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Re: OReb vs. DReb

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  • John Hollinger
    My answer is Yes/No , but it still holds together at a team level for this reason: To whatever extent an offensive rebound is being overvalued at the team
    Message 1 of 22 , Dec 28, 2003
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      My answer is "Yes/No", but it still holds together at a team level
      for this reason: To whatever extent an offensive rebound is being
      overvalued at the team level, the missed field goal is by definition
      being overvalued by the exact same amount. Thus, the negative and
      positive effects still exactly offset each other, and no harm, no
      foul.




      --- In APBR_analysis@yahoogroups.com, "Charlie Board" <cboard@t...>
      wrote:
      > --- In APBR_analysis@yahoogroups.com, "John Hollinger"
      > <alleyoop2@y...> wrote:
      > > Here's another way to look at it:
      > >
      > > A missed shot + a defensive rebound must equal the value of a
      > > possession. The value of a missed shot, however, is defined by
      the
      > > probability of getting the rebound.
      >
      > I think here we've come back full circle to a question I asked
      > a month or two ago - whether a "possession" should be defined
      > as most here define it (everything that occurs between the time
      > team A gets the ball and the time they relinquish it) or, as I
      > defined it when I was doing statistical odels a few years ago
      > (every FGA ends a possession, every rebound creates one). I
      > believe it was either you (John) or Dean that pointed out that
      > you called my possessions "plays".
      >
      > It was pointed out in that discussion that the consensus definition
      > works well for team ratings because by definition each team
      > ends a game with basically the same number of possessions and
      > thus the team whose offensive efficiency minus defensive efficiency
      > is higher generally wins a given game.
      >
      > But I noted then, I chose my definition because I was mainly
      > concerned with calculating *individual* contribution from
      > available stats and the "play" definition made dealing with
      > rebounds both easier and more intuitive. Every rebound
      > creates a possession. Every rebound is worth the same amount
      > (thus eliminating the paradox that comes from valuing one higher
      > and then noting that since they're mutually exclusive the lesser
      > one must have a preventative value at least equal to the greater
      > one).
      >
      > And I pointed out that under the usual definition of possession,
      > it was even possible to view offensive rebounds as absolutely
      > worthless -
      > possession-changing events are all that matter and offensive
      > rebounds leave you on the same possession. They can be viewed as
      > non-events. Which is surely wrong. lol
      >
      > >
      > > Suppose each possession was worth 1 point, and the defensive team
      has
      > > a 2/3 chance of getting the rebound.
      > >
      > > Then the value of a missed shot is 1 minus the probabily of
      getting
      > > the offensive rebound. Since that's around 1/3, the value of a
      missed
      > > shot ends up being around 2/3 of a point, and the value of the
      > > defensive rebound accounts for the other 1/3.
      > >
      > > On the other hand, the value of an offensive rebound must
      completely
      > > offset the value of a missed field goal, so that if I miss a shot
      and
      > > grab the rebound, I'm back where I started. Thus, the value of
      an
      > > offensive rebound is 2/3 of a point, or twice that of a defensive
      > > rebound.
      > >
      > > It's paradoxical, but if you're accounting possessions by
      individual
      > > contribution, it's the only realistic model. Hope this makes
      sense...
      >
      > Here's where I see a problem...I think there are separate optimal
      > definitions of possession for team valuations and individual
      > valuations and no clear way to make the latter sum up to the
      > former. And it seems to me you're trying to force the square
      > pegs of individual contributions into the round hole of team
      > value at a clearly paradoxical (and hence, invalid) slighting
      > of defensive rebounds.
      >
      > John, do you hold - as Ed said he did and thought you did - that
      > the higher valuation of ORs over DRs applies only at the individual
      > level because of the marginal probabilities argument? Or do you also
      > hold that it applies to teams?
      >
      > If the respective answers are "Yes/No"
      > then I think (but I could be wrong and mis-seeing it) your argument
      > above self-destructs. Partly because there's no hope of simply
      > "accounting possessions by individual contribution" if one of the
      > basic stats has fundamentally different vcalue at the individual
      > vs. team levels.
      >
      > If your respective answers are a combination other than "Yes/No",
      > then you're saying offensive rebounds ARE also more valuable
      > at the team level and I'd go back to asking how you resolve my
      > initial objections (that defensive rebounds ALWAYS correspond
      > to successful defensive possessions while offensive rebounds only
      > SOMETIMES correspond to successful offensive possessions; and
      > that the exhaustive and mutually-exclusive relationship of the
      > two means they must be closely valued)? If I understood Ed
      > correctly, he resolves them by basically saying they don't apply
      > at the individual level even though they do at the team level.
      > If you hold they don't apply at the team level I'd like to hear
      > your resolution.
      >
      > I'm enjoying this discussion. I hope my obstinate inability to
      > square the two views isn't annoying anyone... ;)
      >
      > >
      > >
      > >
      > >
      > >
      > >
      > >
      > >
      > >
      > >
      > >
      > >
      > >
      > >
      > > --- In APBR_analysis@yahoogroups.com, "Charlie Board"
      <cboard@t...>
      > > wrote:
      > > > --- In APBR_analysis@yahoogroups.com, igor eduardo küpfer
      > > > <igorkupfer@r...> wrote:
      > > > >
      > > > > From: "Charlie Board" <cboard@t...>
      > > >
      > > > Ok, I need to think about the rest of your comments for awhile.
      > > > But a couple of very quick comments here:
      > > >
      > > > > > only if the statement above is true. Has it been validated
      or
      > > > > > tested? It would seem to say, for example, that a team's
      > > > > > defensive rebounding pct doesn't change much when a great
      > > > > > defensive rebounder such as Russell or Rodman or Wallace or
      > > Duncan is
      > > > > > out of the game. Is this true?
      > > > > >
      > > > >
      > > > > If you remove a great rebounder from a team, it may be true
      that
      > > the
      > > > team's
      > > > > rebounding ability decrease -- but the decrease is equal to
      the
      > > player's
      > > > > marginal rebounding value, not his absolute value. If you
      remove
      > > a 10
      > > > > rebound/game player from a team, the team's rebounding will
      not
      > > > decrease by
      > > > > 10 rebounds per game. It will decrease by the marginal value
      of
      > > those 10
      > > > > reb/game. Why? Because while 10 reb/game players may be rare,
      > > there
      > > > are any
      > > > > number of 8 reb/game players who can replace him. In this
      > > > hypothetical case,
      > > > > the marginal value of a 10 reb/game player is 2 reb/game.
      > > > >
      > > >
      > > > But isn't this true to one degree or another of pretty
      > > > much *all* individual stats? You take a 25ppg scorer
      > > > off of a 100ppg team with an injury and you don't expect
      > > > the team to drop to 75 ppg. Yet in evaluating that player
      > > > I've yet to see a researcher say that only some of his 25ppg
      > > > should be counted in his rating? (Well there is the whole
      > > > method of measuring against replacement value, but that's
      > > > agnostic to the oreb/dreb argument, I think). Why are
      > > > Def rebounds singled out for special marginal treatment?
      > > >
      > > > >
      > > > > > And is the complementary statement (that a team's offensive
      > > > > > reb % DOES change significantly when an individual strong
      > > > > > offensive rebounder sits) also shown by evidence?
      > > > > >
      > > > >
      > > > > This is my conjecture. I have no evidence for it, just an
      > > argument from
      > > > > plausibility.
      > > >
      > > > Fair enough.
      > > >
      > > > But what I'm basically hearing is that orebs should have
      > > > more value (in individual but not team assessment)
      > > > because they have more marginal value. What I'm not
      > > > hearing is anything that I find convincing showing that
      > > > they *do* have more marginal value.
      > > >
      > > > Anyway, I'm gonna think about your other comments a bit more.
      > > > Hope others will jump in on this one. Rebounding is the
      > > > second oldest and second most prevalent basketball stat
      > > > out there (next to points, whose value is pretty well
      > > > understood). If we can't adequately explain our mathematical
      > > > treatment of rebounds then I don't think mathematical
      > > > analysis of basketball is going to get anywhere near
      > > > the level of acceptance that James & Palmer have gotten in
      > > > the baseball world.
      > > >
      > > >
      > > > >
      > > > > The value we give to a rebound should also reflect, not its
      > > > importance, but
      > > > > its "price," minus the price of the next best option. A
      center
      > > grabs
      > > > a miss,
      > > > > with a teammate further along the baseline. The board was
      > > important
      > > > in that
      > > > > it ended the opponent's possession, but its marginal value is
      the
      > > > value of
      > > > > that rebound minus the probability of his teammate getting
      the
      > > rebound.
      > > >
      > > > I like this explanation. But I need to think about it. And
      > > > for it to have value that "probability of his temmate getting
      the
      > > > rebound" needs to be better fleshed out for both DRs and ORs.
      > > > IMO.
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