the different metrics.

Or not, of course.

If one does, one can check the correlations between them for the overall league. And maybe by position and by player type or role too. The various tools and data should be interesting and useful for thinking further about pieces and putting pieces together into lineups and rotations and teams. You don’t get to a final perfect answer about everything but you have a good shot to get further than those who use fewer tools or fewer comparisons. One could also consider blending the results of the metrics for the broadest possible “one number” evaluation. I have been doing a lot of this ad hoc for years with the counterpart PER data and Adjusted +/- and sometimes other metrics.

Going to a counterpart basis improves WP’s handling of rebounding a good deal but a local / global impact Rating would go even further in general and with respect to rebounding.

Take boxscore data as far one can and take Adjusted +/- as far one can and see where each goes and how much they meet up or not. That is what I’ll do with counterpart WP data from play by play when it arrives.

Crow

12/24/2010

It probably would be a more reasonable / better to weight the player’s offensive data 2-3 times more than the team offensive data in the combination metric while on defense 50 / 50 or not far from it may be wiser ratio to select or at least more broadly palatable.

Crow

12/24/2010

When I said some metrics treat defense as equal across teammates, I meant and should have said “shot defense” instead of all defense.