First off some administrative detail, the Free agent Guide is updated.

Reader Alex asks:

*Arturo – I’m having a little trouble I’m hoping you can help me with. Let’s say I’m the 10th man on an average team; the team wins 41 games during the season. I earn 1% of the teams wins, which is .4 wins. I do this playing only 4% of the team’s 3936 minutes (assuming no overtime), which is 157 minutes. My WP48 should be (.4/157)*48 = .125, right? (or more like .121 without rounding). So the average 10th man on an average team is an above average player? Or have I missed a step? Shouldn’t many players at the bottom of the rotation be negative contributors?*

I can certainly understand his confusion I posted some incomplete tables (i.e WP48 was missing). Since we’re all about the fanservice here, I’m giving you all the by Minute ranking WP48 tables you can handle. Enjoy.

Regular Season Since the Merger:

Regular Season Last Ten Years:

Regular Season Last Year:

Some Points:

- The main point is the gradual flattening of talent over time.
- Bench Talent over time improved tremendously. To the point where last season better players where on average being kept out of the rotation.

Playoffs Since the Merger:

Playoffs Last Ten Years:

Playoffs Last Year:

Some Points:

- Same flattening as in the regular season for talent
- Players above the 6th man are negative contributors in the Playoffs in 2010.

So with these tables, you can now fill in the blanks for empty rosters with average bench players as per WP48. just like ESPN does.

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*Related*

nerdnumbers

07/29/2010

Arturo,

What are your thoughts on what the heck happened to the benches last year? I know Sheed got to play 4 series and was terrible so may have helped, but were all of the teams really that bad from beyond the top 6?

arturogalletti

07/29/2010

Andres,

I’m doing 4 posts to answer just this question. Hopefully I’ll start getting them up today. 🙂

Jimbo

07/29/2010

Arturo – unrelated to this post, but hopefully you can provide your thoughts… I was just reading the article on NerdNumbers about Iggy vs Melo (Face of the Franchise), and couldn’t help thinking that one thing missing from the comparison, and perhaps from the Wins Produced model is the use of a “double teams drawn” statistic (ie the number of times a player who has possesion of the ball is double-teamed by defenders). Ever since reading about (and getting into) the Wins Produced model, I’ve been thinking about things it doesn’t account for that help to win basketball games (in the nicest possible way), and this one seems like it should matter. If 2 players have similar offensive stats, but one of them gets his while drawing a lot of double teams, he is obviously going to help his team by creating space on the floor. I’m guessing Melo does this quite a lot, and therefore this is something that probably should be taken into account in the comparison…

PS please share this with the other writers in the network if you think it would generate some discussion 🙂

arturogalletti

07/29/2010

Jim,

I think this is actually something that is built into the model. Let me explain. Teams that double scorers will double team the most obvious offensive threat on every team. So if Melo and Iggy both take the most shots on their teams( and they do) they would both logically draw the most defensive attention. So when we work out the Avg. ADJP48 by position for SG & SF (where the scorers who draw double teams play) which is the baseline for comparison against the mean and WP48 defensive attention should be included. I will concede that this may be unfair to players who take many shots to compare them to players who don’t (but Iggy and Melo are both primary scoring options). So a good exercise to answer your question would be to look at the ADJP48 of SG & SF who take more than a certain number of shots (primary scoring options) and calculate marginal value (i.e adjusted WP48 for scorers). Sounds like a future post.

Chicago Tim

07/29/2010

Could we put Kurt Thomas down for one year and $1.5 million with the Bulls? That’s the best estimate I’ve heard, and I’m despairing of getting an exact figure in the near future, since the Bulls don’t release that information and Kurt Thomas’s agent isn’t going to brag about it.

Any chance you could address my question on Wages of Wins Journal about whether we should consider a player’s position, and his standard deviation from the average player’s performance at that position, when evaluating his worth?

Guy

07/29/2010

Great stuff, Arturo. This shows a clear pattern of talent becoming more equal over time, as the overall talent level improves. That pattern also exists in other sports, but I’ve never seen it demonstrated for basketball. Could you create tables for 78-90 and 91-200 regular season as well, to make the change over time more clear?

arturogalletti

07/29/2010

Guy,

Sounds like a plan. Let me see when I can get it done.

Shawn Ryan

07/29/2010

Hey Arturo, you’re missing Kyle Lowry’s new contract.

Here’s the “Done Deals” spreadsheet row, delimited by commas CSV style (non integer numeric values to a precision of 8 decimal places):

Player,Current Team,A,S,Type,Avg Wins,Avg WP48 Adjusted to a min of 400 min,Projected Wins as a starter (at least 2460 MP),Avg Value,Value as Starter,Signed for/Offered,Years,Per Year,New Team,Net Value

Kyle Lowry,HOU,23,4,Restricted,5.30333333,0.14081362,7.21669796,9.06870000,12.34055351,24,4,6,Houston,3.06870000

arturogalletti

07/29/2010

Got it.

Guy

07/29/2010

Chicago Tim (and Arturo): Some have suggested evaluating players in terms of performance relative to others at their position, measured in standard deviations (SD), and Prof. Berri has done this on occasion. However, this would be an unnecessary step if you fixed a small but consequential error in the original position adjustment. As you know, the position adjustment is done by subtracting a constant value for each position. But a little algebra shows this creates inconsistencies within WP. Making the adjustment via multiplication instead would give you logically consistent player values, while also revealing that the spread of talent is about the same at every position.

WP is based on the Productivity metric, with regression-based values for each boxscore stat. Average Productivity varies dramatically by position, but the WOW authors believe that wins produced at each position must actually be equal. So they adjust each player by subtracting the position-average Productivity from his Productivity score. But this creates mathematical impossibilities.

Using rough numbers, average Productivity for all players is .30 and by position is: P-C/F = .39, P-SF = .30, P-G = .25. So, WP assumes that .39 P-CF = .25 P-G, which must mean that 1 P-CF = .64 P-G. That is, .64 units of measured productivity for guards produce as many wins as one full unit of center/forward productivity. However, WP also says that a .59 Center/Forward is equal in wins to a .45 Guard (both have WP48 of .300), which means 1 P-CF = .76 P-G. Clearly, one unit of C-PF cannot equal .64 P-G and also .76 P-G. By subtracting the position average, WP creates an inconsistency: it first says that each unit of measured productivity by a C/F is less valuable than a unit generated by a guard (hence the need to adjust). But it then treats these very same units of measured Productivity as having equal win value regardless of position. Both things cannot logically be true: either the productivity metric overvalues C/Fs relative to Gs, or it doesn’t.

The way to adjust consistently is to multiply rather than subtract. Simply multiply each player’s productivity by overall average player productivity divided by average position productivity, or .30/Position Average. Roughly, multiply big men’s productivity by about .77, and guards by 1.2. Then the rest of the WP48 calculation is exactly the same, comparing players to the average (about .30). This gives you a metric where each unit of position-adjusted productivity has the same meaning. You could call this Position Neutral Wins Produced, or PNWP.

Note that this does NOT reduce WP48 for big men by 23%! For example, a center with a .200 WP48 would have a PNWP of about .177 (a drop of about 11%).

One of the nice side benefits of fixing this error is that big men will no longer have a vastly larger variation in productivity. In WP48 the SD for big men is about .11, but for guards is just .07; in PNWP big men and guards both have a SD of about .09. So there is no longer a “mystery” to explain: the WP48 variation for big men is larger for the same reason their position average is larger, which is that the Productivity metric for some reason overvalues big men relative to small. If you adjust both things at the same time, then there is no need to evaluate players in terms of SDs — players’ WP48 can be compared directly, without worrying about position.

I imagine some people, accustomed to the current WP values, will be reluctant to change. But note that PNWP is entirely consistent with WP in that all positions are equal, and the total spread of productivity is the same. It simply applies the position adjustment in a more consistent manner.

Chicago Tim

07/29/2010

Guy — I’m not competent to critique your critique, but I sure hope someone who is competent does so.

Guy

07/29/2010

Chicago Tim: No specialized knowledge (beyond simple algebra) is needed to evaluate the two methods of adjusting for position. So I fear I haven’t explained it well. Short version: the Productivity metric that is the heart of WP says that Cs and Fs produce about 60% more wins, on average, than PGs and SGs. The WOW authors suggest this is not likely to be true, because teams need both types of players, so they force all positions to be equal in win value. However, they continue to use the non-position-adjusted Productivity metric to determine how far a player is above or below average. Since that metric inflates the value of C/Fs (if it didn’t do that, you wouldn’t need a position adjustment in the first place), you get the predictable result: far more big men get very high (and very low) WP48 values.

For example, in 2010 just 20% of the “star” players (WP48 of .20 or higher) were Gs or PGs, while 40% were centers. So centers are FOUR TIMES as likely as guards to be a star under WP48. Using the position adjustment I suggest, you won’t get this kind of huge position disparity.

Chicago Tim

07/29/2010

Guy — Very interesting, and clear.

It’s not the technical knowledge I lack (I suppose, although it’s been a long time since I’ve regularly used algebra), it’s knowledge of the facts you cite. I could pull out my copy of Prof. Berri’s books and research it, but I’m hoping that someone authoritative will cooborate what you are saying without necessitating further research by me. In short: I’m lazy, and my eyes glaze over when I see math. 😉

But if I don’t get an answer, maybe I will pull out the books and look it up.

BPS

07/29/2010

The positional adjustment is correct. Standard deviations above the mean and value above the mean are not measuring the same thing – and, crucially, the value of a standard deviation is not equal amongst the positions. A standard deviation of C is worth more than a standard deviation of G – because it’s worth more production, in real terms.

Normalizing multiplicatively to get standard deviations, instead of raw deviation, is good for evaluating how rare a talent a given player is. But you’re no longer predicting wins; you’d need to multiply the positional adjustment back in to get it. So while it’s still potentially an interesting metric, it’s not going to be predicting wins – and the regressions will show that.

You’re right that, for instance, a 2 sigma C has a higher adjusted WP48 than a 3 sigma G. But that’s a feature, not a bug.

Guy

07/29/2010

BPS: You say “A standard deviation of C is worth more than a standard deviation of G – because it’s worth more production, in real terms.” But then you are arguing that the Productivity metric really does measure win contributions accurately for players regardless of position. And if that is true, then it must be wrong to apply a position adjustment in the first place — big men really are much more valuable. That is a coherent position (though I think few would accept it), as is my suggested approach. The current WP construct is not coherent: it can’t be true both that .25 Productivity from a guard is worth as much as .39 Productivity from a center, AND also that additional productivity has the same value regardless of position. It’s logically impossible.

The only way this could logically be true would be if there were some large amount of win value (generated only by guards) that isn’t captured at all by the WP variables. But that logically can’t be true, since since WP explains 95% of wins. So the real win value of “P” must vary by position.

arturogalletti

07/29/2010

Guy,

Big men are more productive and more valuable.

All centers produce more than Point Guards but only the productivity differential matters to generating wins.

However, there’s much more risk associated with center/pf so the criticality of filling the position with a replacement level player is much greater than in any other place. If you applied Reliability Management techniques in the NBA, you would play it safe with big men and take your risks everywhere else cause your margin for error is greater.

Center are high risk/high reward pieces (see Greg Oden) and are thus more important to success on the average.

See my next post though for the full response.

Guy

07/29/2010

Arturo: As you obviously know, the proposition that “big men are more productive” directly contradicts the WP metric. So is your position that the position adjustment is an error, and that Productivity (without the position adjustment) is the true measure of a player’s win contribution? It seems to me that would have to follow from your position.

arturogalletti

07/29/2010

Guy,

They’re really not mutually exclusive.If NBA players are like films, then big men are like tentpole movies. Studios (Teams) have to have them. Sure They make more money (their productivity) but they cost a lot more to make (opponent’s productivity). And at the end of the day success and profit (wins) is measured by the net not the gross. We still must have animated flicks that score big (let’s say sf) and the chick flicks (SG-hello Kobe) and rom coms (PG) because the audience demands variety to make a profit (win).

Guy

07/30/2010

I don’t think I quite follow, Arturo. Let’s define “productive” as generating wins for the team (as Dr. Berri does), so we can be sure we are talking about the same thing. Do you think big men produce more wins for their team than small men, as AdjP48 implies? Or do you think they are equally productive, as WP48 indicates?

arturogalletti

07/30/2010

Guy,

The Film Analogy is the best one.

The Player’s ADJP48 is gross box office receipts

The Opposing Player’s ADJP48 is the films budget

Wins Produced is the difference between the two

Big men are big budget films . They certainly and demostrably are more productive overall but more of their production is offset by the opposing teams big man. So the treshold for generating value (wins) is higher for a big man that a Guard.

All things being equal the simple answer is that a .100 WP48 Center and a .100 WP48 PG will generate the same amount of wins for a team.

However, practically I would attach more value to the big man since he can probably play at least one more position at a higher win rate. So if I have 2 .100 WP48 Centers I can probably play one at PF (where his WP48 goes up to about .150 WP48 when I do the position adjust or about 2.5 additional wins at 2400 minutes). If I have 2 .100 WP48 PG and I slide one to SG? His WP48 stays about the same and I dont get that multiplier. So all things being equal Big men are better hence the short supply of tall people.

BPS

07/30/2010

The core of the issue is ‘what is the right way to break up the zero point?’

When you add up the production of an average team without re-zeroing, you get 129 wins. But you know that the average team wins 41 games, by definition, so you have to subtract out 88 games to get the proper zero point, team-wise. Similarly, if you don’t re-zero the team WP48, you get 1.573, but by definition you know it’s 0.500, so you have to subtract out the difference.

Now in order to assign value to the different players, we need to, in this case, break down the 1.073 WP48 that is subtracted to re-zero the function between the players.

In the traditional WP48 model, this is broken down as a position adjustment, so that the average player at each position has a WP48 of 0.100; this makes it easiest to understand at a glance, since every player’s score is being compared to the same positional average. It’s not quite the basketball equivalent of value over replacement player, instead being value compared to average player. This basis makes it very easy to see who is under or over performing at their position, which is what you want for analyzing team strengths.

But a key insight is that it doesn’t actually matter how you break up the adjustment between players for the purposes of calculating total wins. Each team is always going to have the same positions, so the sum of the adjustment is always going to be the same, no matter how you break it down. So you’re free to pick any basis you want, as long as the sum is the same you’ll get the same team wins.

This is problematic when it comes to assigning wins, and by extension contract value, to individual players. An average player across all positions who plays, say, 30 minutes a game produces about 5 wins, and would be worth about 8.5 million dollars a year to a team. Under the positional adjustment used with WP48, we treat this as equivalent across all positions. But the individual positional adjustments are arbitrary, only their sum is fixed. Since the average center puts up 1.75x the stats of the average 2-guard, why isn’t the average center thus worth 10.8 million, and the 2-guard 6.2 million?

Either basis would make the exact same prediction about team wins.

So I think there is a very good question buried in here. The standard WP48 positional adjustment certainly is convenient to work with, but there isn’t anything in the model that forces it to be the way it is. Is the choice of basis truly arbitrary, and thus is makes sense to use whatever is convenient? I can only conclude the answer is no.

arturogalletti

07/30/2010

BPS,

Your point:

“But a key insight is that it doesn’t actually matter how you break up the adjustment between players for the purposes of calculating total wins. Each team is always going to have the same positions, so the sum of the adjustment is always going to be the same, no matter how you break it down. So you’re free to pick any basis you want, as long as the sum is the same you’ll get the same team wins.”

Is the one that people most often miss.

The value question comes down to the fact that different skill sets are required at each position so player value has to be assigned based marginal value at their position (much like you would in a fantasy auction draft). But your exact opinion of value does not have to be static. As I said earlier, all things being equal a .100 WP48 Canter is more valuable to me than a .100 PG because of scarcity, criticality (the amount of risk involved in the position) and flexibility. So in a mock player draft of all NBA player I would use tall as my tie breaker.

BPS

07/30/2010

I agree entirely that player value needs to be assigned based upon marginal value at each position; however the zero points are arbitrary. Within the same position, it doesn’t matter what zero point you use. An extra win is an extra win, and that extra win has a value. But when assigning value across positions, your zero point does matter.

The standard method normalizes around league average players, but league average players are scarce talents. You can’t just go out and get average players. If it’s harder to find an average center than an average guard, why isn’t the average center worth more?

Look at the way the zero point is currently calculated for a given position. You figure out the average for a position, and assign that the value of 0.100. Then you work backwards down the regression line to find the 0 point. But why is that no value point? Pulling numbers out of thin air, imagine I can go to the D-league and pull a half dozen 2-guards from there who can give me 0.050 WP48, but the best center I can find only gives me -0.050 WP48. Why would we say that the former, utterly replacable 0.050 2-guard is worth a 4 million contract, while the -0.050 center isn’t worth signing?

If that is the alternative, why isn’t the 0.000 WP48 center, who will win you ~2.5 more games than a D-league center, also not worth signing under the model?

arturogalletti

07/30/2010

BPS,

I love your comments. the .100 is meant to be a reflection of the break even point for wins and is really a construct to make our zero point for WP48 reflect zero wins and make the number friendlier. If you ignore that and do the following:

Marginal Wins Produced (MWP) = (ADJP48 Team -ADJP48 Opponent) *Minutes

We’ll get a number that would represent the delta from 41 wins or .500 ball. So a Team with 10 MWP would be expected to win 51 games.

For the Player we would calculate

MWP48= (ADJP48 Player -ADJP48 Avg.Opponent)

and above zero values would be marginal wins and below would be marginal loses.

The zero value for the number is the mean and the mean represents 41 wins.

Now, the value of an asset will vary depending on the buyer. If your assigning 1000 minutes to eddie curry a -.050 WP48 will improve our team. But in general, WP48 will provide you a good guide for value (I do value bigs higher as I explained before). But there would probably be more than one good strategy to construct a successful team.

BPS

07/30/2010

Reducing everything to MWP48 is a fine metric and, on a team level, gives you exactly the same predictions as the standard model. It’s another perspective of the same thing that has its own advantages.

When you look at MWP48 instead of WP48, though, the relationship between that stat and how big a contract you should bid with for that player gets blurry. Your 30 minute, .100 WP48 player gets credit for ~5 wins, and through an easy model that’s 8.5 million; but under MWP48 he’s worth 0 marginal wins. What’s that worth?

I can’t argue with the metric for predicting team wins, the correlation coefficients are unreal. But there isn’t anything in the regression that gives you a preferred basis for assigning wins between positions. Since that breakdown implies salary, I think it needs a closer look.

Guy

07/30/2010

“I can’t argue with the metric for predicting team wins, the correlation coefficients are unreal. But there isn’t anything in the regression that gives you a preferred basis for assigning wins between positions.”

That’s kind of like saying, “other than that, Mrs. Lincoln, how did you like the show?” I mean, predicting team wins is easy. You can create DWP (Dumb Wins Produced) = PTS48 – PTS48(Opp)/5, and that will predict team wins with a .95 R^2 just like WP. Don’t even worry about those controversial coefficients for rebounds and assists! But that hardly makes it a good way to measure individual players’ productivity, right?

The $64K question is dividing credit among the players. And BPS is saying that the regressions don’t really answer that question. The WOW authors decided to set all positions = .1. But they could have set Guards = .11, SF = .1, and C/F = .09. Or anything else that averages .10 and satisfied their intuition.

arturogalletti

07/30/2010

BPS,

I agree. The reality is that it really would depend on your strategy and priorities in building your team. Value is up to the buyer. The linear assumption is a good one and would lead to success. I, as a gm, would go the Lakers route and stock up on bigs (Gasol,Bynum,Odom) since it gives me huge advantages at the riskiest positions (C,PF,SF). Teams that get productivity out of multiple bigs as a general rule succeed. You could go out and get value from guards but by not covering C you leave yourself extremely vulnerable.

Guy

07/30/2010

“But the individual positional adjustments are arbitrary, only their sum is fixed.”

BPS, I think we are in agreement. You are of course right that one has to reconcile marginal wins with real wins, since players generate about 3x as many marginal wins. But that does not require a position adjustment. WP could just ignore position and subtract the average AdjP48 from all players. The decision to add a position adjustment is separate, and based on the idea that “positions can’t be this unequal,” not on any specific scientific basis. I think the intuition of Dr. Berri, et. al. is correct in this case: the position disparities in Productivity (AdjP48) are implausibly large, and an adjustment is needed.

The unresolved question “buried” in WP is how can it be simultaneously true that Productivity perfectly allocates wins among players, AND also that all positions are equal despite hugely different measures of productivity? Both things can’t be true.

So in making the position adjustment you have to decide which is more important: getting the highest possible correlation with team wins (which the current method preserves, as you correctly note), or getting the best possible measure of individual player contributions. If you want the latter, then you should do as much as you can to correct for the metric’s inherent overvaluing of the big men. Since it’s a player metric — we hardly need WP to measure team differential — I think the latter is clearly the higher priority. The player adjustment I suggest would do more to correct the big man bias in the metric that must exist, if one believes in a position adjustment.

Basically, one can reasonably believe that the productivity metric is correct and big men are much more valuable — in which case you should remove the position adjustment. Or you can reasonably believe positions are equally valuable, in which case WP needs a different adjustment (and the higher SDs for big men are just a function of Productivity inflating big men’s value). But the current WP, with its jerry-rigged position adjustment, tries to have it both ways. It says productivity is inaccurate for determining the average contribution at each position, but then accurate for comparing players to that position average. Mathematically, this just can’t be true.

arturogalletti

07/30/2010

Guy,

I think we’re really just going to have to disagree on this. Sadly no one is going to give us NBA teams to test our differing model out (wouldn’t that be something though, I got dibs on the Warriors, love the unis and SF). 🙂

Guy

07/30/2010

Arturo: agreeing to disagree is a perfectly good resolution. (Though I admit I’m still a bit unclear on whether you believe big men really are, or are not, much more productive.)

I hope you’ll find time to add those tables for 1978-1990 and 1991-2000. I think they will tell an important story of the game’s evolution.

arturogalletti

07/30/2010

Oh definitely.

BPS

07/30/2010

The positional adjustment / method you’re suggesting (finding equivalent standard deviations above or below average) doesn’t regress onto wins; it doesn’t regress onto anything as far as I can tell.

You can add or subtract positional adjustments from each position and still maintain wins (the regression is to marginal wins, which is finding the gradient of the win function with respect to different variables, so you can add or subtract any constant you want without changing that gradient). But if you multiply or divide, you warp the function.

If you really wanted to you can make that change, and build a model around it. But it does involve making an entirely new model with new regressions. You can’t just make that one tweak without breaking the instrument.

Guy

07/30/2010

BPS: I didn’t say anything about using SDs. Just normalize AdjP48 by multiplying by League P48 / Position Average P48. As it happens, if you do that it turns out the SD for every position will be similar (but it didn’t have to turn out that way). You are correct that this will predict team wins less well, though I suspect the difference is marginal. But it will produce MUCH more accurate player ratings, assuming you agree with Berri et. al. that all positions deliver equal productivity.

I agree my fix isn’t perfect. But you haven’t addressed my main point: how can AdjP48 be wrong for the purpose of measuring the average production at each position, and yet right when calculating marginal wins? It’s logically impossible for both things to be true, don’t you agree?

BPS

07/30/2010

From what I understand, your main point is something like, 3 / 2 = 1.5, but (3+1) / (2+1) = 1.3-, and 1.5 != 1.3-, therefore inconsistency.

I understand what division signifies, but I do not understand why you think that ratio should behave a particular way. So I cannot address your main point because I cannot make any sense of it.

Guy

07/30/2010

Almost. It’s more like WP says 3*A = 2*B, but also that (3+1)*A = (2+1*B). Which would have to mean 8=9.

My point is this: WP begins by measuring marginal productivity with Win Score/AdjP48. But when it turns out the average C is .431 and average PG is .247, WP says these players have equal value. Every unit of AdjP48 clearly isn’t equal, and it’s true win value is position-dependent. So .431 C-AdjP48 = .247 PG-AdjP48, but WP also says that .531 C-AdjP48 = .347 PG-AdjP48. Both of these expressions cannot be true. (Alternatively, if AdjP48 had the same true win value at all times and for all players, then there should be no position adjustment.)

Putting it into English, if true productivity is equal at every position, then by definition the AdjP48/Win Score metric must overstate the productivity of big men and understate the productivity of guards. And if that’s true, why wouldn’t it continue to do that when used to measure marginal wins above/below average?

BPS

07/30/2010

It is not clear to me that the latter follows from the former.

Guy

07/30/2010

I’m not sure how the latter cannot follow. .431X=.247X is impossible. So a point of AdjP48(center) is not as productive as a point of AdjP48(guard). Or look at it this way: a .400 center is equal to another .400 center, but he is much less productive than a .400 guard. How can .400 = .400 =!.400? I think that can only be true if the the value of AdjP48 varies by position.

But maybe I’m missing something. Can you suggest a theory or scenario in which AdjP48 has a constant value at all positions, and yet the average productivity at all positions is equal?

BPS

07/30/2010

The marginal value of production at each position is the same, or very close to the same (that would be a curious experiment actually). But clearly the absolute value of production at each position is not the same, since some positions are naturally more productive than others. The confusion lies with trying to apply assumptions for marginal values to absolute values, and seeing that it melts down.

I don’t think of the 0.100 normalization over position as being a shift in valuation of absolute production. It’s a measure of the average marginal value of production. As in, you don’t value what the total production is, you value production above replacement, or above average, or some other metric that ultimately looks at marginal value. You pay for the effect of that marginal production on wins. The absolute baseline isn’t particularly useful.

I’m thinking of baseball in particular when I say that, where the spread between the best and worst players is tiny compared to the baseline productivity. It’s all in the margins.

arturogalletti

07/31/2010

I endorse this comment 🙂

BPS

07/30/2010

Well I for one actually believe the positions are that unequal. The center position is actually that much more productive and valuable than the wing players.

The caveats are that:

1) A certain amount of that productivity is a function of the position itself. Hanging out close to the basket to scoop up high percentage shots and easy rebounds gives you high productivity.

2) There are exclusion principles and/or diminishing returns that keep you from just putting the 5 biggest guys you can find under the basket. They start to step on each other, and instead you have to start adding complimentary players.

This is to say that each additional player you put on the court has diminishing returns, as each one is pushed into increasingly marginal space around the more key pieces.

What the positional adjustment is acknowedging is that there are baseline production differences in the positions themselves; basketball is very much a game of picking low hanging fruit, and the players picking that will dominate the numbers. That doesn’t make the marginal production of the different positions any more or less valuable, however; I don’t care if I’m a bit better at getting low hanging fruit than the other guy and pull ahead there, or if I have superstars cleaning up at the margins. I just care about totals, and my baseline is what’s available cheaply.

Guy

07/31/2010

Arturo/BPS: I think I understand your position. You two are in agreement that A) AdjP48 does measure players’ marginal productivity accurately, and does so at all positions, and B) there is a wider spread of productivity at C/F than at the wing positions. (If one believes A, B must be true.) However, this must also mean that average productivity is not the same at every position. If the difference between the best and worst centers is larger, and the worst players at all positions contribute zero (be definition), then the average center must be more productive. (The only alternative is to say the worst guards are somehow more valuable than the worse centers, which as PBS suggests above makes no sense.)

But in that case, WP is wrong to force all positions to have equal value. It needs to set a zero value (or “replacement level”) to compare players to. For example, you might decide to set that at -1 SD at each position. That would make centers (SD .11) about .04 WP48 more productive than guards (SD .07). Then your productivity metric would have a direct connection to value/salary. Right?

All of this assumes that AdjP48 correctly measures marginal productivity, which of course is a controversial proposition. But with that sssumption, everything will add up if you compare players to a replacement baseline rather than the mean.