Arturo’s Half Baked Notion

Arturo at Arturo’s Silly Little Stats has been looking at the idea that while a deep team is useful for getting to the playoffs, a top-heavy team is best for winning the championship.  That idea came from the post here, which focuses on two tables.  The first is a table showing the percentage of minutes played by players on a team (sorted by minutes played, so the number one player is the guy who played the most minutes) and the percentage of team wins that each player generated.  My assumption is that this table shows the average value for every regular season team over the last 30 years.  It shows that your top six players, who play 70% of a team’s minutes, produce 89% of your team’s wins.  Thus, the rest of the guys play 30% of the minutes and produce 11% of the wins.

The second table is the same thing but for the playoffs.  Thus I assume it averages together the playoff data for every playoff team for the past 30 years.  It shows that your top six players play 81% of the minutes and produce 99% of the wins.  This sharp difference, that in the playoffs 6 guys produce all your wins while in the regular season they produce 90%, is what Arturo focuses on when he says you should prefer a top-heavy team: the better your top 6 guys are, the better you should do in the playoffs.

There are a couple issues that I think come up from the start.  First, there is no direct connection to actual success here.  For example, the Clippers could follow the playoff minute allocation here and they wouldn’t win much because their players aren’t very good.  Second, this result has to occur to the extent that better players tend to play more minutes.  In the regular season, the top six guys played 70% of the minutes; in the playoffs they play 81%.  They produce more wins in those extra 11% of the minutes; the bench guys who don’t get into the game produce fewer wins relative to the regular season; and thus the top six produce a greater percentage of their team’s wins.  As long as the top six are positive win producers, this must be true (they can even be below average, so long as they don’t produce negative wins).  So I’m not sure if the data that Arturo is looking at support his conclusion.

However, we can still ask the question, would you rather have a top-heavy team or a deep team?  I’m going to take a look at this with a thought experiment using Wins Produced.  Let’s take the top-heavy team to the extreme: Your top six players have WP48 of .32, .25, .21, .16, .12, and .1.  Everyone else on the team is a 0.  Using Andres Alvarez’s automated WP numbers from 2010 to put some names on the numbers, that would be (roughly) like running out a line-up of Tim Duncan, Chris Bosh, Andre Iguodala, Tyreke Evans, and Baron Davis with Shane Battier and a bunch of Chris Kaman’s or Ben Gordon’s coming off the bench.  I picked those numbers because if you use Arturo’s playoff minute allocation, that team would be expected to produce 16 wins in 19 games; in other words, they should only ever lose three games before winning the 16 needed for a title, even though 19% of the playoff minutes go to guys who don’t produce a single win.  This team would also do well in the regular season; using Arturo’s regular season minutes allocation, those guys should win almost 60 games.

Now let’s say you have a more typical, deeper team.  How could you counter such a behemoth?  First, we want to make sure the teams have equal strength.  We don’t want to find that top-heavy or deep is better in the playoffs if one is fundamentally better. So I played with some Wp48 values across 10 players using Arturo’s regular season minute allocation to create a team that would also win just under 60 games, with the limitation that the top 4 players (by minutes played, and coincidentally WP48) would be worse than the top-heavy team’s top 4 players.  I accomplished this by running out a squad with scores of: .25, .21, .19, .15, .13 (the starting five might be David Lee, Nicolas Batum, Brandon Roy, Russell Westbrook, and Kenyon Martin), .13, .11, .07, .06, .03, and 0 (for players beyond the tenth).  How does this team do in the playoffs?  With Arturo’s playoff minute allocation, this team should produce 15.5 wins in 19 games, or 16.23 in 20, meaning that they would still be a good pick to win the title but not quite as effective as the top-heavy team.  So what should the ‘deep’ team do?  Shorten their bench even more.

As it stands, the top-heavy team (which is using an average playoff team’s minute allocation) is giving 19% of its minutes to guys who aren’t very good.  Why should you do that?  The deep team can sit everyone after the 8th man and have the top 8 guys play an extra 2.5 minutes per game.  Now, in 19 games the deep team wins 16.4 games – more than the top-heavy team.  So if you really shorten up your bench and run an 8 man rotation, you can be as effective, if not more so, even when your top four guys aren’t as good as the other team’s top four.  If you’re worried about fatigue, you can produce the same 16 wins as the top-heavy team by just giving players four through eight extra minutes (player four still only plays 33.6 minutes per game), and your top three play just as much as the top three on the other team.

In the end, I think this is still what Arturo was talking about.  The playoffs aren’t quite the same as the regular season because coaches shorten their bench and play the starters more minutes, which makes them more important.  But that doesn’t mean that a deeper team, who has equal talent that is more spread out, can’t compete.  It means that they have to be willing to shorten their bench even more than the other guy, to further cut out the weak contributions of the mid and deep bench players and emphasize the top 7 or 8 guys.  With the particular numbers I used, your top players could be 2 or 3 playoff wins worse and you can make it up by giving your middle players more minutes.  In the end, it comes down to a game of chicken: which coach is willing to run his best players the most?