I ran a field test of Shadow Pip chance in Velo City with my level 130 balance wizard to compare how often I got shadow pips with two gear sets: one that gave no shadow pip bonus and one that gave a 17% shadow pip bonus (+4 from hat, +4 from robe, +3 from boots and +6 from two Shiny Pip Hematite jewels). I battled Sheriff's Deputies for 1000 rounds, 500 rounds with each gear set.
In the first case, with no shadow pip bonus, the 500 rounds comprised 64 matches, and I received 107 shadow pips, for a base shadow pip chance of a little more than 20%, or one every 4 1/2 rounds or so. In 10% of the matches I had a shadow pip starting off, and in about 1/5 of the matches I had a shadow pip by the third round.
With the shadow pip bonus gear, the 500 rounds made up 81 matches, and I received 160 shadow pips, for a shadow pip chance of 32%, or one shadow pip approximately every three rounds. In 25% of the matches I had a shadow pip starting off, and in 2/3 of the matches I had a shadow pip by the third round.
I made an effort to use up the shadow pips almost as quickly as they came, to avoid rounds in which I had two shadow pips and therefore could not receive another. A simpler way that occurred to me afterwards is to simply not count the rounds in which it is impossible to get a shadow pip. In any case, I was carrying two shadow pips in fewer than a dozen of the thousand rounds.
I believe the shorter match length (and consequently greater number of matches) in the second sample is mostly due to the other attributes of the gear I was wearing, although having bountiful shadow pips did mean it was usually a question of waiting on my deck instead of waiting on the shadow pip.
If anyone else does any similar testing, please post the results here, I would be interested to see what you find. If you have any specific questions about this I would be happy to answer them if I can.
I can't explain why the bonus gear increased my shadow pip chance by only 11% rather than the 17% advertised, I think the sample size is plenty large enough to avoid rounding errors in the RNG. Based on the numbers, I think it's fair to ask if the hematite gems are actually improving the pip chance, oh man I don't want to do another 500 rounds that way.. ugh.
I'd also like to offer my condolences to the families of all the 307 Deputies who made the ultimate sacrifice in the interests of science. They should be remembered as valiant, generous, and uncomplaining mobs; as well as tough little healers (in comparison to their Boss, who is a shifty-eyed weasel).
I posted a follow up question to this subject in Halston's Laboratory, and Arthur had a very enlightening answer, if this topic interests you, the thread is called Question for Tech Support about Shadow Pip Chance.
I applaud your efforts in trying to figure out how often shadow pips occur but in all honesty not have 100% shadow pip chance is just the random outcome of it happening. So 6% shadow chance is better than no shadow chance at all.
Something has to be done about the unfairness of one person getting 4 shadow pips by the time the other person gets one, with the 4 pip mirage spells someone can just shrike and spam them there is nothing anyone can do unless they are jade to counter that.