i recall at one point hearing about a system(possibly an older white wolf one, but i'm not sure) where, due to the way botches were calculated, increasing your stats for at least some rolls also had a slight mathematical increase in your chances of getting a botched roll. do you happen to remember anything like what i'm describing, by chance? i'm not really well-versed enough in dice statistics to be able to look through games and tell which ones would work out that way, unfortunately
Classic World of Darkness systems use hit-counting dice pools with variable target numbers (i.e., you roll a bunch of d10s and count how many are equal to or greater than a given number), but also have 1s subtract hits, so it's possible to roll zero or fewer hits; for example, if you're rolling five dice against a target number of 7 and get 1, 1, 3, 5, 8, that's technically negative one hits, since you get one hit for the 8, but subtract two for the 1s.
The wrinkle lies in how a botch is defined. In the system's modern iterations, you need to score zero hits (i.e., no dice showing higher than the target number) and at least one 1 in order to botch; as originally designed, however, any roll with negative hits was a botch. This creates two distinct mathematical quirks:
Using the modern definition of a botch, the absolute likelihood of a botch trends strictly downward as the number of dice increases, since the odds of rolling no hits at all become increasingly remote; however, the portion of your failures that botch rises with the number of dice, as – given that all of your dice missed – more dice means a greater likelihood that at least one of those misses is a 1. This isn't impossible to account for narratively – the idea that highly skilled characters tend to biff it big on the rare occasions that they fail makes some sense – but some players find it unaesthetic.
Using the old-school definition of a botch (i.e., any roll with negative hits botches, not just rolls that had zero hits before subtracting 1s), only when your target number is higher than 6 increasing the size of your dice pool legitimately can increase the absolute likelihood of a botch. It does fall off again as dice pools become very large, and the likelihood of a botch never rises faster than the likelihood of success, but it does create objectively goofy situations like the absolute likelihood of a botch versus target number 9 starting at 10% for a single die, peaking at 17% for four dice, and not going back below 10% until ten dice. A lot of sources recommend just not letting your target numbers go higher than 8 for this reason.
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