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589Re: [APBR_analysis] Re: nice methods

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  • Michael K. Tamada
    Feb 5, 2002
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      On Tue, 5 Feb 2002, HoopStudies wrote:

      > Also, if you have a team that wins only 15 games, it doesn't make
      > sense to have one player on that team who wins 16 games like a Shaq
      > or a Jordan or Duncan do. Those guys make winning teams. Elton
      > Brand, though a good player, clearly doesn't add more than the 15
      > wins that Chicago had last year; it's impossible. My first cut was
      > an addition of 6 wins by Brand. I frankly am coming to believe that
      > it was more like 9 wins, but that's all a little theoretical right
      > now. And it always seems strange to me if someone contributes more
      ^^^^^^^^^^^
      > than half of his team's wins (especially since the Bulls are on pace
      > to beat 15 wins this year). It's hard to argue that even Jordan ever

      I think it depends on how were define "contributes"; see below.

      > won half his team's games when he was scoring 35 ppg and the Bulls
      > were winning only 40 games. Actually, Jordan should be a very good
      > example of what MikeG was asking for. I don't have all my info in
      > front of me (again), but
      >
      > http://www.rawbw.com/~deano/articles/JordanvsOlaj.html
      >
      > shows that Jordan was 19.4-0.7 in 1988. I don't think the Bulls were
      > that good that year, maybe 40-42 (help?). So, sure, it is indeed
      > very possible for win-based ranking methodologies to show stars (or
      > superstars in this case) on mediocre teams.

      The 19.4-0.7 won-loss record for Jordan I am okay with. From your
      article, it appears to be based on a solid notion of looking at a player's
      offensive and defensive ratings, comparing those to what teams of similar
      off. and def. ratings would achieve in won-loss terms, and calling that
      the player's won-loss record. I have no problem with that.

      But I don't think Jordan's 19.4-0.7 won-loss record can be regarded as
      being on the same measurement scale as the Bulls' 40-42 record (actually
      they were 50-32 in 1988, but that doesn't matter). Nor can Brand's 6 or 9
      individual victories be compared to the Bulls' total of 15.

      We can calculate the Bulls' individual won-loss records in 1988, but we
      cannot say that the sum of those won-loss records should equal 40-42 (or
      50-32), nor can we say that 19.4 is almost half of 40. Those are apples
      and oranges.

      If we do want to claim that those 19.4 individual wins can be directly
      compared to the team's 40 or 50 wins, we are imposing an overly simplistic
      model upon how a team's record is determined by its players production.
      Implicitly, it requires that the model be: Bulls Wins == sum of Jordan's
      wins + Pippen's wins + Grant's wins + etc. etc. And that equation is
      almost certainly an incorrect one for determining how individual players,
      when put on a team, determine the team's won-loss record. It is extremely
      unlikely that the correct model is a simple linear sum.

      And if it is not a simple linear sum, then we can't directly compare
      Jordan's 19.4 wins to the Bulls' 40 or 50 wins.


      An analogy: if someone gets a 1400 SAT score, and such students usually
      get 3.6 GPAs in college, we cannot say that the student's college GPA is
      3.6/1400 = .0026 of their SAT score. Well we can say it, but it's not a
      useful calculation. Nor is it useful to say that Brand or Jordan
      contributed to half of their teams totals, based on their individual
      won-loss stats.


      It's much the same problem that you've pointed out with linear weights
      systems: much of the world is not linear. If 10% of Microsoft's costs
      are spent on systems analysts, can we claim that systems analysts
      contribute to 10% of Microsofts production? It's not a useful ratio (the
      second one I mean; the 10% of costs figure is useful for analyzing costs);
      if Microsoft cut its systems analysts roster in half, would its production
      fall by half? If it doubled its roster, would its production double? No
      and no. Nor can we say that Jordan's 19.4 wins are about half of the
      Bulls 40 wins.

      Yet another way of looking at it: divvying up the 40 wins and saying that
      so-and-so is responsible for x of them is an exercise doomed to failure.
      How many of the 40 wins were due to Jordan, Pippen, etc.? After we finish
      divvying them up, we then better ask: wait, how many wins would the Bulls
      have had if they didn't have a coach? And for that matter an equipment
      manager, ticket takers, stadium maintenance, etc.

      Just as we can't look at Microsoft's sales of x million pieces of software
      and say "Bill Gates produced y million pieces of software, Steve Ballmer
      produced z million of them, the new programmer they hired produced w of
      them, etc." That linear divvying up of production is not how the
      production function works. Nor can a team's wins be linearly divvied up
      among its players.


      What we CAN do with players is try to estimate their MARGINAL value: how
      many wins did they contribute compared to how many player X would have
      contributed (where X could be a player that Jordan was traded for, or a
      chosen comparison player, or a replacement level player if we could agree
      on what the replacement level is, or whatever). And the 19.4 wins and 0.7
      losses might be good estimates of that marginal value.

      BUT: there is no requirement that the sum of players' marginal wins
      equate to the team's total wins. Only with (in economics terms) "constant
      returns to scale" -- e.g. a simple linear sum -- would that happen.

      The marginal values can often be well-approximated by linear methods.
      But at extreme values even the marginal wins can't be interpreted
      literally, or in a linear fashion. Does adding Jordan add 19 wins to a
      team's total? Could be, in the case of the 2002 Wizards compared to 2001.
      But if we're looking at the 1972 69-13 Lakers, it is mathematically
      impossible that adding Jordan to their roster would add 19 wins to their
      total.

      Similarly, if Jordan were to play for a really bad team that won only 15
      games, would we say that subtracting Jordan from that team would cause
      them to decrease their win total by 19?

      Yet 19.4-0.7 might still be quite a good measure of Jordan's prowess. But
      we can't interpret that 19.4 figure as one that can be directly compared
      to the Bulls' 40 wins, or 15 wins, or 69 wins, or whatever their total is.
      We can say that Jordan "contributed" 19.4 wins at the margin, but that
      does not literally mean that he would add 19 victories to a team's total.
      Wizards, maybe yes. 1972 Lakers no.


      Non-linearity. Individual won-loss records can be a fine way of
      measuring players' production, but the jump from those individual won-loss
      records to the team's actual won-loss record is not a simple one. Team
      stats are a complex function of the stats of the individual players. Not
      a simple linear sum.

      And therefore Brand's, or Jordan's, individual victories cannot be
      directly compared to their team's victories.


      --MKT
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