Board Game Arena

As someone with a rather strong mathematics background (and as a person with a best friend who is a Doctor of Applied Mathematics), I would like to make two suggestions.

ELO
In games with more than 3 players, the adjustment for ELO should be the sum of the greatest gain and the greatest loss. So, if I am in a 5 player game and I some in third place, I would not have losses from two players and gains from two players. It should just be the greatest gain I have added to the greatest loss I have in that game.

The system, as it currently stands, creates swings that are way, way too large.

KARMA
The Karma system is alright, I suppose, but the fact remains that the system has a lot of down without a lot of up. I suggest something like this:

Base Karma is 50. Minimum is 0 and maximum is 100

The ranks of Karma could be:
[*] 0-10 --- Abysmal
[*] 11-20 --- Terrible
[*] 21-40 --- Poor
[*] 41-60 --- Fair
[*] 61-80 --- Good
[*] 81-90 --- Great
[*] 91-100 --- Superb

When you are between 21-80, each game in which you had no time issues grants you +2 Karma.
When you are above 80 or below 20, each game in which you had no time issues grants you +1 Karma.
Any game in which you had time issues without being expelled, you lose -1 Karma.
Any game in which you had time issues and were expelled, you lose -5 Karma.

Karma should not be seen as a percent -- it isn't.

That said, after the Karma rating, a Karma percent could be listed where that value is the percentage of games where you have had no time issues.

Thus, a good player might have something that reads: Karma 83 (99.3%) Great

Interesting idea on karma. I might vote for it if you submit it for consideration.

As for Elo, you begin with an argument from authority (including touting a friendship with a mathematician?!), and then provide zero content based on this purported expertise. You could very well have said "this works because I know math. Trust me bro." It probably won't surprise you that there are many people on BGA with rather strong mathematics backgrounds, including at least one professional mathematician. They will probably not be impressed if you don't show your work.

Given your rather strong mathematics background, you might be interested in this paper detailing a proposal for an Elo system actually designed for multi-player contests.

Generalizing the Elo Rating System for Multiplayer Games and Races

Abstract: We introduce a non-standard generalization of the Elo rating system for competitions involving two or more participants. The new system can be understood as an on-line estimation algorithm for the parameters of a Plackett-Luce model which can be used to make probabilistic forecasts for the results of future competitions. ...

Elo was designed for a game like chess, where a substantially stronger player wins almost all the time.

Elo is not suitable for luck-based games. There are games on BGA where a player who knows the basic strategy will win at least 45% of the time, and skill only affect the remaining 10%.

The karma system is awful. You can time out of a tournament game for -4 and then play a couple of quick regular games and recover the loss.

Tournament karma should be tracked separately from regular karma. If someone has a habit of running out of time in tournaments, there should be an option for tournament organizers to block them. For example, if someone has timed out for more than 3 tournament games in the past 3 months, I want to have an option to ban them from my tournaments. I would allow for forgiveness of one timeout for every 10 tournaments finished with zero timeouts. (tournaments, not individual games) Also, timeouts older than 3 months expire just like all other karma penalties, so a player always has a chance to recover their good standing.