APBRmetrics

I used individual player APM (traditional and RAPM) as the only performance guide to build a lineup for teams (within position constraints and only using main rotation players) and checked to see how they did last season. In a few cases when player were with a few tenths of a point of each other or traditional and RAPM disagreed I was willing to pick either. Here is the list:

Atlanta
Teague-Crawford-Johnson-Smith-Horford
used 21 minutes, +21 per 48 on raw +/-

Boston
Rondo-Allen-Pierce-Garnett-O'Neal
used 266 minutes, +19 per 48 on raw +/-

Charlotte
Livingston-Henderson-Wallace-Diaw-Thomas
used 15 minutes, +5 per 48 on raw +/-

Chicago
Rose- Korver-Deng-Gibson-Asik
used 9 minutes, +29 per 48 on raw +/-

Cleveland
Gibson-Davis-Parker-Jamison-Varejao
used 0 minutes

Dallas
Kidd-Terry-Stojakovic-Nowitski-Chandler
used 21 minutes, +49 per 48 on raw +/-

Denver
Lawson-Smith-Anthony-Martin-Hilario
used 0 minutes

Detroit
Stuckey-McGrady-Prince-Wilcox-Monroe
used 126 minutes, +9 per 48 on raw +/-

Golden State
Curry-Williams-Wright-Radmanovic-Udoh
used 28 minutes, +52 per 48 on raw +/-

Houston
Lowry-Martin-Budinger-Scola-Hayes
used 298 minutes, +10 per 48 on raw +/-

Indiana
Price-Dunleavy-Granger-McRoberts-Foster
used 14 minutes, +12 per 48 on raw +/-

LA Clippers
Davis-Gordon-Gomes-Griffin-Jordan
used 329 minutes, +9 per 48 on raw +/-
(most used lineup)

LA Lakers
Fisher-Bryant-Artest-Odom-Gasol
used 953 minutes, +14 per 48 on raw +/-
(most used lineup)

Memphis
Conley-Mayo-Battier-Randolph-Gasol
Unknown (lack of reported data), but probably pretty good

Miami
Wade-Jones-James-Bosh–Haslem
used 44 minutes, +26 per 48 on raw +/-

Milwaukee
Jennings-Dooling-Mbah a Moute-Ilyasova-Bogut
used 13 minutes, +42 per 48 on raw +/-

Minnesota
Ridnour-Johnson-Beasley-Tolliver-Love
used 37 minutes, +18 per 48 on raw +/-

New Jersey
Harris-Farmar-Morrow-Humphries-Lopez
used 38 minutes, +14 per 48 on raw +/-

New Orleans
Paul-Belinelli-Green-West-Okafur
used 53 minutes, +39 per 48 on raw +/-

New York
Billups-Fields-Anthony-Stoudemire-Turiaf
used 94 minutes, -2 per 48 on raw +/-

Oklahoma City
Maynor-Harden-Durant-Collison-Mohammed
used 40minutes, +22 per 48 on raw +/-

Orlando
Nelson-Richardson-Turkoglu-Anderson-Howard
used 215 minutes, +4 per 48 on raw +/-
(most used lineup)

Philadelphia
Holliday-Meeks-Igoudala-Young-Brand
used 185 minutes, +23 per 48 on raw +/-

Phoenix
Nash-Carter-Hill-Dudley-Frye
used 24 minutes, +33 per 48 on raw +/-

Portland
Miller-Roy-Wallace-Aldridge-Camby
used minutes, + per 48 on raw +/-
used 0 minutes

Sacramento
Udrih-Evans-Greene-Thompson-Dalembert
used 40 minutes, +11 per 48 on raw +/-

San Antonio
Parker-Hill-Ginobli-Bonner-Duncan
used 63 minutes, +34 per 48 on raw +/-

Toronto
Calderon-Wright-Kleiza-A Johnson-Dorsey
used 7 minutes, +37 per 48 on raw +/-

Utah
Watson-Miles-Kirilenko-Milsap-Jefferson
used 31 minutes, -2 per 48 on raw +/-
(but a +11 traditional Adjusted +/- estimate)

Washington
Wall-Young-Lewis-Blatche-McGee
used 255 minutes, +5 per 48 on raw +/-
(most used lineup)

24 positive, 23 at or over +5 per 48 minutes (about 85% of those used), 18 at or over +10 and 12 at or over +20. Just 2 negative.

Individual player Adjusted +/- seems like a pretty good guiding tool in constructing strong performing lineups to me.

But only 7 of these lineups were used over 100 minutes for the regular season and just one over 350 minutes (or a bit over 4 minutes per game for the season). And they were the most used lineup just 4 times. 3 were never used all season while hundreds of other lineups got used by that team.

Is Adjusted +/- inaccurate and unreliable? At very small minutes it would be far to say that using strict statistical significance standards. Is it still worth paying some attention to right now even with that issue and would it possibly be more valuable if these lineups got tested for more or a lot more minutes next season? I'd tend to think so, vs. ignoring or scorning the existing Adjusted +/- information.

It seems like the data by itself (at player and lineup level) isn't swaying more than a few teams much at all in their minute allocation, as only 1 Adjusted +/- maximizing lineups got used more than about 8% of the total available time and only a half-dozen other got more than 2.5%. Maybe analysts (of whatever kind, traditional or quantitative) are needed to see this data and decide whether to advocate it be considered carefully and perhaps followed more (based on this data and everything else available, including of course video, if the other sources of information generally concur with the Adjusted +/- information). This is not hard to put together but I don't recall seeing any comprehensive list built on this basis in public before. You rarely even see it for a single team.

If teams had used this lineup recommended by player APM data (and perhaps other variant lineups with 4 of the best choices and someone else who wasn't too damaging) a lot more I'd think it could have made a material difference in the regular season finish and playoff performance in at least some cases. The same type of analysis could be used to spot lineups that based on APM would seem to have elevated prospects of yielding below team average or bad performances. No method is going to be infallible but using player APM as a guide for building lineups looks very strong, at least based on what limited data is actually available.

Only 30% of teams most used lineups were negative on raw +/- so that much is pretty good based on whatever current mix of data teams consider / rely upon. About 35% of best used lineups were +5 or better on raw +/-. But you don't have to argue for replacing the very most used lineup to favor increased used of the lineup built upon the best available player APMs. There a number of other relatively highly used lineups that look bad or quite bad or even just not as good as these player APM recommended lineups that could be reduced or replaced. The key is better targeted, more intensive, better analyzed tests. Prioritize based on available information, test, evaluate, re-prioritize lineup minute usage and repeat every month or couple of months. Somehow, to some greater degree than now, the tactical inclinations of coaches for lineup construction and use of many or most teams need to be better reconciled with season level, playoff and long-term franchise strategic analysis.

How many GMs, coaches and media who cover a team full-time would know immediately what lineup represents the best combination of players at the 5 positions using APM? (There are a few cases where another lineup is close to being as good but in at least 80% of the cases the lineups on the list above appears to be a pretty clear best answer for the team.) Putting that challenge aside, how many would be surprised by the lineup indicated by this method over other candidate lineups? In how many of the 30 cases would they indicate significant skepticism that these are potentially good lineups? In the 80% of cases where these lineups got less than 100 minutes, how many would defend that low level of use & testing beforehand or after some or all of the test data for all other lineups was in? How many of these lineups would you defend the very low testing of? How many insiders or outsiders would defend the greater use of the bigger or biggest minute lineups in spite of cases of weak raw or Adjusted lineup +/- or weak player APM sums? How strong are the counter data and arguments?

Year to year changes in lineup minute usage would seem to be a good area for further research and writing. I've done it a bit for a few teams. I understand Ian Levy was going to looked into that topic when he had the time. How much of the advancement or decline of teams is attributable to changes in lineup minute allocation as opposed to development, aging, shot selection and other things? And checking his site one more time I see he has published an article on this topic:

http://www.hickory-high.com/?p=2006

The correlations between minutes that lineups played and their weighted Net Rating for Coaches overall and by season are quite interesting to look at. Adelman and Gentry didn't make the playoffs but, it appears, were top 16 on strength of minute / performance correlation (there were a few teams missing). Scott Brooks had one of the lowest 2010-11 regular season correlations among the teams who made the playoffs. Correlations for all playoff teams would be interesting if you get to it Ian.

Thanks for the mention Crow. I have one other way of looking at minute distributions for lineups based on +/- that I'm working on. The plan is then to take both methods and apply them to playoff data for the past few seasons. It will probably take me a few weeks, but it hopefully it will be up soon.

I don't think it's entirely correct to pick players with good APM ratings, build a 5-man-lineup and then see if that lineup performed well during the same time frame you used to compute the player ratings. Of course the lineups will have performed well because if they didn't the specific players would not have a positive rating!

I think it would make more sense to take half a season RAPM, pick your lineups, then see how they do in the other half of the season.

A had a similar idea which I posted on the old forum where I argued that a coach could simply play all possible lineup combinations in the first couple (~5) of games*, and then roll with the best performing (as in "best raw +/-") lineup as your main starting unit. If that unit is actually not the best unit, their raw +/- should drop relatively to other units in the following games, and another, better, unit should be chosen as starting unit. Obviously it's not all that easy, foul trouble and fatigue must be taken into account. Maybe it's even optimal to not play your best unit because not doing so might enable you to play your 2nd and 3rd best uni more

*if you have 10 players, and exactly 2 centers, 2 PFs etc there are only 32 combinations

I didn't set it up as using prior season player APM to predict the next season's lineup performance on raw +/-, though maybe that it is what people expected or perhaps what I should done.

I agree it would be better / more a real-world decision-making situation to take half a season RAPM, pick your lineups, then see how they do in the other half of the season. I talked about testing and adjusting. Unfortunately I don't have half-season Adjusted +/-. You probably do or could. If you want to publish that, I'd probably re-look at the list and the performance.

I did look at 2 year traditional APM to avoid players who had a major APM change in 2010-11. I had previously found at least 2/3rds of big minute player RAPMs to be reasonably close one season to the next so I don't think it would change the recommended lineups a lot. Still I might check further and perhaps post another version that better represents making a prediction. If I had used previous year to predict next year someone might still say the half year approach was better. Team labels in the RAPM database would make such work easier / faster.

Assume for simplicity for now that the player APMs don't change in the season and that values used for the whole season were experienced in the first half of the season and could have been used to refine minute allocation in the second half.

I agree there are limitations to what one should conclude from picking players with good APM ratings, building a 5-man-lineup and then see if that lineup performed well during the same time frame you used to compute the player ratings. Most will perform well but I think it was interesting to see the few that didn't (especially the new NY lineup, the APm before the trade may not be accurate for after the trade). You compared 5 man lineups to the sum of the individual APMs yourself for the same time period and I found that useful to identify which lineups over or underperformed. You weren't trying prediction, just same season comparison and that is what I actually did as well. There was quite a range. Actual lineup performance did not follow sum of individual APM in lockstep. The data I presented has some uses even if it is not ideal for one purpose (prior prediction).

One of the main points I was making was how little the lineups built on individual player APMs position by position got used. That was probably true the season before as well, so the lineup data is going to have little proven validity anyways regardless of the season base. But at least I named lineups with a fairly strong basis for believing they might good (built with a full season of RAPM and 1 and 2 yr views of traditional APM for players) and highlighted the issue of why they weren't being given decent trial & adjust use as I intended and you also suggested.

Even despite the very small minutes it seemed worth seeing that lineups almost always performed well and usually very well. If player APM was as poor and unreliable a metric as some suggest the actual +/- results probably shouldn't be this strong but a true prediction test would be appropriate to run before claiming too much.

Prediction

Construct best lineup by position using 09-10 player APM & RAPM data and then check 2010-11 performance.



Atlanta

Bibby-Crawford-Johnson-Smith-Horford
used 233 minutes, +7 per 48 on raw +/-

Using 09-10 data 4 players stay the same; Bibby used instead of Teague.


Boston

Rondo-Allen-Pierce-Garnett-J O'Neal
used 127 minutes, +6 per 48 on raw +/-

Using 09-10 data 4 players stay the same; Jermaine used instead of Shaq.


Charlotte

Livingston-Jackson-Wallace-Diaw-Thomas
used 37 minutes, -27 per 48 on raw +/-

4 the same; Jackson instead of Henderson.


Chicago
Rose- Korver-Deng-Boozer-Noah
used 166 minutes, +11 per 48 on raw +/-

3 the same; Boozer over Gibson (a young player developing) and Noah over Asik (hadn't played yet)


Cleveland

Gibson-Davis-Parker-Jamison-Varejao
would have picked the same lineup
but not used on 10-11


Dallas

Kidd-Terry-Marion-Nowitski-Haywood
used 54 minutes, -4 per 48 on raw +/-

3 the same; Marion over Stojakovic and Haywood over Chandler.


Denver

Billups-Smith-Anthony-Martin-Hilario
used 15 minutes, +28 per 48 on raw +/-

4 the same; Billups over Lawson.


Detroit

Stuckey-McGrady-Prince-Wilcox-Wallace
not used.

4 the same; Wallace over Monroe perhaps since no info on rookie Monroe.


Golden State

Curry-Williams-Wright-Radmanovic-Udoh
used 28 minutes, +52 per 48 on raw +/-

I'd say all the same; no info on Udoh but one might have picked over Biedrins anyways. If you didn't those 4 with Biedrins instead only played 1 minute and was neutral.


Houston

Lowry-Lee-Battier-Scola-Hayes
used 13 minutes, +24 per 48 on raw +/-

3 the same, Lee over Martin, Battier over Budinger.


Indiana
Price-Dunleavy-Granger-McRoberts-Foster
used 14 minutes, +12 per 48 on raw +/-

all the same; went with Foster over Hibbert because of better RAPM and better previous seasons.


LA Clippers

Davis-Gordon-Gomes-Griffin-Kaman
used 53 minutes, -43 per 48 on raw +/-

4 the same; Kaman over Jordan.


LA Lakers

Fisher-Bryant-Artest-Odom-Gasol
used 953 minutes, +14 per 48 on raw +/-
all the same.


Miami
Wade-Jones-James-Bosh–Ilgauskas
used 23 minutes, +51 per 48 on raw +/-
4 the same; Z over Haslem.

Milwaukee
Jennings-Dooling-Mbah a Moute-Ilyasova-Bogut
used 13 minutes, +42 per 48 on raw +/-
all the same; split decision at PG but Jennings stays over Ridnour because jenings was better on RAPM.


Minnesota
Ridnour-Johnson-Brewer-Tolliver-Love
used 19 minutes, +34 per 48 on raw +/-
4 the same; Brewer over Beasley


So far 11 positive performing 10-11 lineups on raw +/- using 09-10 player APM to construct them, 3 negative, 2 with no results to determine. On average a bit over 4 of the players are the same as selected when using 10-11 player APM data.

Of 16 cases only 4 were used over 100 minutes in 10-11 and only one over 250 minutes, despite the suggestion that those lineups would be good based on the full prior season player APM values, which they turned out to be in almost 80% of the cases where there is data.

I can understand that teams might not play their best five on APM together the max possible. Perhaps there is a possible issue in some cases of not have enough of something (scoring, rebounding, assists or defense, etc.) in that lineup concerning enough to decide to not give it the most minutes. Or maybe there is not enough talent left over to do that a lot and fill other necessary lineups decently (with at least 3 of the best 5) . But it is still notable how little the full 5 suggested by player APM play together in most cases and in many of those cases there does not appear to be an obvious discrete stat shortfall that rules it out. I'd think the 5 suggested by player APM should usually, baring a significant issue, be a top 3-5 lineup (perhaps playing a good share of crunch minutes).

On average it appears the most used lineups of teams have about 3.5 of their best 5 on APM on the court together. 1 of the remaining is not that bad player on APM but 0.5 were below -5 on traditional APM. That is not terrible but does it really deserve to be the most used?


Lineup management should preferably be assessed globally. Ian's data analysis does that.

Jackson had the best correlation, in part because he played his best APM 5 three times as much as anybody else. 69% of their minutes went to the 10 biggest minute lineups (that is probaly one of the higher frequencies). They averaged +10.1 per 48 minutes on raw +/- and had an average of 3.7 of the big 5 on APM. The sum of all their other lineups got only 31% of minutes and average -2.9 per 48 minutes.

4 of the top 6 lineup minute vs performance correlations last season belonged to Coaches who used their best APM 5 for 4 of the 5 most minutes of the orignal list of APM5 lineups.

Boston and Houston had at least 4 of their best 5 on APM in all 5 of their top 5 most used lineups. Orlando, LA Lakers, San Antonio and Orlando were more typical at around 3.5 (give or take a bit).

Of the 4 worst correlations, Avery Johnson and Kurt Rambis had just a bit over 3 of their best 5 on APM in their top 5 lineups while Byron Scott and Jay Triano were at an average of about 2.5 of their best 5 on APM in their top 5 lineups.

If your 5 best players (by APM, otherwise or overall) can / do play an average of 32 minutes, there are several ways to deploy them. If you use all 5 together for the maximum of 32 minutes, then the other 16 minutes will have none of them on the court. If you decide you want a minimum of 3 of the best 5 on the court at all times, then you could have 3 on the court for 20 minutes and about 3.5 on the court for the other 28 minutes. If you make the minimum 2 of the best 5 on the court, you could do that for 20 minutes and have an average of 4.3 on the court for the other 28 minutes. There are other combinations.

If your 5 best players (by APM, otherwise or overall) can / do play an average of 36 minutes and you use all 5 together for the maximum of 36 minutes, then the other 12 minutes will have none of them. If you decide you want a minimum of 3 of the best 5 on the court at all times, then you could have 3 on the court for 12 minutes and 4 on the court for the other 36 minutes. If you make the minimum 2 of the best 5 on the court, you could do that for 20 minutes and have all 5 on the court for the other 28 minutes.

Of course the best 5 are not all equally impactful or equally compatible with particular starters or bench players or necessarily as impactful as their APM average when out there with 2, 3 or 4 other top players. Some of your top 5 APM players may not be able to go big minutes or go big minutes at the APM level set at lower minutes. Each team would need to customize their lineup set for these details.

Whether there is a overall performance premium across all minutes from a lineup distribution that maximized the lineup minutes with 4 or 5 on the court (and more with just 2-3) than a distribution that tries to spread the top 5 out as evenly as possible could be analyzed in further depth for a specific team or the league and perhaps over multiple season. I think that could be a pretty imoortant strategic decision and I wonder how carefully and directly it is considered by most teams. The above data suggests (limited in minutes though it is, too limited) that playing all of the top 5 together is often very very good. I also see that weak and really weak performing lineups often have 2 poor APM players on the court and that 3 poor APM players together makes really weak performers even more likely. How those lineups balance out would take careful accounting and could vary by team. There are obviously lots of lineup sets that could be considered & reviewed. If you set it up right you could check all sets and find the projected optimal set.

If you have a star player who can turn a lineup of himself, 1-2 other top 5 APM players and 2-3 ok to weak players into a decent or better performing lineup that would be a big help. The better a star can carry such a lineup the more you can concentrate 4-5 of the top 5 together in the other minutes.

I agree that more teams should play their top unit more often and I think it would make sense for almost everybody to play your best unit at least 5-6 minutes a game: the last minutes in the 4th quarter.

One instance where it seemed extremely obvious to me that lineups could be optimized was last year's series between OKC and Dallas. Collison was a beast in every +/- related statistics, already so in the regular season, then played 16 minutes in the first game and 24 minutes in game 3, which they both lost.
In that game 3 he went 4 for 4 from the field, with one and1/2OffR/4DefR/1Assist/2Steals/2Blocks/0TO
He ended up with a +17 for the playoffs. Starters Ibaka at -11 and Perkins at -13, both played ~20% more minutes than Collison

Sometimes though it seems a team's main goal doesn't seem to be "winning". Or does anyone have another explanation why Toronto wasn't playing Amir Johnson more than 26 minutes last season?

J.E. wrote:I agree that more teams should play their top unit more often and I think it would make sense for almost everybody to play your best unit at least 5-6 minutes a game: the last minutes in the 4th quarter.

One instance where it seemed extremely obvious to me that lineups could be optimized was last year's series between OKC and Dallas. Collison was a beast in every +/- related statistics, already so in the regular season, then played 16 minutes in the first game and 24 minutes in game 3, which they both lost.
In that game 3 he went 4 for 4 from the field, with one and1/2OffR/4DefR/1Assist/2Steals/2Blocks/0TO
He ended up with a +17 for the playoffs. Starters Ibaka at -11 and Perkins at -13, both played ~20% more minutes than Collison

Don't know if anyone has the time and inclination, but it sure would be interesting to see, on this particular point, what the correlation was between regular season and post-season Nick Collison line-ups vs. the Mavs. The data is right up there on basketballvalue.

J.E. wrote:Sometimes though it seems a team's main goal doesn't seem to be "winning". Or does anyone have another explanation why Toronto wasn't playing Amir Johnson more than 26 minutes last season?

An amusing and astute observation in the first sentence. To be hoisted to another string for further comment....

schtevie wrote: Don't know if anyone has the time and inclination, but it sure would be interesting to see, on this particular point, what the correlation was between regular season and post-season Nick Collison line-ups vs. the Mavs.

In the regular season Collison had a +/- of [-4, +13, -8] -> +1 in 3 games, which OKC lost by the sum of 14 points. Obviously it's possible he played against the Mavs bench more than against the starters.

In the playoffs he went [+7, +10, +3, -14, +3] -> +9 in 5 games which OKC lost by the sum of 20

I was referring to the "aggregated disaggregated" team vs. team, line-up data on BV. The thought was it would be interesting to see how all, specific Collison line-ups performed in the regular season vs. the playoffs. If these line-ups were highly correlated, that would be rather informative, in a variety of dimensions.

More generally, of course, it would be really neat-o to see how all line-ups compared between the regular and post-season. But that is a bit more work.

Collison was in 3 of the top 5 (by minutes) lineup units in the playoffs for Okl, of 56-62 minutes each:

- Going 160 min. in the season: Westbrook, Harden, Durant, Ibaka and Collison were +8.5 APM, and in playoffs +5.8
- Going 120 min. in the season: Maynor, Cook, Harden, Collison, and Muhammed were +7.4 APM, and in playoffs +4.5
- Given just 22 minutes in the season, that first lineup but with Perkins (repl. Ibaka) were -35 unadjusted, but +30 in playoffs -- +13 adjusted.

Lineup units playing >25 minutes in the 2011 playoffs, along with their regular season data: That Philly unit line is not a typo on my part.
http://basketballvalue.com/teamunits.ph ... s&team=PHI
That's their regular starting lineup. In 5 playoff games, 1st quarter scores were 31-19, 13-19, 29-21, 28-16, and 23-27.
This accounts for 11.2 minutes per game, vs Miami. And it Adjusts to merely +1.3
Memphis regular season numbers are from 82games.com

Of the 48 lineups listed, a bit less than half that had full data for a comparison improved on unadjusted and Adjusted +/- in the playoffs compared to the regular season.

That would be an average of 3 lineups used 25+ per team if they were evenly distributed but they weren't. All playoff teams had at least one except NY but only 7 had 3 or more, in part due to playing more games. Miami had the most with 9. The 4 conference finals had almost 60% of them.

Of the 15 lineups used for 15% or more of the total team playoff minutes only 4 improved on change in Adjusted +/- estimate (Playoffs-Regular Season) and one of these was just barely positive. 7 improved on unadjusted +/- change. Philly and Boston had the lineups with the biggest Adjusted +/- change with Dallas third on that but the clear leader on unadjusted +/- change (Kidd Terry Marion Nowitzki Chandler) with a +8.4 change in unadjusted +/- per 100 possessions. Dallas though also had the lineup with the 2nd worst change unadjusted and worst estimated change on Adjusted +/- (Kidd Stevenson Marion Nowitzki Chandler). Miami had the lineup with the 2nd worst change on estimated Adjusted +/- (Bibby Wade James Bosh Anthony).

Someone somewhere wrote how predictable the Mavs championship run was, in spite of their being a below-average Dallas team of the last decade.
Going by these 5 most-used units -- totaling some 57% of their playoff minutes -- I don't see anything predictable in these numbers.
The awesome regular season APM of what would be their starting lineup through the playoffs was actually pretty bad in playoffs : from +25 to -2 .
Replacing Stevenson with Terry was key.
One would not have expected line 3 would improve by 25 pts/100
Barea-for-Stevenson (line 5) was not nearly as bad in playoffs.