In my previous article, An Important Discovery, I speculated that for human chess players, each doubling of the time of the clock results in a gain of about 200 Elo rating points in playing strength. After reading the resulting discussion (in comments to the previous article and on Chess Tempo), it occurred to me that I had the data to test this hypothesis for problem solving. I sorted the results for my first pass through Coakley into ascending order of solution time, and calculated:
(1). The total time taken on all the problems that I had solved (correctly or incorrectly) within each of these solution times.
(2). The time taken on all the problems that I had not solved within each of these solution times (i.e. the solution time multiplied by the number of unsolved problems).
(3). The average time taken per problem for each of these solution times, i.e. (1) + (2) divided by the total number of problems.
(4). My score, as measured by the fraction of the problems that I solved correctly within each of these solution times (i.e. the number of problems solved correctly divided by the total number of problems).
The graph below plots my score against the average time taken per problem (in seconds):
I made almost linear progress here. I calculated the Elo point rating difference -400 * log(1/score - 1) for each point on the graph above (see my earlier article Rating Points Revisited). The graph below plots these rating point differences against the average time taken per problem:
From this graph we get:
Seconds Points Increase
6 -242 -
12 -62 180
24 170 232
An increase of 200 Elo rating points for each doubling of the total solution time taken appears to be about right, judging from this example.