On Thu, 13 Jan 2000, James Cherry wrote:

 As a couple people have pointed out, I neglected to account for what
 happens to players' average scores with volatility.  I tend to agree
 with them that in the example I cited with a beginner and an expert,
 volatility increases the expert's _average_ score more than that of
 the beginner.  It'll also increase the width of the score
 distribution, but although the effect on the overlap area is unclear,
 I agree that it'll probably decrease.  This means an expert will beat
 a beginner more often when volatility is increased.
 
 However, I'm not convinced this is true in all cases.  I was
 envisioning the case of me (rated 1900, averaging about 400 a game)
 playing Dave Boys (rated 200, averaging 420 a game).  If Dave makes a
 volatile move, I have just about as good a chance of making use of the
 move as he does -- his is slightly better than mine, but not much.
 Therefore, a volatile move will increase his average score only a
 little more than mine, which will tend to reduce the overlap between
 our distributions.  At the same time, the widths of our score
 distributions increase, which will increase their overlap.  I don't
 know which effect will dominate, but I suspect the latter will -- the
 net effect will be to increase the overlap, meaning I win more games
 after a volatile move.  Dave, therefore, should avoid volatility
 against me.
 
 I'm trying to think how this could be simulated, e.g., using ACBot
 vs. a stupider version of itself, but this would require some effort.
 It might well be that against people slightly worse than you,
 volatility means you lose more games, but against people much worse
 than you, volatility wins you more games.
 

In aggregate, I think moving the outside clump farther to the right than the left clump will of course yield a larger volume in overall score differential. This should be intuitive without drawing bell curves on a plot of n versus s. James opines that flattening the curves simultaneously will cause the left clump to overtake the right clump more often on individual bases. I agree. I have a real life simulator that tests just this premise when v is increased. It's called SOWPODS. In the long run, the better players are going to distance themselves more, but in the short run(1 game) it's anything can happen. This is based on my experience playing SOWPODS and OSPD with players of similar average strength below mine. The frustrating thing is that 24 data points every two years makes it hard to get to the long run. But I assert the empirical evidence backs James' intuition.

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