Earlier, Caelan asked me to help him test his observation that his entourage hit enemies faster if he gives them orders before the enemy enters the room. This raised interesting questions about how the time intervals between attacks is distributed, and I gathered some data on the time interval between attacks with Caelan's help.
For the first animal we tested, the distribution is approximately bell-shaped (but not normal; the tails are too heavy). The sample mean was 7.485 seconds (we can reasonably assume the true mean to be 7.5) and the standard deviation was 0.385 seconds.
A cursory examination of the data showed that it was heavily skewed (this was confirmed with a boxplot). Suspecting the time interval to be exponentially distributed, I fitted it with the exponential model and 'lo and behold, the quantiles corresponded quite well with the theoretical ones (see raven_qqplot.jpeg). There is some squiggliness that I assume to be due to the server running in ticks, and in my opinion this accounts for the low p-value from the Kolmogorov-Smirnov test.
The rate constant was estimated to be 0.101/sec, which corresponds to 9.932 seconds expected between attacks.
The attack time intervals was exponential, with a lower rate than the raven. Rate constant was estimated to be 0.077/sec, corresponding to a mean time between attacks of 13.008 seconds.
The fox attacks consistently around once every 7.5 seconds. Raven and butterfly attack at around once ever 10 seconds and once every 13 seconds, respectively; the distributions of the latter two are memory-less, so knowing it's x seconds since last attack tells you nothing about how long you likely have to wait before the next attack. Consequently, you can pre-attack with the fox, but not with raven and butterfly.
Criticisms, comments, and questions are welcome.
Attached: relevant plots and R script (ent_passive.txt).