I have been continuing work on the discrepancy between per game attack/defends and the daily totals. Assuming that the figures as reported by Ryan are correct, I have come up with a measure of true agressiveness (attacks per round).

Let us designate a player's average number of attacks per round, or true agressiveness, as lambda. Let us suppose that a player's attacks per round follow the Poisson distribution. Then the probability that a player will attack k times in a round would be given by

lambda^k exp(-lambda)/k!

and in particular, the probability that the player would not attack in a round would be exp (-lambda).

Suppose we take the average attack probabilities weighted by number of rounds all the player's games for the day. If the number of times he attacked or defended per round is approximately constant then the actual number of attacks he made per game could be calculated from the percentages.

Likewise for the tally of the player's daily attack/defend. Assuming that the daily average defends/round is the same as the average of the day's defends/rounds, the day's number of attacks can likewise be deduced. If there is a discrepancy between the total number of attacks as determined by the per game stats and the total number of attacks as determined by the daily stats, the discrepancy arises from there having been rounds in which the player neither attacked or defended. This puts a lower limit on the number of times the player did not attack in a round, which in turn puts an upper bound on lambda.

For example, with earlier figures I gave for montecarlo, the attack/defends are congruent for 131 rounds of attack or defend out of a total of 142, for a total of 8.4% of rounds idle. The corresponding value of lambda is 2.48.

This is a crude approximation and takes a lot of effort to calculate. It would be much better if Ryan gave us the raw attack/defend figures instead of the percentages.