Quote:
Originally Posted by Steady Eddy
But the OP didn't mention probability, he mentioned a paradox. A fail (1/n) followed by a success (1/n+1) seems to give greater weight to the second term. Why?
Say a coach has won 9 of 10 games for a 90% win rate. If he wins the next game, his rate becomes 91%, it only goes up 1%. But if he loses, his rate will be 73%, it drops nearly 18%! This doesn't seem fair. With a high success rate, new wins only improve it a tiny bit, but just one loss makes a huge drop. This lack of symmetry between wins and losses explains the puzzle the OP discussed, IMO.

Won't his rate be 9/11 = 82%? Where does 73% come from?