Mongoose, the confusion

Okay, so we know what EJ said, but some friends and I weren't really happy with their explanation or their forumla.  So we played around a little on our own.

BEAR:

Since what we want to know is "How many times do I have to do this task with a %p success rate in order to get %r successes, we can use a negative binomial distribution with r=1 since we only care about the first success.  And we know that p=0.0417 for bear

Therefore, we get (1-0.0417)/(0.0417) = 22.9808

So this tells us that on average it takes 23 attacks for mongoose to proc the first time.

So it takes 21.5625 seconds for 23 attacks to occur.  

So since mongoose lasts 15 seconds, the total time for 1 occurance of mongoose is 36.56 which means that mongoose was active 41.03% of the time, which gives an average of 49.23 agility.  

And since once mongoose is over, we start back again at the "state" we started in, the same equation holds for the next proc.

CAT:

For catform, we know that p=0.0167 so plugging in we get (1-0.0167)/(0.0167) = 58.8802

So this tells us that it takes 59 attacks for mongoose to proc the first time, which means it takes 47.104 seconds for 59 attacks to occur.

Since mongoose lasts 15 seconds, the total time for 1 occurance of mongoose is 62.1 which means that mongoose was active 24.15% of the time, which gives an average of 28.9855 agility.

Which means that mongoose is much better for bear, but really sucks for cat.

And I would like to give special thanks to Gurggy, he did the real work and Rusted for keeping on my ass with questions so we got them answered.