https://boardgamearena.com/faq?anchor=f ... reputation describes the existing karma penalties.
If someone runs over time in a game, but is not kicked out, there's no karma penalty.
Regaining karma by playing a bunch of short fast games is easy for folks who are online a bunch.
It used to be that if you checked the reputation section of someone's profile you could see not just a count of the number of times they'd been over time and/or expelled for it, but also a list of recent karma penalties ("on X recent games" under the counts), That hasn't worked for a while;
https://boardgamearena.com/bug?id=163913 and
https://boardgamearena.com/bug?id=161895 (and probably other bugs) ask that this be restored. Looking at the "games played" section of someone's profile gets you some of that information but it's a lot more to dig through rather than a summary.
There are other bugs/suggestions open that propose changes to the karma system. IMO, tracking karma/reputation on a single, bounded scale is too easy to game. A selection of recent & overall statistics could be interesting -- and also take more thought to review & draw a lot of complaints.
"Give them a red thumb and move on" is unsatisfying but pragmatic advice if the issue is only game speed. I wish I had better to offer.
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