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Do Star Players Make Good Head Coaches?
In the N.B.A. they do, say Lawrence Kahn of Cornell, and Amanda Goodall and Andrew Oswald of Cornell and Warwick University:
We measure the success of National Basketball Association (NBA) teams between 1996 and 2004, and then attempt to work back to the underlying causes. We have information on 15,040 regular season games for 219 coach-season observations, for which we compute winning percentages; in addition, we study post-season playoff success for these coaches. Perhaps unsurprisingly, a main explanatory factor is the quality of the group of players. But, less predictably, there seem also to be clear effects from the nature of a teams coach. Teams perform substantially better if led by a coach who was, in his day, an outstanding player. This correlation is, to our knowledge, unknown even to experts in basketball (perhaps because, without statistical methods, it is hard to glean from even detailed day-to-day observation of the sport).

Is the same result true for other sports? A simple look at the best managers in the history of baseball makes me think it's not. The average OPS+, a good measure of offensive ability, for managers that managed at least 1,000 games and where offensive players during their careers is 94. A number above 100 means better than average, and below 100 means worse than average. So, the average best manager was less-than-average during his playing days. The same metric for all players in MLB history who had at least 3,000 at-bats is 104.
(Hat tip: Andrew Leigh)
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