Tom: great, well, I’m happy we were able to get somewhere, and I thank you for putting in all the effort.  I really love it when the Straight Arrow readers roll up their sleeves.

Yeah, I hope somebody else already has sanitized PBP data and can run it.  It was an interesting result that they matched up really well through 2 and 3 before really diverging.  I’ll probably have the data 6 months from now if it’s still an open question.

Tango, so if I have this straight, you got the 30 points per win number by dividing a teams point differential by their win total?

(Points scored per game - points allowed per game)
divided by
(win% - .500)

Tangotiger - 23 May 2013 01:23 PM

(Points scored per game - points allowed per game)
divided by
(win% - .500)

Based on that method I got 24.1 points per win this season and 28.5 points per win the year before that.

Well, I remember getting 30, and that’s what TomC also got.

Be careful how you do it.  You might have done it on a team-by-team level, then averaging it.  You really have to apply it at the league level, which means running a correlation.

I found some data here,
http://basketballvalue.com/index.php

I processed it into win probability vs time remaining and score differential (for the home team). I put the results (for the 2007, 2008 and 2009 regular seasons) in a google doc,
https://docs.google.com/spreadsheet/ccc?key=0ArY9z_A556ebdG45UnJiY1RCTUNMREw4b2N3WDRfVmc#gid=0

at a fixed time remaining, the win probability as a function of score differential looks like an inverse logit,

p = 1/(1+exp(-a*(x-x0))

where x is score differential.

I fit this function at a bunch of different times, and this the result,

time a x0 a/4
    1 1.6059 -0.1077 0.4015 
   11 1.2037  0.0632 0.3009 
   21 1.1551  0.0610 0.2888 
   31 1.0673 -0.0599 0.2668 
   41 0.9484 -0.0437 0.2371 
   51 0.8391 -0.0771 0.2098 
   61 0.7318 -0.0974 0.1830 
   71 0.6780 -0.1385 0.1695 
   81 0.6792 -0.1825 0.1698 
   91 0.6466 -0.2164 0.1616 
  200 0.4373 -0.3377 0.1093 
  400 0.2870 -0.5834 0.0717 
  600 0.2336 -0.7782 0.0584 
  800 0.2058 -0.9461 0.0514 
 1000 0.1829 -1.3920 0.0457 
 1200 0.1632 -1.6770 0.0408 
 1400 0.1443 -1.9970 0.0361 
 1600 0.1345 -2.2131 0.0336 
 1800 0.1206 -2.6325 0.0302 
 2000 0.1134 -2.9718 0.0284 
 2200 0.1168 -2.9663 0.0292 
 2400 0.1066 -3.5210 0.0267 
 2600 0.0953 -4.1950 0.0238 
 2800 0.0860 -4.7362 0.0215 
 2850 0.0890 -4.6178 0.0223

the last column is the derivative at x=x0, i.e. a/4, which is the win-probability value of a point, if it were independent of score differential.

so early in the game a point is worth ~0.025 win-probability, but is already starting to increase. by halftime it’s ~0.036, and it really starts to shoot up beginning at maybe the last 300s of the game or so.

wow, I just caught the last 3 minutes of 1st quarter of spurs heat and that might be the best basketball Ive ever seen; spurs up 41-25.
anyway, my model (http://tangotiger.com/index.php/boards/viewthread/151/P15/#374) says with 16 pt lead for the away team is an 82% chance of winning the game…

a 19 point lead by the away team at half-time is a 92% chance of winning the game (a = 0.1427, x=-19, x0=-1.983 in #22 above)...