I know that there have been studies of Punch UV rates in the past. In this thread I'd like to present some data specifically on bombs.
- total bomb 1-UV tickets bought: 88
- fraction of those giving CTR: 17 / 88
- fraction of those giving CTR+1: 17 / 17.
What is the chance of getting CTR?
There are seven types of UVs possible on bombs. So one would expect CTR to have a 1 / 7 chance, or about 14%. In our data, we estimate the chance at 17 / 88 = 19%. But there is some uncertainty in that estimate. The 95% confidence interval (based on the normal approximation, which is valid in this case) is [11%, 28%]. Because 14% falls into this interval, we cannot reject the idea that the chance is 1 / 7.
If you're going to get CTR, then what are the chances of getting more than +1?
Suppose, for the sake of argument, that chances were programmed like this: 80% for +1 and 20% total for +2, +3, +4. Then the probability of getting 17 +1 UVs would be (0.8)^17 = 2%. So our data would be pretty strange. Therefore we reject the premise that the chances are programmed that way. It seems that the chance of getting +1 is more than 80%.
In other words, almost every bomb CTR that you get from Punch is going to be +1. :(
Question
Have you ever gotten bomb CTR+2, CTR+3, or CTR+4 from Punch? Recently?
(Please notice that I am not asking about UVs from crafting, nor UVs on non-bombs. I've gotten large bomb CTR from crafting, and I've gotten some great UVs from Punch.)
My results are probably part of your data set, so I can't confirm independently. But the following threads from 2012 have some large Punch bomb CTRs.
http://forums.spiralknights.com/en/node/65203#comment-537030
http://forums.spiralknights.com/en/node/67295#comment-557847
They also have status UVs on shields. So they may be too outdated to be relevant. I wonder whether anyone has gotten large bomb CTR from Punch since he was changed.