Is basketball scoring a random walk?

by on September 22, 2011 at 4:24 am in Sports | Permalink

Not when there’s a strike on!  Otherwise, maybe so, as Gabel and Redner report (pdf):

We present evidence, based on play-by-play data from all 6087 games from the 2006/07–2009/10 seasons of the National Basketball Association (NBA), that basketball scoring is well described by a weakly-biased continuous-time random walk. The time between successive scoring events follows an exponential distribution, with little memory between different scoring intervals. Using this random-walk picture that is augmented by features idiosyncratic to basketball, we account for a wide variety of statistical properties of scoring, such as the distribution of the score difference between opponents and the fraction of game time that one team is in the lead. By further including the heterogeneity of team strengths, we build a computational model that accounts for essentially all statistical features of game scoring data and season win/loss records of each team.

For the pointer I thank Michelle Dawson.

1 Sandy September 22, 2011 at 7:50 am

So the paper tries to show that, like the concept of the individual “hot hand”, the concept of “momentum” does not stand up to the data. The authors analyse patterns in scoring in basketball while controlling for the effects of “human nature” (i.e. the leading team relaxing and the trailing team working harder) and the fact that ball-possession changes after a score in basketball.

It makes me wonder if they also thought about looking at the effects of calling a time out. It is pretty standard coaching practice, at all levels including the NBA, to call a time-out when the opposing team makes a big run. The underlying assumption being that in doing so a coach can dissipate the “momentum” the opposing team has generated. Could it be that strategies employed by one team to counteract “momentum” are successful in decreasing the likelihood that a run will continue? So calling time-out makes it less likely the team on the run will continue to score, and thus decreases any time correlation in scoring probabilities.

By analogy, for the individual with a “hot-hand”, I suppose from experience that defence gets much tighter on a player who has scored a lot recently, making his shots more difficult. This plays a big role, again I suppose, in decreasing the chances that his/her hot shooting will continue.

I have never understood how, in the words of this article, “impartial analysis” can lead to the conclusion that the “hot-hand” for an individual, or “momentum” for a team do not exist. The analogy here is that there are no such things as “hot dice” or “hot coins”, where the string of heads that one has flipped means the next flip is like to be heads, for example. Clearly, for the coin or the dice, the probabilities are independent because nothing in the coin or its environment has changed.

In sports, however, it is not nearly so clear. In most sports, it is possible that both the player or team has (internally/psychologically) changed, and that the environment/opponent has changed. How one can conclude from the a situation where outcomes are jointly produced by a player and his/her environment/opponent that the player only has one objective state, i.e. that “hot” or “cold” do not exist, is beyond me. But I would be grateful for some enlightenment.

2 Mo September 22, 2011 at 10:50 am

By analogy, for the individual with a “hot-hand”, I suppose from experience that defence gets much tighter on a player who has scored a lot recently, making his shots more difficult. This plays a big role, again I suppose, in decreasing the chances that his/her hot shooting will continue.

Not to mention, “hot” shooters tend to take difficult heat check shots as they gain confidence that everything they’re shooting is going in. The hot hand studies do not take into account defense or shot location.

3 jtg September 22, 2011 at 12:49 pm

I believe the point of the paper is that they have constructed a random walk model that matches the observed data — which is very unlikely if the underlying process is not stochastic.

They built a pretty simple model of scoring that produces output that matches the real world data on several fronts along entire seasons — scoring distributions, streaks, % of game time spent leading, season long team winning percentages.

Their model has 3 parts:
intrinsic team scoring probability
an anti-persistence factor (possession changes hands, so Team B is more likely to score after Team A scores)
a weak restoring factor (the odds of Team A scoring next decrease as Team A’s lead grows)

So the model accounts for factors like time-outs, momentum, urgency, etc with the weak restoring factor. (.0022*delta in their model). Their model has a weak rubber-band effect bias to keep game scores close. They added this factor to fit the data.

I’m no stats expert, that’s just my take from a quick read of their paper.

4 MD September 22, 2011 at 9:06 am

Lockout, not strike.

5 Gene Callahan September 22, 2011 at 11:55 am

“I have never understood how, in the words of this article, “impartial analysis” can lead to the conclusion that the “hot-hand” for an individual, or “momentum” for a team do not exist.”

Right. They can’t. The conclusions go way beyond the data that supposedly supports them.

6 Walt French September 28, 2011 at 1:13 am

One thing that WOULD exist whether streaks predict subsequent success, is the likely enthusiasm from having hit your last 5 three-pointers. That’d lead you to attempt riskier shots. If you are normally too conservative — and I’ve seen a wonderful paper on the PGA which shows even the pros leave huge amounts of money on the table by worrying about par on a per-hole versus per-round basis — then the enthusiasm will increase your odds of success and therefore the existence of streaks beyond unconditional percentages.

In fact, given the known subjective biases, a *lack* of such findings seems suspect.

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