This is our old blog. It hasn't been active since 2011. Please see the link above for our current blog or click the logo above to see all of the great data and content on this site.

Layups: 5-Man Unit “Chemistry”

Posted by Neil Paine on July 21, 2010

Here's an extremely interesting study from Jamie Merchant's blog Numeranda, regarding the "chemistry" of a given 5-man unit. Merchant used BasketballValue's 2010 adjusted plus/minus data for both lineups and individuals, and calculated which combinations were literally greater than the sum of their parts:

"Here was my thinking: we have at our fingertips (thanks to Aaron) two measures of APM, an individual measure and a five-man unit measure; is there some way to connect the one with the other? My first instinct would be to simply add the individual APMs together and see how they compare to the five-man unit APM. If player impact works in a simple, additive fashion, the two measures should be roughly equal. Is that the case?"

The usual APM caveats about samples sizes and standard errors apply, but the results are fascinating. For instance, we would expect Houston's Aaron Brooks/Shane Battier/Trevor Ariza/Carl Landry/Luis Scola lineup to be highly negative (-7), but they ended up being average (+0). And at the other end of the spectrum, we would expect Boston's Rajon Rondo/Ray Allen/Paul Pierce/Kevin Garnett/Rasheed Wallace combo to be very good (+8), but instead they were downright bad (-6).

Sometimes the pieces just fit... and sometimes they don't (we've already commented on how Wallace negatively impacted the C's when on the floor last season). This has been a basketball aphorism forever, but now we actually have some data to quantify the phenomenon.

17 Responses to “Layups: 5-Man Unit “Chemistry””

  1. Rashad Says:

    Couldn't this just as easily be taken as evidence that APM is a pretty noisy measure of performance, as opposed to "proving" that chemistry exists?

  2. Neil Paine Says:

    Sure, I never said it "proved" anything. But if chemistry does exist, this would be one way to actually quantify it.

  3. izzy Says:

    What would be interesting is this: comparing a player's teammates' APM for when he i on vs. off the floor. Regular APM examines how the team does when he is on vs off the floor, but what I am saying is to investigate whether a given player's teammates' individual APM improve/decline when the given player is on the floor. This would measure a sort of "compatibility." Essentially, instead of looking how a player impacts the +/- of the score overall, you can look at whether his teammates improve with him on the floor. Has this been done before? I'd love to know your thoughts Neil...maybe it overlaps with APM too much?

  4. DSMok1 Says:

    Izzy: that's completely the same thing as APM right now. It just measures how much better the team is, and attributes all of the change to the player being added.

  5. Daniel Song Says:

    Considering how noisy this measure is, I think I will defer to the coaching staff on this one. They SHOULD be able to tell if the unit they send out has good chemistry, one would hope...

  6. Neil Paine Says:

    #5 - You'd think so, but I come back to something Mark Cuban said at the MIT Conference, which is that he could tell which teams were working from the data vs. teams working from gut instinct by the lineups they used. He could understand why coaches thought certain lineups would work, but the numbers showed that they clearly didn't... and yet the coaches continued to play them. In a small sample, obviously you're working with a large amount of noise, but in a number of cases, you can say with some certainty that a lineup works or doesn't work.

  7. Daniel Song Says:

    In that case, I think the best way to proceed is to pick out the outlier cases (i.e. frequently played lineups that had bad chemistry numbers) and have the coaches examine the game film to see if they can spot anything.

    I like numbers as much as anyone but I've learned that numbers largely depend on the context. The numbers will tell you that Josh Powell is a toxic waste dump who would cost his team 10-15 wins a year if he played regularly in the rotation compared to a replacement-level player; obviously this is not the case.

    Still, this is a useful piece of information that coaches could make good use of - especially when it comes to analyzing game film and scouting.

  8. Anon x 2 Says:

    Indiana, Washington, and Philly have lineups near the top of the list, whereas the Lakers starting lineup is around 0.


  9. Jason J Says:

    That was pretty much my reaction Anon X 2.

  10. Crow Says:

    Izzy is right that other players' APMs are the average from all their minutes with and without a player. The APM of the "without" minutes only could vary from their APM of the "with" minutes if calculated separately and are not necessarily exactly equal to the APM of the with / without player. That would only be true if there are no or no meaningful player interaction effects. The average APMs are only the best fits for all minutes, all players on average. If you want to explore the relationship between 5 man lineups and individuals, Adjusted +/- player pairs or triplets or quads are a potentially useful, even necessary, intermediary dataset.

  11. Crow Says:

    Make that... use Adjusted +/- player pairs or triplets or quads or player interactive terms or I'd guess it would be helpful to have both.

  12. Brian Tung Says:

    This is the "linearity" assumption that APM implicitly makes. It can be masked somewhat by including some off-diagonal values, but the assumption itself remains, and is essentially unvalidated. I wrote about this at

  13. Dan Says:

    re Jason J and Anon X2, unless i'm missing something, the Lakers have 2 of the top 10 units for APM. sort of suggests that at least during the regular season they were better w/o bynum. might explain why they managed to win their 2nd title despite him being hurt.

    here's the link for those who are curious and yet lazy:

  14. Dan Says:

    just realized that was for the playoffs. the lakers still have 3 of the top 50, tho, including #13. but miami and atlanta have the #1 and #2 units and 4 of the top 10, so it is actually a bit strange.

  15. Dan Says:

    oh, and here's that link:

  16. Jason J Says:

    #13 - Not sure how I missed that!

  17. Jan Blanchet Says:

    I’m not that much of a online reader to be honest but your blogs really nice, keep it up! I'll go ahead and bookmark your website to come back in the future. Many thanks