March 4, 2018

Why is Standard Deviation of NBA scores about point spread 12 points.

Filed under: Uncategorized — wwinston @ 9:53 am

The wonderful Steve Ilardi started a great discussion on Twitter concerning variability of margin of victory in NBA games. The standard deviation of the margin of victory relative to the point spread is near 12 points. Can we use basic probability and statistics to explain this fact? We know

  • Average NBA team takes 86 FGA per game
  • EFG is around 50%

For a back of the envelope estimate on the  difference between margin of victory and point spread note that based on teams playing, each team has its own mean EFG (say MeanEFGFav and MeanEFGDog) for that game. What would be the standard deviation of the actual EFG percentage                                           difference (EFGpercentageFav-EFGpercentageDog) for this game? From basic stats standard deviation of observed EFG  percentage     for each team during a game  is sqrt(.5*.5/85).

  •   Therefore standard deviation of difference in observed EFGpercentages for a game is sqrt(2)*sqrt(1/340) = 7.6%.
  • Difference in FGs for games should have a standard deviation of around 85*(.076) which is near 6.
  • This translates to around 12 points.

I am assuming the actual EFGs for each team are independent (probably not true, since team behind probably tries better lineups to make game closer and this would reduce my 6 FG difference number)  and the rest of the analysis is oversimplified, but is comforting (to me at least) to see a reasonable explanation for the  12 point variability about the point spread.

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