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Re: When to leave a game?

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  • aaronkoo
    ... game theory ... seen journals ... to see ... sports would ... Game theory comes about from sports, but also from politics. It often focuses on political
    Message 1 of 6 , May 6, 2003
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      --- In APBR_analysis@yahoogroups.com, bchaikin@a... wrote:
      > Has anyone compiled such a thing? Is there research out there in
      game theory
      > journals that discuss this?
      >
      > is there really something such as a "game theory journal"? i've
      seen journals
      > for pretty much every branch of science, math, medicine, etc, but
      to see
      > something from academia that was actually keen to professional
      sports would
      > be neat...

      Game theory comes about from sports, but also from politics. It
      often focuses on political decisions. I know that was how I was
      introduced to "game theory" -- through Poli Sci 12 in college. Game
      theory rests on the fact that competing people have to outstrategize
      the opponent. Consider what they will do and try to optimally select
      a strategy to counter what they will do. The movie A Beautiful Mind
      was about John Nash, whose Nash Equilibrium theory is one of the
      centerpieces of game theory. This concept that there is an optimal
      set of strategies given the nature of the rules of a game helps
      determine both how to win and how to change the game so that the game
      itself arrives at better results (perhaps socioeconomically better,
      for example). Or, if we wanted to change basketball to increase
      scoring, we could wing it or you could do a serious analysis of what
      effect the rule changes may have, assuming that winning games is
      still the goal of all teams, regardless of pace.

      Besides that, I think SABR has an ongoing newsletter of baseball
      research. Chance magazine has statistical studies with one almost
      every issue on sports -- that's what I forwarded a little while ago.
      I wasn't very impressed with that article on pace management,
      though. They pretty much assumed the answer that they got, something
      I discussed with schtevie offline for a while.

      Not sure if there are any others.

      DeanO
    • igorkupfer@rogers.com
      ... From: aaronkoo To: APBR_analysis@yahoogroups.com Sent: Tuesday, May 06, 2003 4:18 PM Subject: [APBR_analysis] Re: When to leave a game?
      Message 2 of 6 , May 6, 2003
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        ----- Original Message -----
        From: aaronkoo
        To: APBR_analysis@yahoogroups.com
        Sent: Tuesday, May 06, 2003 4:18 PM
        Subject: [APBR_analysis] Re: When to leave a game?


        <snip, on game theory>

        > Besides that, I think SABR has an ongoing newsletter of baseball
        > research. Chance magazine has statistical studies with one almost
        > every issue on sports -- that's what I forwarded a little while ago.
        > I wasn't very impressed with that article on pace management,
        > though. They pretty much assumed the answer that they got, something
        > I discussed with schtevie offline for a while.
        >
        > Not sure if there are any others.
        >
        > DeanO


        Can you post some of your comments? I tried to follow the argument on the article, but
        the math was slightly beyond me.

        ed
      • aaronkoo
        ... on the article, but ... Will do. Hopefully tonight, but life/work may get in the way. Generally, they assumed that the percentage of possessions on which
        Message 3 of 6 , May 6, 2003
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          --- In APBR_analysis@yahoogroups.com, <igorkupfer@r...> wrote:
          >
          >
          > Can you post some of your comments? I tried to follow the argument
          on the article, but
          > the math was slightly beyond me.

          Will do. Hopefully tonight, but life/work may get in the way.

          Generally, they assumed that the percentage of possessions on which a
          team scored was optimal at some pace and lower at either a higher or
          lower pace. Then they simulated the games and, sure enough, the team
          won fewer games at higher and lower paces than at their optimal
          pace. My point has been that we don't know where that optimal pace
          is and that the optimal pace in basketball may be actually a large
          range of paces. The average time of a possession is about 15 s and I
          believe that teams perform about equally well whether they use 10 s
          or 20 s (beyond about 20 s, rather, with <=3s on the clock, they do
          worse).

          DeanO
        • aaronkoo
          ... something ... on the article, but ... p. 43: We remark that for simplicity we will think of a team s unconstrained mode as its best scoring offensive
          Message 4 of 6 , May 7, 2003
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            --- In APBR_analysis@yahoogroups.com, <igorkupfer@r...> wrote:
            > > I wasn't very impressed with that article on pace management,
            > > though. They pretty much assumed the answer that they got,
            something
            > > I discussed with schtevie offline for a while.
            > >
            > > Not sure if there are any others.
            > >
            > > DeanO
            >
            >
            > Can you post some of your comments? I tried to follow the argument
            on the article, but
            > the math was slightly beyond me.

            p. 43: "We remark that for simplicity we will think of a team's
            unconstrained mode as its best scoring offensive style of play versus
            the current opponent."

            This is the assumption that ruins everything. They assume that there
            is exactly one pace at which the teams is optimal, rather than an
            array of paces or a range of paces.

            p. 44: "A popular belief among sports analysts is that, when the
            score is tied or a team is ahead, a lengthy possession is better than
            a short possessions. Surprisingly this belief, as a general
            statement is false."

            This is the kind of analysis that is nice to do, but they biased
            their answer by assuming that a team gets worse by holding the ball.
            Now that may be true if they hold it too long -- I have seen that --
            but they need more to strengthen such a statement.

            Figures 1 through 3 use the notation (P, time units), where P is the
            probability of scoring and time units is how many time units each
            possession takes. Note that in each case, the intermediate time unit
            case (=2) has the highest P. If they had left all the P the same and
            just changed the pace, their arguments would have been potentially
            stronger, but now their results are clouded by changing P.

            Too bad.

            DeanO
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