The restoring force in basketball (or the “poor get richer” phenomenon)

Random Walk Picture of Basketball Scoring, a recent paper in JQAS, is well-worth a read; it’s one of those ideas that when I read about it, I thought “why had no one ever tried this before!?”

I wanted to share a quote from it that is incredibly intriguing and, after my brief searching, has never been expressed before:

The [ubiquitous feature augmenting random scoring in a basketball game] is the existence of a weak linear restoring force, in which the leading team scores at a slightly lower rate (conversely, the losing team scores at a slightly higher rate).  This restoring force seems to be a natural human response to an unbalanced game – a team with a large lead may be tempted to coast, while a lagging team likely plays with greater urgency.

The authors revisit this feature later in the article, but only so much as to re-describe the phenomenon and relate their adjustment approach to a common physics model.  I do not intend on talking about the implications or existence of this feature, but rather, I want to focus on its cause.

The authors, who admittedly approach this features origin naively, do not thoroughly explain why the phenomenon occurs, except to link it to a “natural human response” that has been referenced previously in economic competitions.  While I do not doubt that said response exists, I am skeptical that it is the most influencing component of this phenomenon.

Consider the strategy of a coach when his/her team is leading.  If the lead is often great enough, a coach may choose to bench their starters in hopes of keeping them fresh (and, thus, more efficient).  This would almost certainly decrease the talent level of the team in the lead.  In an effort to keep themselves in the game, the opposing coach often takes the corresponding risk by keeping their starters on the court during that time to exploit the temporary drop in talent.  A perfect example of this is this year’s Sweet 16 game between IU and UK, where Zeller stayed on the court with IU trailing when Davis went off, both of whom were in foul trouble.

A less obvious way that coaching strategy could lead to this “poor get richer” phenomenon can be found in the response to a team gaining a lead or going on a run that produces a lead: timeouts.  It’s almost exclusively the case that coaches take timeouts when there is very little time on the game clock or their opponent has been going on a scoring run.  In both of these scenarios, the coach taking the timeout is likely trailing the other team.  It’s also believable that a timeout “interrupts” the scoring ability of an opponent and increases a team’s chances of scoring in the next possession (note: what little research exists on the effect of timeouts has been shown it to be significantly in the favor of the team calling the timeout).  Thus, team’s down, who much more frequently call timeouts, would see themselves increasing their probability of scoring compared to play before the timeout.

There are likely other explanations for this restoring force (e.g. players are more often fatigued after scoring than after failing to score).  Regardless, I believe very strongly that this phenomenon, in general, deserves further attention.  What causes it?  Are we sure it’s a weak force?  Is this exclusive to basketball, a sport with infinite substitutions, or does this carry over into other sports like baseball, where roster depth places an even bigger role via relievers, removals after substitutions, etc.?

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I am Director of Data Science at Two Six Capital, Co-Founder of Krossover, Ph.D in Stats from Wharton and a proud Savannah-ian.

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