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Lineup Optimization or: How I Learned To Stop Worrying And Love Sam Mitchell


Measuring the effect and importance of coaching is a notoriously thorny issue. A reliable and reasonable statistical method to evaluate coaches is the Loch Ness monster of the APBR community. There are many who don’t believe such a thing exists, but the legend persists. The crux of the challenge is sifting out what part of performance is purely attributable to the players, and what part a coach has had their hand in. Statistics are generated by players and using them to evaluate a coach inevitably means the inclusion of a multitude of other variables.

There is however, one place where a clear distinction between player and coach can be made. In this one instance, the responsibility for a statistic, which is attributed to a player, falls primarily in the domain of the coach. I’m talking about minutes played, and specifically, how minutes are distributed to the various players on a team. It’s one of a coach’s most basic duties – deciding who will play, when, for how long, and in what combination. Other than in cases of injury or suspension, this distribution is usually the sole discretion of the coach, and therefore provides a set of statistics which can be attributed directly to them. The question then becomes – Can you quantify how adept a coach is at distributing those minutes?

I have a few different ideas to try and answer that question. To start with, I’m going to re-introduce a technique I used briefly while writing for The Two Man Game during the Finals. In one of his Finals’ recaps, John Hollinger mentioned that the Mavericks had pursued Rick Carlisle, in part, because their statistical analysis showed he had a clear tendency to give the most minutes to the most effective lineups. To check this idea, I borrowed the playoff five-man unit data from Basketball Value and ran a correlation between the number of minutes each lineup played for the Heat and the Mavericks, and the Net Rating (ORtg. – DRtg.) of that lineup. To account for absurd Net Ratings from small samples, I weighted the Net Rating for each lineup, multiplying it by the number of minutes played. Rick Carlisle and the Mavs had a 0.692 correlation between the effectiveness of the unit and the number of minutes that unit played. The correlation for Erik Spoelstra and the Heat was -0.177. Those numbers certainly dovetailed with the more qualitative and subjective evaluations of the way each coach handled their lineups.

For this piece, I’ve taken that simple correlation method and applied it to all the regular season five-man unit data from Basketball Value, covering the last four seasons. There were, unfortunately, a few exceptions to that data. Since Basketball Value’s data covers the entire season, I wasn’t able to include any year in which a team changed coaches mid-season. Aaron Barzilai who runs the site is also a consultant for the Memphis Grizzlies which means their data isn’t listed on the site and therefore, is not included.

The table below shows the correlation between minutes played and weighted Net Rating for each unit, of each team (other than the Grizzlies) who had the same coach for the entire season, for each of the last four seasons. I’ve also included the Win % of each team.

[table id=22 /]


Doc Rivers is one coach who looks incredibly effective by these numbers. Three of the top six individual seasons in this sample belong to him, including the highest correlation I found, his 0.953 mark in 2008. Rivers has had the benefit of coaching some incredibly talented rosters, but has also clearly demonstrated the ability to maximize the available talent.

Sam Mitchell also stood out quite a bit. His 2008 Toronto Raptors won just half their games, but Mitchell’s minute distribution showed a 0.763 correlation between the effectiveness of the unit and the number of minutes they played. This was the 17th highest mark in our sample. There are several different ways to interpret these numbers. In this case, I see a coach with a limited roster who did a terrific job doling out minutes and managing his rotations.  In a cruel twist for Raptors’ fans, the coach who replaced Mitchell, Jay Triano, had two of the ten worst numbers in our sample.

I also wanted to try and extend these numbers, looking for patterns across seasons. This next table shows the correlation for each coach covering the combination of all the seasons they worked since 2007-2008. For some coaches this is just a single season.

[table id=23 /]


Because these numbers reflect a single season for some coaches, and multiple seasons for others, it’s difficult to draw strict comparisons. However, some of the names which rose to the top (or fell to the bottom) of this analysis were no surprise. Of the coaches who worked multiple seasons over this stretch, the top five, by these numbers, were Doc Rivers, Phil Jackson, Stan Van Gundy, Flip Saunders and Alvin Gentry. The bottom five were Kurt Rambis, Jay Triano, Mike Dunleavy, Jon Kuester and Lawrence Frank. I was also surprised to see Jerry Sloan, George Karl and a few other notables hanging in the middle of the pack.

While these numbers have a lot to say, there are some obvious issues with both the method and results. Weighting a unit’s Net Rating by minutes played may not be an accurate reflection of how that unit would have played given more time on the floor. The options a coach has in determining units can also be limited greatly throughout the season because of injuries or roster moves. In short, the numbers may not be perfect, and they may not entirely reflect a coach’s ability to use what is at his disposal.

Although it will take some time to put together, I have another method I’ll be trying in the next few weeks, looking at this issue from a different angle.  Hickory-High has been on a lengthy hiatus, but the vacation is over!

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  • Alex Sterling

    You should plot out the Correl versus the Win % from your first table… I think you’ll find they are closely related.

    In other words, if a coach has good players who are clearly good players and who can win games, he plays them more often.

    That’s what I would call a “no duh”.

    • ilevy

      Alex, although I didn’t include the number in the write-up, but I actually did run that number. For the entire data-set there was a 0.861 correlation between a team’s minute distribution correlation and their win%. Obviously, coaches like Phil Jackson and Doc Rivers have been working with top-heavy rosters that make deciding on rotations easier. Still, even if you belive that their is a complete cause-effect relationship between win% and minute distribution, going in one direction, the correlation of 0.861 would mean that 13.9% of that relationship is unaccounted for. I happen to believe that the cause and effect nature of that relationship goes both ways, but even if I’m completely wrong, I think that the 0.861 correlation means that there is some room for coaches to maximize or minimize the abilities of their players by how they are used in lineups.

      Obviously, this study is splitting hairs, but I think there is some value in looking at these numbers. I have another look at coaching minute distributions coming soon, using a different technique. Hopefully, you’ll come back and check that one out.

  • Crow

    Some of the best coaches are very consistent. But then with others, considered good or not, there are vilent year to year changes in the sixe and sign of the correlation. This gives a starting point for then going back to the data and seeing how lineup allocations changed and how lineup performances changed and seeing how much of the change is associated with each.

  • Crow

    Of the Hawks 3 biggest minute and good lineups under Woodson in 2008-9, one completely nosedives in performance and gets played significantly less. The other 2 keep working fine but only get played by Drew for 40% of the previous time. I simply don’t understand how that choice is made or allowed.

    • ilevy

      I wonder how often it’s a mental block for a coach. By that I mean taking over for an established coach who had a pattern of success and feeling like you need to put your own stamp on the team, changing things just to prove it’s yours now. Obviously it’s a terrible idea if it makes the team worse, but I wonder if emotion clouds the judgement and leads to that situation.

  • Crow

    In the odd years listed Popovich finds 5-6 positive lineups to give 1000-1200 minutes and lead his lineup rotation. In the even years he just finds 4 positive lineup leaders and they only get 600-800 minutes. And 2 dud lineups make the top 6 most used. That is probably partly Pops’ fault.

  • Crow

    In the even years he just found 4 positive lineup leaders and they only get “600″ minutes. Only get to 800 minutes when you count the bad lineups.

    What were his bad big minute lineups like in the even years?

    In 2009-2010 they both had Bogans with his fairly high negative APM, another of the worst 4 main rotation players on APM and only had one of the 2nd, 3rd &4th best on APM (Ginobili, McDyess and Bonner). Pop got away with that with a couple other lineups but maybe that was too thin, he relied on the system too much and should have had a higher concentration of his best players out there together. You might have thin lineups but a thin lineup should not be a top 6 most used lineup. (The only time when that could be the case would be if you used your very biggest lineups a huge amount and you simply ran out of top guy minutes to put out there. Rivers faced that situation more but handled it well always.)

    In 2007-8 the big minute bad lineups were pretty similar in this regard- too thin on top guys, too high on weak APM guys.

    Either APM is a useful guide in diagnosing lineup problems or maybe I just selected a case that fits that claim. I’ll continue to look further when I have more time.

    • ilevy

      I think you nailed a key point – Pops’ situation seems like a stark contrast to Doc Rivers. They both have relied heavily on a triumvirate of aging stars, trying to get the most out of them while still keeping their minutes low as possible to prevent wear and tear. My gut tells me that the Spurs have had a better supporting cast the past four years, but Rivers has figured out a structure to keep those weaker rotation guys from hurting them as much.

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