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BGonline.org Forums
Maybe not entirely OT, given the importance of equity in backgammon
Posted By: Jim Stutz In Response To: An interesting question! (Bob Koca)
Date: Sunday, 21 January 2024, at 7:13 p.m.
Bob Koca wrote: “Your analysis is making the rebounds twice as valuable as they are. Like I said in the other post the opponent will be getting the ball back.”
I think what you’re actually asserting with this logic is that the value to Team A of ANY possession of the ball, measured by average points scored per possession, should be discounted by the value (WHATEVER that may be) of Team B’s guaranteed right to the next possession. The fact that Team B always “gets the ball back” is only worth something extra to Team B if it goes on to finish the quarter with one more possession than Team A from that point on, which happens 50% of the time. So you’re arguing, I guess, that a random possession is only worth ˝ of the average points that an NBA team scores when it has the ball. We have stipulated -- based on NBA stats -- that a team scores, on average, 1 point per possession, so you’re logic argues that a random possession is "worth" ˝ point, not 1 point. ( If you apply this logic consistently, then you must also accept that 2-point basket by Team A is actually worth only 1.5 points when you subtract the value of Team B’s guaranteed right to the next possession, and a 3-point basket by Team A is accordingly only worth 2.5 points.)
Regardless of the merits of your logic above, my fundamental position on the relative value of a rebound is unchanged: The value of an uncontested possession (say, to the team inbounding after an opponent’s score) is X. Whatever value X you care to ascribe to an uncontested possession, the successful rebound of a contested ball is worth 2X: i.e: The value of possession of the ball (X) + the value of denying the opponent that same possession (X) = 2X.
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