In fact, mumble failure rates in the low single digits are sufficient to ban many users.
Here's a simulation of users who join mumble every time but are randomly counted out-of-mumble due to disconnects, mumble going down, bad detection code, etc.:
8% mumble failure rate => 98.6% of users experience mumbility 2 or more 79.6% of users experience mumbility 3 or more 47.0% of users experience mumbility 4 or more 25.1% of users experience mumbility 5 or more 5% mumble failure rate => 84.3% of users experience mumbility 2 or more 36.6% of users experience mumbility 3 or more 11.3% of users experience mumbility 4 or more 3.9% of users experience mumbility 5 or more 2% mumble failure rate => 28.9% of users experience mumbility 2 or more 3.4% of users experience mumbility 3 or more 0.4% of users experience mumbility 4 or more 0.1% of users experience mumbility 5 or moreIf mumble works perfectly 98 times out of 100, and every user joins mumble every time, you can still expect 40 out of 1000 users to receive an unjust 2-day ban, and 10 users will be banned for a week.
I think two adjustments are needed:
1. if a user has positive mumbility, keep counting good lobbies when they miss.
"miss, 4 hits, miss, hit" should have the same end result as "miss, 5 hits, miss".
2. if a user has zero mumbility, give partial credit for lobbies played before a miss. Even 10:1 would be enough. So if you play 30 mumble lobbies and then miss one, only two hits (not five) are needed to reset the mumbility.
Simulation code is in spoiler, if anyone wants to check my math.
EDIT: "40 out of 1000 users ..." should read "out of 10000". It's 4/1000 banned for two days, 1/1000 banned for a week.