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Re: WNBA turnaround

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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 1 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 2 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 3 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
          >
          >
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        • 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 4 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 5 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 6 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 7 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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