APBRmetrics

Win Shares underrate stars. Think about it APM and PythagWL wise...

The top 6-year rAPM guys are around +8/+9, and that's with a lambda still pushing those numbers somewhat to zero. Ilardi/Barzilai's 4-year APM with standard errors around 1 had the top guys slightly higher. Let's ballpark it at +9, for an estimate of an elite elite player's impact on the game per 100 poss.

On average, NBA teams played 3967 minutes this year, scored 8163pts, allowed 8163pts (for a pace of 92.1), and won 41 games. A star who is healthy all season will play around 3000 minutes, or 5756 possessions.

Figure also that, if a star were to be injured preseason and his minutes had to be replaced, he'd be replaced with 6th-7th man caliber players in a typical situation, with other teammates adding to their minute totals. Let's ballpark the replacement minutes at -1 per 100 poss, for a +10 difference overall.

Over 5756 possessions, the +10 difference per 100 amounts a 575 point gain over opponents. Let's assume the star has a typical offense/defense breakdown among stars, say +7/+3, meaning the star is adding 403pts to the offense and improving the defense by 172pts as well. Plug that into the pythagorean wins/losses formula, and a team scoring 8566pts and giving up 7991pts is expected to finish 60-22, for a WS total of +19.

Note that this APM method of calculating wins starts with a 41 win baseline, while regular Win Shares starts with a 0 win baseline, and as a result gives positive win totals to almost every NBA player. Figure an average (+0) player playing 3000 minutes would earn (3000/(3967*5)*42=6.3 wins, and I'm going to guess that a -1 player at 3000 minutes will earn around +5 wins in that system.

Add that +5 to the +19 from earlier, and via the Win Shares 0 win baseline, elite NBA players should be getting credit for around +24 wins. And that seems plausible to me, especially when I look at the Cavs rosters without LeBron vs their win total, or the Wolves rosters without Garnett vs their win total, or even last year's Heat without Wade vs their win total. (Even Hollinger estimated around +24 for elite players in his wins added column.) But in the actual Win Shares stat LeBron had the NBA's highest total this year at just +15.6, with the elite grouping of players around +14.

There's also problems with Win Shares in that, compared to APM numbers, they grossly overrate rebounders and underrate elite passers (Al Jefferson having almost identical win shares compared to Steve Nash this year is a joke), and it can't see stuff like who spreads the floor well or moves off the ball well or defends the post well, or how a player is getting his points within his offense. As a result, I think Win Shares is mostly bunk. Rant done.

Scaled to the 2800 minutes that Wade played last year, here were the 2010 Win Shares for the players you mentioned that the Heat lost, along with Wade:

Wade: 13.1 WS
Haslem: 7.7
Jermaine: 7.9
Beasley: 5.5
Wright: 8.0

That's just bad. Wade should've been up around 20-22, and each of his teammates should've had a bit knocked off theirs.

Also, Haslem+Jermaine+Beasley+Wright combined for 8000 minutes last year compared to 2800 for Bosh this year. So it's not as easy as just counting up their win shares, counting up Bosh's, and saying theirs was more. You have to also account for the WS total of the remaining 5200 minutes.

My guess is, with Bosh being a +5/+6 APM player over his career, he accounted for more wins last season on the Raptors than Haslem+Jermaine+Beasley+Wright combined. On this weird 2011 Heat team where some of his impact is diluted, it could be close, I don't know. But unless Bosh is stripping mass amounts of impact away from Wade's/James' games, I don't see a plausible argument that Bosh made less of an impact than those four schlubs combined, especially with how bad Beasley was in 2300 minutes.

YaoPau wrote:... Haslem+Jermaine+Beasley+Wright combined for 8000 minutes last year compared to 2800 for Bosh this year. So it's not as easy as just counting up their win shares, counting up Bosh's, and saying theirs was more. You have to also account for the WS total of the remaining 5200 minutes.

I agree, and that's why I mentioned the 8000 minutes. Who is going to play those other 5200? You can't just fabricate average NBA production out of nothing.

The Heat have 3 above-average players and nobody else even close. They don't have average 6th-7th men. Chalmers, House, Miller, Bibby? These are 9th-12th men on an average team.

They may be the closest thing ever (in the real world) to the hypothetical question: What would 3 all-NBA players and a bunch of replacement-level players do? Opponents can only double-team 2 of them, and 1-2 guys are always open.

I think Jones and Chalmers were average to above average players given their role. Their APM numbers look good, both guys helped keep the floor spread with the 3pt shot, both have rated out as average+ defenders. Eddie House played fine in 1000 minutes, so did Bibby in 500 minutes.

The point about the remaining 5200 minutes though is that Win Shares almost never gives 0 wins out to players on a decent team. For example, Dampier/Arroyo/Ilgauskas/Miller/JoelAnthony all stunk this year, but they still combined for 5256 minutes and 11.3 win shares. So to respond to your point:

Mike G wrote:Beasley, Haslem, O'Neal, and Wright are credited with 20.5 WS for 2010, Bosh with 10.3 this year. That tradeoff suggests 4 to 8 fewer wins, taken alone.
LeBron with 15.6 WS this year. Seems to add up, intuitively and otherwise.

Wade remained healthy this year, had career highs in OReb, DReb, eFG%; near bests in TS%, Blk, TO, ORtg, DRtg.
They lost four players totaling 8000 minutes in 2010. Without LeBron, this team is a mess.

Beasley+Haslem+Jermaine+Wright = 20.5 WS in 2010 in 7992 min
Bosh+Dampier+Arroyo+Ilgauskas+Miller+JoelAnthony = 21.6 WS in 2011 in 8051 min

YaoPau, in response to your recent observations and analysis, I would say that RAPM for "stars" is giving them a good deal of the credit for the positive value delivered by teammates when on the court with them whereas WinShares and other box-score based metrics will give all the credit for teammate actions to them alone.

Further WinShares will give credit for good or great team shot defense to everyone based on minutes played rather than actual impact on team shot defense that RAPM will at least try to distribute fairly based on the play by play data.

The Heat were 2nd and 3rd best on team shot defense these last 2 seasons. That gets recognized by both WinShares and RAPM but the allocations are probably different or at least can be. Which approach to shot defense credit is better, Win Shares or RAPM? Or neither exactly right and average them or leave it open for further interpretation?

How much of the Heat support casts' wins are from defense? I would think a lot of it, though some is also their offensive contributions, probably especially when playing with the stars.

It would seem appropriate to at least look at the offensive value created by non-Stars when not on the court with stars (though this will no tbe that often) to help gauge how much credit they deserve alone for their offense and how much credit should be shared with the stars.

How could a 6-year rAPM rating, with standard errors presumably below 1, be considered a less accurate metric than one based purely off minutes and box score numbers? I ask because I've never heard that reasoning before.

This stems from a bigger issue: what % of a player's value is found in box score numbers? Based on everything I've looked at, I'd guess maybe 50-60%. Then again, that comes from comparing box score numbers to low-error APM values, and getting r^2 values in that range. Factor in that Win Share coefficients aren't statisical APMs, and therefore have relative biases, and to me that explains why we see absolutely crazy results like equating Jefferson and Nash, despite that not passing the eye test and being maybe 8 standard errors away from what rAPM would deem plausible. Utah was -3.1 net per 100 poss with Jefferson on the court this year compared to +4.7 for Nash, despite them both being starters on 39-40 win teams. How is Jefferson 33rd in the NBA in win shares when his team was positive without him, negative with him, and he played the biggest chunk of his minutes alongside Deron, Kirilenko, and Millsap?

Crow wrote:Further WinShares will give credit for good or great team shot defense to everyone based on minutes played rather than actual impact on team shot defense that RAPM will at least try to distribute fairly based on the play by play data. The Heat were 2nd and 3rd best on team shot defense these last 2 seasons. That gets recognized by both WinShares and RAPM but the allocations are probably different or at least can be. Which approach to shot defense credit is better, Win Shares or RAPM? Or neither exactly right and average them or leave it open for further interpretation?

Why is distributing defensive credit based on minutes played a legitimate method compared to a regression?

Obviously, rAPM needs context. A +3 for a defensive specialist is different than a +3 for a starter. A +1 for James Jones on the Heat doesn't mean he's a +1 on the Wizards. Even error rates of less than 1 can make things hard to interpret. And so maybe if an APM number seems off you look at PER, or Synergy stats, or Win Shares, or player pair +/- info to gain more information, and maybe you conclude that the player's true value is a standard error or two different from what APM is saying. If your view of Win Shares is that it's a decent ballpark index for a player's offensive or defensive value, and so it's worth weighing in slightly to smooth out rough edges in rAPM, I can get behind that. If you're starting with win shares though, or averaging them equally, I don't understand the logic.

I agree with YaoPau on this one. RAPM does NOT "give 'stars' a good deal of the credit for the positive value delivered by teammates". Quite the contrary; the ridge regression effect will hurt the stars. In addition, I would say box score stats capture ~75% of the offensive value and maybe 35% of defensive value. Because of this fact, box-score metrics must necessarily rely on team adjustments to get in the right ballpark, particularly for defense.

I think YaoPau's estimate of a +10 value over replacement level for a top player is pretty close. In fact, I think I agree with YaoPau on just about every point made here... Once sample size is big enough, and collinearity damped, RAPM is certainly the most accurate way to go. The issue thus far (one I'm working on figuring out) is how to get "instantaneous" measurements from RAPM, when you must necessarily use several years' worth of data. In other words--how good is KG RIGHT NOW?

"How could a 6-year rAPM rating, with standard errors presumably below 1, be considered a less accurate metric than one based purely off minutes and box score numbers? I ask because I've never heard that reasoning before."

I assume this is an open question / statement. I hope and assume it is not a projection onto what I said.


"Why is distributing defensive credit based on minutes played a legitimate method compared to a regression?"

I didn't say I fully supported it or supported it period. It is a simplifying assumption with a certain logic to it but it is worth evaluation and comparison with other models. Hence I spoke with more of an open question than a statement or final opinion even if I have something of a view so far and not that strongly for the equal defensive credit choice I might add and maybe more against it though I am open to refine the degree for or against.



"I agree with YaoPau on this one. RAPM does NOT "give 'stars' a good deal of the credit for the positive value delivered by teammates". Quite the contrary; the ridge regression effect will hurt the stars."

I accept the second statement in this taken on its own; but not the first statement, if taken generally. It is a 2-step process in my view, that would be giving stars part of the credit for increase value from others when on the court with them by the simple regression itself but takes part of it away thru the addition of the regularization to address the possibility the data analysis produce over-fit, over-stretched values or to fit with current wisdom about the proper range of relative values or whatever.

Maybe I am having a dense moment but how can you reconcile the different values of stars under RAPM and Win Shares without giving 'stars' a good deal of the credit for the positive value delivered by teammates? Isn't there an even bigger gap between traditional APM and WinShares?

And what specifically did YaoPau say on this point that you agree with? I am not seeing these statements / responses spelled out clearly or following their logic or leaps. But maybe it is me. Regardless a more detailed explanation would be appreciated.

If you agree that WinShares undervalues stars, based on what RAPM finds, then RAPM is finding more value than WinShares finds for Stars and, I guess (now), that can either be for what I suggested or alternatively it would have to be for the RAPM scoring of what a Star does thru the boxscore that finds even more value than what boxscore metrics find. I guess it could be some of both and probably is, but I don't think it is exclusively the latter with none of the former in all cases as I read your statement suggesting.

And what are the things that Stars do directly and individually that RAPM is giving Stars more credit for than WinShares and that Stars are doing more heavily than and in sharp distinction to non-Stars? If it was direct boxscore actions that RAPM has valuing more implicitly than WinShares and only that wouldn't the Star and non-Stars groups overlap much more and not explain as much of the gap between them given that there is a good deal of overlap between the two groups at the discrete stat level?

Is offensive usage a or the main area where they differ? And beyond offensive usage, are RAPM defensive stars, stars on RAPM often in large measure because of high defensive "usage"? How much can teams affect defensive "usage" up or down by scheme and which teams are effectively doing this, consciously?



I'll also note the observation by Jerry (J.E.) that good offense contributes to good defense and vice versa. For star contributions, then it might not just be individual offensive impact to team offense and individual defensive impact to team defense but also the crosses of offensive and defensive impacts on the other.


Another question would be how much of a star's RAPM value is a zero-sum taking from the opportunities for (shots & assists and maybe more and often the first and / or best opportunities for these) and RAPM scores of the supporting cast? How much of a RAPM value above neutral is really net team gain vs opponents and how much is just allocation of player credit among teammates? A team with high continuity except for the addition of a RAPM "Star" (probably be free agency or draft) would be a good thing to look for and at.

If a +10 RAPM star were truly individually and worth 24 wins at least usually on different teams, then they could essentially turn any intact .500 team from last season or an otherwise .500 support team assembled around them into the leading team in the league most years and I am not so sure about that happening fully. I think there can be some level of diminishing returns to a Star RAPM addition to a new context.

The Miami experience is not a totally simple case, but it seems to suggest possible and fairly significant diminishing RAPM returns in a new context, at least this one with 3 Stars. Maybe a certain part of RAPM of Stars is from the "Star" role, activities or opportunity levels. Perhaps it is not that easy to fully credit 2 or more likely 3 Stars when together as much as they might get credit when alone and get more of the opportunities to gain the Star portion of RAPM credit alone.


In the history of the league only 7 teams have had an average margin of victory of more than 10 points per game. If the very top players can actually reach +10 RAPM and they play 36+ minutes or .75 of the minutes = +7.5 team impact then they are usually playing on teams where everybody else almost always (except these 7 cases) sum to +2.5 or less and would win little above .500 without them? Do we fully believe that for all teams with a top RAPM player?

How to explain the 93-94 Bulls winning 2 less games without MJ then the year before with MJ? Was the addition of Kukoc and the other changes in players enough to explain things fully? Or did the opportunities and win credit move a lot from Jordan to other returning players? Yes the Margin of Victory changed more than the wins and the 93-94 team overachieved expected wins by 5 but isn't it wins that we are most interested in? Do these factors explain nearly all of it or maybe only about half of it with the reallocation of opportunities and credit among teammates explaining about the other half of it? I am not sure there is one universal answer. I do think that a heavier allocation of credit opportunities per minute and credit to Stars could perhaps explain up to half of it or probably at least a quarter of their rating and the with / without comparison.)

I don't really have time to answer in full, Crow, but I want to make it clear that I don't necessarily agree with the translation from points/eff.dif./plus-minus to wins. That translation has diminishing returns by the very nature of the Pythagorean equation, so I prefer to measure everything in terms of points if possible, since that's the currency at the individual level.

That's one hell of a meaty response, Crow I want to get into it more later, but some initial thoughts...

Interesting way you're looking at rAPM. But yeah, the answer is of course that stars improve their teammates' performance. I think the effect shows up more blatantly in football. Put Randy Moss on the Patriots, and it makes defenses cover him with their best cornerback, leave a safety deep, and have a linebacker shade him if he comes near the middle. Suddenly Wes Welker is open to catch a million passes. Win Shares would call Wes Welker a superduperstar, when in reality Moss deserves a lot of that credit.

The equivalents in basketball: Steve Nash being a PnR god because of his passing ability and shooting threat (Suns finished 2nd in the NBA at 1.19 PPP on PnR's despite not having a notable PnR big man. Win Shares give Nash some credit, but it's mostly him imo). Rose/Wade/LeBron's threat to penetrate and ability to pass, forcing defenses to pack the lane and leaving them susceptible to the drive and kick (and if that leads to an additional pass for an open 3, Rose/Wade/LeBron get zero credit on Win Shares despite their making that play happen. Also, because they're such great scoring threats, sometimes they attract doubleteams leaving a 4on3 situation, and also their opponents can't leave them to play help defense.

Of course, none of this is proven fact without, as you said, data that shows teammates do better when on the floor with stars. I emailed Aaron Barzilai a few months back to see if he could get that info, and he probably just laughed at that massive request, but I think it's important, at the very least interesting info and would be fairly easy to scrape for somebody who knows slightly more programming than I do.

DSMok1: "I prefer to measure everything in terms of points if possible, since that's the currency at the individual level."

I think it is at least better to know both points and wins than just wins. Converting points to wins is probably right as a last step and it probably should be seen in team context or perhaps even converted with recognition of differing context.


YaoPau:

Maybe Evan Z. can help you and us with the with / without data from a play by play perspective for boxscore stats (and shot defense impact) if Aaron has not gotten to and doesn't get to that request for assist.

Wayne Winston has also occasionally helped with releases of APM for players with / without other players on the court. Perhaps Jerry (J.E.) can help us further with that.



On varying defensive usage, it does not necessarily conflict with a choice to give equal credit to all for shot defense on principle but varying defensive usage could be part of the variation that defensive RAPM shows along with the quality of the 1 on 1 defense and team help defense.

Crow wrote: Maybe Evan Z. can help you and us with the with / without data from a play by play perspective for boxscore stats (and shot defense impact) if Aaron has not gotten to and doesn't get to that request for assist.

Thanks, for volunteering me!

Seriously, though, I am interested in this. I would propose to look first at teams with one "legitimate" "star" (I felt like I had to quote both terms), otherwise, the sample size will probably be very small. If a team has 2-3 stars (BOS, LAL, MIA), one or more stars are almost always on the court, except for garbage time. Teams that I would propose fit in the one-star category:

Minnesota (Love)
Orlando (Howard)
Clippers (Griffin)
New Orleans (Paul)
Chicago (Rose)

Though, maybe a more systematic way to go about doing this is to look at the impact of each position. How do the teammates perform when their starting PG/SG/SF/etc is off the floor? I would hypothesize that - on average - PG has the greatest effect on offense, while C has the greatest effect on defense.

DSMok1 wrote:... In fact, I think I agree with YaoPau on just about every point made here...

Also with this from earlier?

... LeBron's regular season performance didn't change that much, especially when compared to how Rose's regular season performance helped the Bulls. ..
last year, ... Beasley and Haslem might have been net negatives.

And we've discussed this before, but I'll inquire once again about:

I don't necessarily agree with the translation from points/eff.dif./plus-minus to wins. That translation has diminishing returns by the very nature of the Pythagorean equation, so I prefer to measure everything in terms of points if possible, since that's the currency at the individual level.

What if there could be an individual currency of Winlike entities that is not distorted by the ~14th power? What if there were a fairly simple conversion to some kind of equivalent wins, independent of team success?

I'd be curious to see what others can do with this concept. Pythagorean equivalent wins is based on the entirely arbitrary 48-minute (or 90-ish possessions) NBA game. Sometimes with extra chunks of 5 minutes.

The Bulls have scored 51.2% of the points in their 5 games vs Atl, yet they hold 2/3 of the Pythagorean wins. If a wins-allotment system says Chi players have had twice as much contribution (toward winning) as Atl players, that is intuitively disturbing to some of us.

Others might be more bothered by supposing that Game 4 in Dallas, in which the Lakers did score 41% of the points, that Lakers' players should have 41% of allotted win-producing contributions for that game.

Mike G wrote:
The Bulls have scored 51.2% of the points in their 5 games vs Atl, yet they hold 2/3 of the Pythagorean wins. If a wins-allotment system says Chi players have had twice as much contribution (toward winning) as Atl players, that is intuitively disturbing to some of us.

Others might be more bothered by supposing that Game 4 in Dallas, in which the Lakers did score 41% of the points, that Lakers' players should have 41% of allotted win-producing contributions for that game.

Both of these are ok with me, actually. I think the case you are trying to make is equivalent to questioning any small or partial sample with a predictive model. The correlation between point differential and wins is extremely high over the course of a season. Right? I mean how many models in the real world have R^2>0.95? That's ridiculously high in my opinion. Obviously, we can pick out circumstances where the model isn't "perfect", but in my mind, those cases seem to be so few and far between, that it may not be worth the effort.

What are we trying to do here? Get R^2>0.9999999?

Awesome, Evan.

For what it's worth, when I emailed bv, I said I'd be interested in seeing each player's raw box score numbers added to each line of the "List of each matchup of one unit against another" data. So it would look like this (all on the same row):

Game# HomePlayerID#s AwayPlayerID#s HomePlayerNames AwayPlayerNames Minutes PossHome PossAway PtsHome PointsAway HomePlayer1'sID# HP1'sFG HP1'sFGA HP1's3P HP1's3PA HP1'sOREB HP1'sDREB..... and on and on until AwayPlayer5's box score numbers are also added for that particular stint.

With that information, I could just use a basic Excel filter and a couple lines of VBA to compare, say, Kyle Korver's stats with Rose on the floor vs with Rose on the bench.

Anyway, maybe you have a different/better/easier system in mind, but that's the best I've been able to come up with.

I see. I like that format. I'll think about how much work that would be for me. It does seem like it would be very useful, though.

I would say, however, that the file is going to be gigantic! In my ezPM code, I keep track of about 40 different statistical categories. Multiply that time 10 players for each unit, will make 400 columns (+ the 30 or so that are in the matchup file already). Multiply that by the number of matchups in a season (~36,000 this season), gives a total of about 15.5M entries.