Goosing your Height

A fun post on reddit asked the question: “I hardly ever see a NBA player that is 6’2, is there a reason why?”

This asks two questions — first, is it actually true that there aren’t very many players that are 6’2″? Or is this just a recall bias? Second, if it’s true, why?

To verify the first question, I pulled all of the player heights from the current NBA rosters, and plotted the distribution of player heights in inches.

 heightsHist

What is interesting about this distribution is how weirdly unsmooth it is. There are three jumps that I have marked — between 5’11” and 6’0″, 6’2″ and 6’5″ and 6’6″. Height tends to be relatively bell-curved in its distribution (once you control for gender) and so these types of jumps are very bizarre. First, they suggest that the poster is absolutely correct in thinking it’s bizarre how few 6’2″ individuals he (or she) sees — there are far less than there should be. Second, many basketball players are skewing their heights upwards to 6 foot, 6’3, and 6’6. 

As for reasons why, I’m less sure. There is the easy answer that players tend to just inflate their heights — there’s no set measure on how do the measurement (shoes on or off?) and I don’t think the league particularly cares much. What is funny is the fact that someone cares enough to fake it. These sorts of habits probably begin in high school (I certainly remember saying I was six foot when I wasn’t quite there) and they just die hard.

Update: 

At the suggestion of a commentator on reddit, I pulled the pre-draft stats on height from DraftExpress. In the interest of speed, I just pulled the heights of everyone measured pre-draft, and plotted the distribution of heights.heightsDraftHist

 

In this case, we don’t see the same kinds of jumps — there is perhaps a little bit of funny stuff going on between 6 foot and 6’3, but that is likely more because of my bin choice (although I could be wrong). So this confirms our intuition that this is simply a reporting fact, not any underlying real selection factor. 

Paying to Win?

When Russian billionaire Mikhail Prokhorov bought the Nets in 2009, the only fact known by most American basketball fans was that he was extremely rich. Four years into his tenure as owner, his willingness to spend money has become obvious: this year alone, the Nets’ salary is $102 million, putting them at the top of the pile of NBA team salaries. This extraordinarily high salary reflects, on top of large salaries for Joe Johnson and Deron Williams,  the team’s trade for Paul Pierce and Kevin Garnett this past off-season. He himself, following the trade said that It’s not (my) way to wait 10 years for championship.”

Can an owner buy wins? Bulls fans often complain that owner Jerry Reinsdorf is particularly tight-fisted, and that given the income stream the Bulls bring in, he should open his wallet to ensure a championship team. And there really is quite a bit of variation in how much teams pay, as you can see below. The Nets top out at over 100 million, and the bargain basement Phoenix Suns set the bottom at roughly 53 million this year.  (Note: all data comes from http://storytellerscontracts.com/).

salaryPlot

 

Does a bigger salary translate into more success? The playoffs aren’t over, so I’ll focus on regular season performance (with the strong caveat that there may be a difference between a team that excels in the regular season and a playoff-oriented team). Below is a plot of every team’s total salary this season and winning percentage. Almost all of the teams line up near the middle on a positively sloped line, except for four teams that I’ve highlighted: the Nets, Lakers, Knicks and Celtics.  It’s possible to construct a lot of stories about these four teams — the Lakers are a cautionary tale of injuries (big injuries to Steve Nash and Kobe Bryant), while the Celtics took on several big contracts from the Nets in the trade this off-season (although last season they also had a large salary hit as well).

salaryWins

If we exclude these four teams, we get a strong relationship. While not perfect, this simple linear fit explains about 50% of the variation in win rates. According to this model, for every million dollars spent by a team, they should expect to increase their win rate by roughly a percentage point. A big caveat, of course, is that this is only one year of data. It may be that in other years that “big salary” teams like the Knicks and Nets do much better in the regular season and justify their salaries. The evidence seems to suggest that while higher salaries can translate to better performance on average it is no guarantee for success.

salaryWins2

Part of this may be due to restricted free agency and other parts of players contracts that make it possible for teams to hold onto the very best players. Hence, those players that teams like the Nets sign are free agents who are good, but not so good that they get held onto by their team. This would imply that drafting your superstar is extremely important (case in point: Tim Duncan). Alternatively, it may be the winner’s curse – teams bidding with incomplete information tend to overpay, and these big salary teams may be suffering from this (realistically, all players should cause the winner’s curse, but it may be that “superstars” cause more incomplete information).

In a future post, we’ll try to see how stable this relationship is, and how team salary relates to post-season performance.