## Re: The Numbers Experiment Results and Explanation

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• ... Let me self-identify as one of the zeros, as someone who knew the equilibrium, and someone who knew he was going to lose. Why follow this course? Well,
Message 1 of 15 , Jun 29, 2004
--- In APBR_analysis@yahoogroups.com, "Dean Oliver" <deano@r...> wrote:
>
> So the experiment was to have people pick a number between 0 and 100.
> The person that gets closest to 0.67 times the average of all the
> numbers selected wins.
>
> With 33 people sending in their numbers, we ended up with an average
> of 27.2, which means that the winning number is 18.2, which is closest
> to what Felipe Jacobsen Junqueira guessed, having guessed 19.
>
> This game is interesting to me because it illustrates the case of If
> everyone does this and I do this, I win, but if everyone knows I'll do
> that, they may do something else, so I should do something else, ad
> infinitum. The so-called "equilibrium" of this game is for everyone
> to choose 0, assuming that we all think deep and hard about what
> everyone else should be doing. And I did get 2 guesses of 0 and 7
> other guesses under 10. But, as I heard in a talk recently, guessing
> 0 is just never going to win (not even when the game is played by game
> theory professors). Picking 0 is, in a sense, overthinking. The talk
> I saw called different guesses representations of how many levels of
> thinking are going on. A guess of 50 is 1-level thinking, a guess of
> 33 is 2-level, a guess of 22 is 3-level, a guess of 14 is 4-level,
> etc. As a group, we ended up at about 2.5-level (not sure where NBA
> GMs and head coaches would end up). We had a lot of people selecting
> numbers around 33. We got a couple very high numbers and, after
> asking a couple people who did that, it sounded like they were chosen
> to throw everyone else off, an interesting choice not to be dismissed.

Let me self-identify as one of the zeros, as someone who knew the equilibrium, and
someone who knew he was going to lose. Why follow this course? Well, besides the fact
that the expected prize was equal to my guess, the motivation was the flip side to the
highenders, it was to throw everyone else on: Long Live the Theory.

But more interesting to me than the game was trying to anticipate the relevance to
basketball. And the example comes from....

> The talk where I saw this was actually a sports-analysis session down
> in LA for a number of investment firms looking at sports for analogies
> to improve what they're doing (or just because it's cool). Strategy
> in understanding what everyone else is doing is definitely part of the
> analysis. In basketball, one of the obvious ways this comes about is
> calling plays out of timeouts. One team designs a play to run, but
> defensive coaches now switch up defenses a lot at timeouts, something
> the NBA does now that they can switch defenses. So now the offense
> has to make an assumption about what defense they will see and design
> the play for that. And, of course, the defense can realize the
> offense realizes this and do something else. Or, what I think is
> happening, is that offenses now call 2 plays at timeouts.

...but I remain entirely unpersuaded that "gamesmanship" is very important in basketball.
This is not to say that a team should not call (at a minimum) two plays on an inbounds
pass; that is clearly optimal to deal with "unexpected" defensive responses. Rather,
basketball seems to me built around, let's call them, dominant strategies. That is to say,
on any given trip down the court, there is an offensive team's best option and a defensive
team's best response, then there are best secondary options if the primary options are
shut down and means to acheive them (screens, passes, and player movement). And then
randomness comes to play...that's the way the ball bounces.

> It definitely takes a while for NBA teams to take advantage of rules,
> but it does eventually happen.

I agree with this, with the emphasis on "a while" - and even when strategies are clearly
dominant. What interests me regarding this point are other peoples opinions on the
degree to which teams willfully diverge from dominant strategies - so defined.

Apparently, the Lakers were reluctant to keep going to Shaquille in the Finals, even
though his ability to score was far greater than the next best teammate (as evidenced by
the actual scoring %ages). And if a well-coached team cannot do what is best for
themselves when the stakes couldn't be higher, it perhaps doesn't speak well of expected
"average" performance.
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