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WNBA turnaround: a mathematical approach

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  • Charles Steinhardt
    I once looked at the question of whether baseball teams were streaky from a mathematical point of view. For anybody familiar with generating functions I d
    Message 1 of 11 , Aug 17, 2001
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      I once looked at the question of whether baseball teams were "streaky"
      from a mathematical point of view. For anybody familiar with generating
      functions I'd be happy to explain the basic approach, though I don't have
      time now (work keeps me *very* busy at the moment).

      However, the correct mathematical approach (which can be exact or
      approximate, as this approach will give you an series to sum for the
      probability) is to, in this case, assume that there are randomly 18 wins
      and 14 losses put together and to look at all 32!/(18!14!) combinations
      for how many have a longest streak of exactly N wins or losses. This can
      be solved directly if in a messy way, and I'll see if I still have my
      program for summing the series that I wrote a few years ago.

      If I don't, then I might be able to rewrite it if I have time.

      The answer for baseball, if you're curious, was that teams have many more
      streaks than expected of length 3-4, many fewer of length 5 or 6, and
      many more of length 8+.

      This can be explained to a large extent by noting that every 5 games, a
      team will have its best and its worst pitchers both pitching, and a team's
      performance is most sensitive (by far!) to its starting pitcher.

      In basketball, I might guess that there would be fewer streaks than
      expected of any length greater than about 3 because the homestands are so
      short and because basketball is so sensitive to the home team. For
      example, in baseball when I did my study, the home team was .511 in the
      previous decade. In basketball I don't know that number, but from seeing
      the best teams in the league frequently just break .500 on the road
      (particularly the Celtics back when they were very good), I might guess
      the home winning percentage to be around .625 or so, good enough to skew
      this sort of result.

      Then again, the other major difference is that in baseball the best team
      in the league will lose to the worst team about 1/3 of the time. In
      basketball, this would be more like 1/20 of the time I believe, or
      certainly more than their records alone would indicate. So while in
      baseball I could generally make the assumption that beyond the length of
      one 3-4 game series (the reason for more of those streaks IMO) the
      schedule was about constant, in basketball this is not true.

      Any thoughts?




      >
      >
      > On Thu, 16 Aug 2001, Dean Oliver wrote:
      >
      > >
      > > I did a quick analysis of the Charlotte Sting, who went 1-10 to start
      > > the season and 17-4 to end the season, to finish at 18-14. I'd like
      > > to do a historical search for streaks of this kind in any league, but
      > > knowing that such a search takes time and doing math doesn't, I
      > > figured I'd present the odds of such a thing occurring.
      > >
      > > Using basic binomial probability theory, the odds of a true 0.563 team
      > > going 1-10 or worse over 11 games is 0.17% (not 17%, 0.17%). Really
      > > low. The chances of a true 0.563 team going 17-4 or better in 21
      > > games is 1.67%. The odds of having both things happening is 0.00285%
      > > (the two numbers multiplied together), ridiculously low. I don't
      > > think I did anything wrong. If anything, a true Bayesian analysis
      > > would arrive at a lower number (it doesn't assume that the team is
      > > truly 0.563).
      > >
      > > So, now can anyone help me find the history of teams that might have
      > > had such streaks in one season? This is truly amazing. (The odds
      >
      > Though you conclusion is correct, I don't think the formula you used is
      > correct. E.g. if a team goes 1-10, with a true probability of winning of
      > .563, then although that event may have a 0.17% probability of occuring,
      > the next event, going 17-4, has a *100%* probability of occuring. Because
      > once a team goes 1-10, if it's going to end up 18-14, it HAS to go 17-4
      > the rest of the way.
      >
      > I.e. we're looking at a team with a fixed 18-14 record (not a random
      > sample of 32 games), and have to use "sampling without replacement"
      > methods rather than "sampling with replacement", as the binomial equation
      > assumes.
      >
      >
      > I think (I'm not sure) that the correct formula is along these lines:
      > there are 32 games, and 18 victories. If we look at the first 11 games,
      > and then the last 21 games, let's call those the "first portion" and "last
      > portion" of the season. How many different combinations are there of
      > winning 0 or 1 games in the first portion (and therefore 17 or 18 in the
      > last portion)?
      >
      > A bit of notation: xCy (pronounced "x choose y") is the combinatoric
      > function [more commonly written like this: ( x ) ].
      > y
      >
      > The formula for xCy is x!/(y!(x-y)!), where ! means factorial.
      >
      > Let "w" stand for the number of wins in the first portion of the season.
      > Then, looking at the first portion, there are 11Cw ways of winning w games
      > in the first portion. The Sting will therefore have won 18-w games in the
      > last portion of the season, with 21C(18-w) ways of doing this. Total
      > number of combinations for w wins is:
      >
      > 11Cw * 21C(18-w)
      >
      > For w = 0 and 1, this is
      >
      > 11C0 * 21C18 plus
      > 11C1 * 21C17
      >
      >
      > which is
      >
      > 1 * (21*20*19/3*2*1) plus
      > 11 * (21*20*19*18/4*3*2*1)
      >
      > or
      >
      > 1,330 plus 65,835 =
      > 67,165 ways for the Sting to win 0 or 1 games in their first 11
      >
      >
      > How many combinations of 18 wins and 14 defeats are there? The answer is
      > 32C18, which is 471,435,600 (there's danger of memory overflows with
      > factorials this big, so I confirmed this calculation by summing all the
      > 11Cw * 21C(18-w) values for w = 0 to 11).
      >
      > So the probability of the Sting winning 0 or 1 games in their first 11 is
      > 65,385 / 471,435,600 = .00001425, or .001425%.
      >
      >
      > This is exactly half of the figure that you came up with, which is
      > probably not a coincidence, though I can't figure out what the reason for
      > the relationship would be. (Possibly, either you or I made an arithmetic
      > mistake somewhere.)
      >
      >
      >
      > --MKT
      >
      >
      > To unsubscribe from this group, send an email to:
      > APBR_analysis-unsubscribe@yahoogroups.com
      >
      >
      >
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      >
      >
      >
    • Dean Oliver
      ... is ... winning of ... occuring, ... Because ... 17-4 ... The multiplication of the two numbers doesn t seem quite right. My calculations would have been
      Message 2 of 11 , Aug 17, 2001
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        --- In APBR_analysis@y..., "Michael K. Tamada" <tamada@o...> wrote:
        >
        > Though you conclusion is correct, I don't think the formula you used
        is
        > correct. E.g. if a team goes 1-10, with a true probability of
        winning of
        > .563, then although that event may have a 0.17% probability of
        occuring,
        > the next event, going 17-4, has a *100%* probability of occuring.
        Because
        > once a team goes 1-10, if it's going to end up 18-14, it HAS to go
        17-4
        > the rest of the way.
        >

        The multiplication of the two numbers doesn't seem quite right. My
        calculations would have been the same (except for the multiplication)
        if it was a team that went 180-140. The assumption that it is a 0.563
        team is where traditional statistics fail in comparison to Bayesian
        stats. The bigger question that Bayesian can help with is whether
        this team truly is a 0.563 team. Their victory over Cleveland last
        night suggests even further that they're better than a 0.563 team.

        I just use the BINOMDIST() function in excel to calculate the
        probabilities of exceedences. This function assumes a fixed
        probability of winning (0.563 in this case). Then it calculates the
        chances of a certain number of victories in a certain number of games.

        What you're looking at are the number of ways to get to 18-14 and the
        chances that they do it the way they did. That is probably a better
        way to calculate the odds of both such streaks occurring in the
        season.

        > I.e. we're looking at a team with a fixed 18-14 record (not a random
        > sample of 32 games), and have to use "sampling without replacement"
        > methods rather than "sampling with replacement", as the binomial
        equation
        > assumes.
        >

        > So the probability of the Sting winning 0 or 1 games in their first
        11 is
        > 65,385 / 471,435,600 = .00001425, or .001425%.
        >
        >
        > This is exactly half of the figure that you came up with, which is
        > probably not a coincidence, though I can't figure out what the
        reason for
        > the relationship would be. (Possibly, either you or I made an
        arithmetic
        > mistake somewhere.)

        Hmm. You calculate lower odds than I. I would have expected higher,
        if anything. Either way, we seem to be saying that the odds of such a
        season (assuming that 0.563 is their true p_win) are ridiculously low.
        This is going to be the case even if you look at home/road
        distribution or at the quality of competition (which was something of
        a factor for Charlotte).

        (Ignore my comment in my previous email about 0.17% vs. 0.14% -- I was
        trying to work on memory and mine is horrible.)

        The apparent big factor in turning Charlotte around was improved
        defense. This seemed to have been sparked by placing Tammy
        Sutton-Brown in the starting lineup over Machanguana (who they got
        for defense, ironically). The team was 16-3 with her starting, I
        believe (I can check tonight). Allison Feaster, despite her 3-point
        shooting, might also have been most influential on the defensive
        end, but I don't have a lot of evidence for that. On the offensive
        side, somehow they got Dawn Staley to cut down on her turnovers, but
        that was not as big as the defensive turnaround.

        Dean Oliver
        Journal of Basketball Studies
      • Dean Oliver
        ... streaky ... generating ... have ... Horrible how work gets in the way of actual quality science. ... more ... and ... games, a ... team s ... Pitching
        Message 3 of 11 , Aug 17, 2001
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          --- In APBR_analysis@y..., Charles Steinhardt <charles@p...> wrote:
          >
          > I once looked at the question of whether baseball teams were
          "streaky"
          > from a mathematical point of view. For anybody familiar with
          generating
          > functions I'd be happy to explain the basic approach, though I don't
          have
          > time now (work keeps me *very* busy at the moment).
          >

          Horrible how work gets in the way of actual quality science.

          >
          > The answer for baseball, if you're curious, was that teams have many
          more
          > streaks than expected of length 3-4, many fewer of length 5 or 6,
          and
          > many more of length 8+.
          >
          > This can be explained to a large extent by noting that every 5
          games, a
          > team will have its best and its worst pitchers both pitching, and a
          team's
          > performance is most sensitive (by far!) to its starting pitcher.
          >

          Pitching and the 4-5 man rotation really is important in analyzing
          baseball streaks. I can't think of any other sports like this.

          > In basketball, I might guess that there would be fewer streaks than
          > expected of any length greater than about 3 because the homestands
          are so
          > short and because basketball is so sensitive to the home team. For
          > example, in baseball when I did my study, the home team was .511 in
          the
          > previous decade. In basketball I don't know that number, but from
          seeing
          > the best teams in the league frequently just break .500 on the road
          > (particularly the Celtics back when they were very good), I might
          guess
          > the home winning percentage to be around .625 or so, good enough to
          skew
          > this sort of result.
          >

          Basketball is between 58% and about 65% typically. It's a strong
          force. I'd love to understand why it's so much more important. We
          can qualitatively say that the fans are much closer, but we should
          also be able to say that baseball teams can tailor their teams to the
          quirkiness of their ballpark. I guess the emotional power is
          stronger.

          > Then again, the other major difference is that in baseball the best
          team
          > in the league will lose to the worst team about 1/3 of the time. In
          > basketball, this would be more like 1/20 of the time I believe, or
          > certainly more than their records alone would indicate. So while in
          > baseball I could generally make the assumption that beyond the
          length of
          > one 3-4 game series (the reason for more of those streaks IMO) the
          > schedule was about constant, in basketball this is not true.

          First, a 65-17 team vs. a 17-65 team should win about 94% of the time,
          so good guess.

          Second, in baseball, a 104-58 team vs. a 58-104 team should win about
          76% of the time, so about 3/4, not 2/3.

          Basketball streakiness should be pretty much on par with what stats
          predict, I'd think. NBA teams don't have too many long homestands
          (the 7 game streak John brought up notwithstanding) to bias those
          streaks. They don't play too many home-home matchups, so their season
          ends up a pretty good random sampling through time. If the East or
          West is particularly weak, that might have an effect.

          Dean Oliver
          Journal of Basketball Studies
        • Charles Steinhardt
          ... Well, the other work I m doing is (hopefully) quality science too... :) ... I might suggest a few things, though admittedly without facts to back them up.
          Message 4 of 11 , Aug 17, 2001
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            On Fri, 17 Aug 2001, Dean Oliver wrote:

            > --- In APBR_analysis@y..., Charles Steinhardt <charles@p...> wrote:
            > >
            > > I once looked at the question of whether baseball teams were
            > "streaky"
            > > from a mathematical point of view. For anybody familiar with
            > generating
            > > functions I'd be happy to explain the basic approach, though I don't
            > have
            > > time now (work keeps me *very* busy at the moment).
            > >
            >
            > Horrible how work gets in the way of actual quality science.
            >

            Well, the other work I'm doing is (hopefully) quality science too... :)

            > Pitching and the 4-5 man rotation really is important in analyzing
            > baseball streaks. I can't think of any other sports like this.
            >
            > > In basketball, I might guess that there would be fewer streaks than
            > > expected of any length greater than about 3 because the homestands
            > are so
            > > short and because basketball is so sensitive to the home team. For
            > > example, in baseball when I did my study, the home team was .511 in
            > the
            > > previous decade. In basketball I don't know that number, but from
            > seeing
            > > the best teams in the league frequently just break .500 on the road
            > > (particularly the Celtics back when they were very good), I might
            > guess
            > > the home winning percentage to be around .625 or so, good enough to
            > skew
            > > this sort of result.
            > >
            >
            > Basketball is between 58% and about 65% typically. It's a strong
            > force. I'd love to understand why it's so much more important. We
            > can qualitatively say that the fans are much closer, but we should
            > also be able to say that baseball teams can tailor their teams to the
            > quirkiness of their ballpark. I guess the emotional power is
            > stronger.
            >

            I might suggest a few things, though admittedly without facts to back them
            up. Certainly the proximity of the fans (and buildings designed for
            maximum noise - look at the decibel level in Utah during the playoffs
            sometime!) helps. Some other ideas:

            1) The rotation is an equalizer in baseball. More to the point, the best
            teams in basketball have a much better winning percentage than in
            baseball.

            2) There is no equivalent of the free throw in baseball, and in fact all
            new stadia are forced to put some sort of blue/black screen in
            straightaway center so that the batter has a good line of sight. Fans can
            have a very direct impact in basketball that I'd guess is worth as much as
            5 points per game (some in increasing the home FT%, some in decreasing
            that of opponents. Maybe somebody has statistics on this?

            3) Basketball is by its very nature a faster-paced game than baseball and
            thus more prone to momentum-based runs. In baseball, it's always easy for
            the struggling team to take the equivalent of a timeout. Can you imagine
            what basketball would be like if there were a 20" timeout after every
            posession? Whatever else you'd expect, I'd think that game would be less
            prone to long runs. Limited timeouts increase the value of momentum, and
            a home crowd is helpful in that respect.

            4) Basketball is a younger sport than baseball, and as a result there are
            many fewer traditional fans of one team that end up in another market. In
            addition, the markets are a little bit better spaced than in baseball and
            include a few more cities that only have one sports team. As a result,
            95% of the fans at a game will be home fans. I was recently at a
            Yankees-Phillies game in Philadelphia at which there were 55000 people,
            about 40000 of them Yankees fans. In that atmosphere any home crowd
            advantage must go away.

            5) Basketball generally sells out, whereas baseball only does in select
            markets. 10000 people at an Expos game isn't going to provide much of an
            advantage, and if anything all those empty seats could be demoralizing.

            6) Baseball can tailor its field to one or two hitters, but rarely an
            entire lineup of 8 or 9 people as well as pitchers. That is to say, the
            park can favor pitching or hitting, and can favor right- or left-handed
            hitters, but any pro team has all of those. So this effect should be
            minor, if any, and is mostly in relation to how fielders react to
            different plays. In addition, with the unbalanced schedule most teams
            that visit play there 8 or 9 games a year, and the rest 3 or 4. So there
            is plenty of time to adjust to a park for a veteran or even by the end of
            a series for a rookie. Incidentally, basketball does have its share of
            home-court advantages if you know where to look: I remember that before
            the Celtics moved out of the Garden, there used to be well-placed/hidden
            dead spots in the parquet for example. But certainly it's not as
            prevalent - basketball doesn't exactly have ground rules to worry about.
            Then again, there were a bunch of complaints a few years ago about playoff
            rims (I forget where) being bad for jump shooters and favoring the home
            team with a strong inside game. And, in basketball one can tailor the
            team's style of play to almost always take inside shots much better than
            in baseball one can get a group of players to always hit to left field,
            say.






            > > Then again, the other major difference is that in baseball the best
            > team
            > > in the league will lose to the worst team about 1/3 of the time. In
            > > basketball, this would be more like 1/20 of the time I believe, or
            > > certainly more than their records alone would indicate. So while in
            > > baseball I could generally make the assumption that beyond the
            > length of
            > > one 3-4 game series (the reason for more of those streaks IMO) the
            > > schedule was about constant, in basketball this is not true.
            >
            > First, a 65-17 team vs. a 17-65 team should win about 94% of the time,
            > so good guess.
            >
            > Second, in baseball, a 104-58 team vs. a 58-104 team should win about
            > 76% of the time, so about 3/4, not 2/3.
            >

            Where are you getting these numbers? Either way, the difference is again
            in the rotation. That 104-58 team usually has starters with the following
            records (let's say records when the team has them start, including W/L by
            the bullpen)

            A: 27-6
            B: 24-9
            C: 19-13
            D: 18-14 (usually a collection of people in this slot at this point)
            E: 16-16

            Some have 3 top starters and two worse ones.

            Meanwhile, the worst team will have pretty much the reverse, with those
            last couple of slots usually a collection of people promoted and demoted
            from starting or from AAA ball. That worst team also will very often
            juggle the rotation to try to win one from the best team, as they're not
            in a pennant race anyway but know that they'll have more people watching
            the game against the good team and want to impress potential fans (and
            play the role of spoiler). As a result, at least one of the three games
            in the series will give the worst team an even chance or better of
            winning, and quite possibly another. As a result, one rarely sees the
            best team in the league sweep the worst team, or at least it is more rare
            than you might predict.

            In basketball, this is not the case. The teams are pretty much the same,
            pending injuries/suspensions.


            > Basketball streakiness should be pretty much on par with what stats
            > predict, I'd think. NBA teams don't have too many long homestands
            > (the 7 game streak John brought up notwithstanding) to bias those
            > streaks. They don't play too many home-home matchups, so their season
            > ends up a pretty good random sampling through time. If the East or
            > West is particularly weak, that might have an effect.
            >

            I might expect otherwise for a few reasons:

            1) Prevalence of young players. Meaning that veteran teams should do a
            little better in the first half of the season and young teams in the
            second half rather than being constant (does somebody have stats on this
            one?)

            2) Coaches make adjustments including an overhaul of the offense/defense
            midseason if they struggle. Should cause the team to play differently,
            one way or the other.

            3) Relative importance of injuries. Baseball is not so sensitive to the
            injury even of a superstar. For example, the Red Sox this year are 66-53
            without the best pitcher in the game, an all-star catcher, an all-star
            shortstop, and a bunch of other players that are important to their team
            all for at least a month (and in the case of the SS and C, 3 months).
            With no injuries, they should not be better than about 72-47, and even
            that would be a very impressive record for this group of players.
            However, what would the Magic have done with Grant Hill last year? The
            Sixers without Iverson? While baseball doesn't have a lower injury rate
            than basketball, an injury to one of five starters is more critical, and
            thus more likely to affect the team's performance. Particularly an
            important starter.

            I'd be interested to see some statistics on this, particularly if somebody
            actually tried to calculate the effect of different injuries/potential
            injuries.

            -Charles

            > Dean Oliver
            > Journal of Basketball Studies
            >
            >
            > To unsubscribe from this group, send an email to:
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            >
            >
            >
            > Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
            >
            >
            >
          • Dean Oliver
            ... Lucky bum. ... baseball and ... easy for ... imagine ... every ... less ... momentum, and ... I have my doubts about this given the general info suggesting
            Message 5 of 11 , Aug 17, 2001
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              --- In APBR_analysis@y..., Charles Steinhardt <charles@p...> wrote:

              >
              > Well, the other work I'm doing is (hopefully) quality science too...
              :)

              Lucky bum.


              > 3) Basketball is by its very nature a faster-paced game than
              baseball and
              > thus more prone to momentum-based runs. In baseball, it's always
              easy for
              > the struggling team to take the equivalent of a timeout. Can you
              imagine
              > what basketball would be like if there were a 20" timeout after
              every
              > posession? Whatever else you'd expect, I'd think that game would be
              less
              > prone to long runs. Limited timeouts increase the value of
              momentum, and
              > a home crowd is helpful in that respect.
              >

              I have my doubts about this given the general info suggesting that
              within game streaks don't exist. (I'm not convinced about the
              validity of that research either.)

              > 4) Basketball is a younger sport than baseball, and as a result
              there are
              > many fewer traditional fans of one team that end up in another
              market. In
              > addition, the markets are a little bit better spaced than in
              baseball and
              > include a few more cities that only have one sports team. As a
              result,
              > 95% of the fans at a game will be home fans. I was recently at a
              > Yankees-Phillies game in Philadelphia at which there were 55000
              people,
              > about 40000 of them Yankees fans. In that atmosphere any home crowd
              > advantage must go away.
              >

              You haven't been to Golden St, have you?

              > 5) Basketball generally sells out, whereas baseball only does in
              select
              > markets. 10000 people at an Expos game isn't going to provide much
              of an
              > advantage, and if anything all those empty seats could be
              demoralizing.
              >

              Uh, Golden St. again.

              > 6) Baseball can tailor its field to one or two hitters, but rarely
              an
              > entire lineup of 8 or 9 people as well as pitchers. That is to say,
              the
              > park can favor pitching or hitting, and can favor right- or
              left-handed
              > hitters, but any pro team has all of those. So this effect should
              be
              > minor, if any, and is mostly in relation to how fielders react to
              > different plays. In addition, with the unbalanced schedule most
              teams
              > that visit play there 8 or 9 games a year, and the rest 3 or 4. So
              there
              > is plenty of time to adjust to a park for a veteran or even by the
              end of
              > a series for a rookie. Incidentally, basketball does have its share
              of
              > home-court advantages if you know where to look: I remember that
              before
              > the Celtics moved out of the Garden, there used to be
              well-placed/hidden
              > dead spots in the parquet for example. But certainly it's not as
              > prevalent - basketball doesn't exactly have ground rules to worry
              about.
              > Then again, there were a bunch of complaints a few years ago about
              playoff
              > rims (I forget where) being bad for jump shooters and favoring the
              home
              > team with a strong inside game. And, in basketball one can tailor
              the
              > team's style of play to almost always take inside shots much better
              than
              > in baseball one can get a group of players to always hit to left
              field,
              > say.
              >
              >

              Well, other than the old Boston Garden, I don't remember hearing of
              any physical reason for an arena to favor one team over another.


              > > First, a 65-17 team vs. a 17-65 team should win about 94% of the
              time,
              > > so good guess.
              > >
              > > Second, in baseball, a 104-58 team vs. a 58-104 team should win
              about
              > > 76% of the time, so about 3/4, not 2/3.
              > >
              >
              > Where are you getting these numbers? Either way, the difference is

              Bill James:

              Win% Team A vs. Team B



              >
              > > Basketball streakiness should be pretty much on par with what
              stats
              > > predict, I'd think. NBA teams don't have too many long homestands
              > > (the 7 game streak John brought up notwithstanding) to bias those
              > > streaks. They don't play too many home-home matchups, so their
              season
              > > ends up a pretty good random sampling through time. If the East
              or
              > > West is particularly weak, that might have an effect.
              > >
              >
              > I might expect otherwise for a few reasons:
              >
              > 1) Prevalence of young players. Meaning that veteran teams should
              do a
              > little better in the first half of the season and young teams in the
              > second half rather than being constant (does somebody have stats on
              this
              > one?)

              Testable. However, the general hypothesis has actually been the other
              way around. Young players supposedly hit a wall and do worse in the
              2nd half. I tend to think you're right, but have had a hard time
              testing it, not having a very up-to-date player directory with
              birthdays.

              >
              > 2) Coaches make adjustments including an overhaul of the
              offense/defense
              > midseason if they struggle. Should cause the team to play
              differently,
              > one way or the other.
              >

              No difference between baseball and basketball on this one.

              > 3) Relative importance of injuries. Baseball is not so sensitive to
              the
              > injury even of a superstar. For example, the Red Sox this year are
              66-53
              > without the best pitcher in the game, an all-star catcher, an
              all-star
              > shortstop, and a bunch of other players that are important to their
              team
              > all for at least a month (and in the case of the SS and C, 3
              months).
              > With no injuries, they should not be better than about 72-47, and
              even
              > that would be a very impressive record for this group of players.
              > However, what would the Magic have done with Grant Hill last year?
              The
              > Sixers without Iverson? While baseball doesn't have a lower injury
              rate
              > than basketball, an injury to one of five starters is more critical,
              and
              > thus more likely to affect the team's performance. Particularly an
              > important starter.
              >
              > I'd be interested to see some statistics on this, particularly if
              somebody
              > actually tried to calculate the effect of different
              injuries/potential
              > injuries.

              The problem is always how you replace a superstar. If you replace
              them with a bad player, the team gets much worse. The Bulls without
              Jordan actually did pretty well the first year, then suffered the
              next. The Sixers did play a few without Iverson this year, so we can
              check. The Raptors without Vince. I am forming this unjustified
              opinion in my head that teams that play 1-3 games without their
              superstar generally do about the same. Teams that play more than
              about 10 games without their superstar really start to hurt. I need
              to form the hypothesis a little better, but I think I've seen it.

              Dean Oliver
              Journal of Basketball Studies
            • Dean Oliver
              Forgot to finish the formula on Win% calculations... ... is ... Win%A_B = [Win%A*(1-Win%B)]/[Win%A*(1-Win%B)+(1-Win%A)*Win%B]
              Message 6 of 11 , Aug 17, 2001
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                Forgot to finish the formula on Win% calculations...

                >
                > > > First, a 65-17 team vs. a 17-65 team should win about 94% of the
                > time,
                > > > so good guess.
                > > >
                > > > Second, in baseball, a 104-58 team vs. a 58-104 team should win
                > about
                > > > 76% of the time, so about 3/4, not 2/3.
                > > >
                > >
                > > Where are you getting these numbers? Either way, the difference
                is
                >
                > Bill James:
                >
                > Win% Team A vs. Team B
                >

                Win%A_B = [Win%A*(1-Win%B)]/[Win%A*(1-Win%B)+(1-Win%A)*Win%B]

                http://www.rawbw.com/~deano/methdesc.html#matchup

                has the detailed info.
              • Dean LaVergne
                ... From: Charles Steinhardt [mailto:charles@princeton.edu] 2) There is no equivalent of the free throw in baseball, and in fact all new stadia are forced to
                Message 7 of 11 , Aug 17, 2001
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                  -----Original Message-----
                  From: Charles Steinhardt [mailto:charles@...]



                  2) There is no equivalent of the free throw in baseball, and in fact all
                  new stadia are forced to put some sort of blue/black screen in
                  straightaway center so that the batter has a good line of sight.  Fans can
                  have a very direct impact in basketball that I'd guess is worth as much as
                  5 points per game (some in increasing the home FT%, some in decreasing
                  that of opponents.  Maybe somebody has statistics on this? 


                  [Dean LaVergne] It doesn't seem to hold out.  For the last ten years:
                   
                  Free Throw Percentage:
                   
                  Season   Away    Home    Diff
                  1992    75.62%  76.12%   0.51%
                  1993    75.19%  75.65%   0.46%
                  1994    73.60%  73.25%  -0.35%
                  1995    73.49%  73.84%   0.34%
                  1996    73.91%  74.03%   0.12%
                  1997    73.98%  73.67%  -0.31%
                  1998    73.54%  73.82%   0.28%
                  1999    72.29%  73.32%   1.02%
                  2000    74.55%  75.44%   0.89%
                  2001    74.48%  74.99%   0.51%
                             
                             
                  However, free throws attempted seem a little more significant:
                              
                             
                  Season   Away    Home    Diff    % Diff
                  1992   28,522  30,553   2,031    7.12%
                  1993   29,715  31,659   1,944    6.54%
                  1994   28,688  30,131   1,443    5.03%
                  1995   29,248  30,690   1,442    4.93%
                  1996   30,587  32,178   1,591    5.20%
                  1997   29,522  30,272     750    2.54%
                  1998   30,704  31,799   1,095    3.57%
                  1999   18,399  19,000     601    3.27%
                  2000   29,410  30,352     942    3.20%
                  2001   28,570  29,308     738    2.58%
                                      
                  Dean L
                   
                • Charles Steinhardt
                  Very interesting (and obviously not what I d expect looking from the point of view of a fan). Anybody know why the FT disparity has dropped (and how strongly
                  Message 8 of 11 , Aug 17, 2001
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                    Very interesting (and obviously not what I'd expect looking from the point
                    of view of a fan).

                    Anybody know why the FT disparity has dropped (and how strongly that
                    disparity correlates with winning %)? Have there been new instructions to
                    officials?

                    On Fri, 17 Aug 2001, Dean LaVergne wrote:

                    >
                    > -----Original Message-----
                    > From: Charles Steinhardt [mailto:charles@...]
                    >
                    >
                    >
                    >
                    > 2) There is no equivalent of the free throw in baseball, and in fact all
                    > new stadia are forced to put some sort of blue/black screen in
                    > straightaway center so that the batter has a good line of sight. Fans can
                    > have a very direct impact in basketball that I'd guess is worth as much as
                    > 5 points per game (some in increasing the home FT%, some in decreasing
                    > that of opponents. Maybe somebody has statistics on this?
                    >
                    >
                    > [Dean LaVergne] It doesn't seem to hold out. For the last ten years:
                    >
                    > Free Throw Percentage:
                    >
                    > Season Away Home Diff
                    > 1992 75.62% 76.12% 0.51%
                    > 1993 75.19% 75.65% 0.46%
                    > 1994 73.60% 73.25% -0.35%
                    > 1995 73.49% 73.84% 0.34%
                    > 1996 73.91% 74.03% 0.12%
                    > 1997 73.98% 73.67% -0.31%
                    > 1998 73.54% 73.82% 0.28%
                    > 1999 72.29% 73.32% 1.02%
                    > 2000 74.55% 75.44% 0.89%
                    > 2001 74.48% 74.99% 0.51%
                    >
                    >
                    > However, free throws attempted seem a little more significant:
                    >
                    >
                    > Season Away Home Diff % Diff
                    > 1992 28,522 30,553 2,031 7.12%
                    > 1993 29,715 31,659 1,944 6.54%
                    > 1994 28,688 30,131 1,443 5.03%
                    > 1995 29,248 30,690 1,442 4.93%
                    > 1996 30,587 32,178 1,591 5.20%
                    > 1997 29,522 30,272 750 2.54%
                    > 1998 30,704 31,799 1,095 3.57%
                    > 1999 18,399 19,000 601 3.27%
                    > 2000 29,410 30,352 942 3.20%
                    > 2001 28,570 29,308 738 2.58%
                    >
                    >
                    > Dean L
                    >
                    >
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