My coworkers and I play board games at lunch. We've taken it so seriously that I've written an application to calculate a "player score" based on how you place in each game played.
Here's how it currently works:
(Positions - Placement) / (Positions - 1) = Score
where Placement is 1st == 1, 2nd == 2, 3rd == 3, etc... and Positions is how many people were playing the game.
4 Man Game Scoring Example
Position Calculation Score
1st (4-1)/(4-1) 1.000
2nd (4-2)/(4-1) 0.667
3rd (4-3)/(4-1) 0.333
4th (4-4)/(4-1) 0.000
Now that that's all figured out, you take your average for all the games played and away you go.
While there may be other issues, the primary concern is that we've had to put a "Minimum Games" requirement when going for the season trophy because if you win a single game, you stand with a solid 1.000 score and if you lose your only game, you sit with 0.000.
We've considered various ways of creating "bonuses" for playing numerous games but nailing that magic number is a hard thing to do. Doing a traditional ELO doesn't appear to be sufficient because it's not 1v1.
If there's anyone with a suggestion as to how to do it better, I'm all ears. And my apologies if this is the wrong forum. The board & card games one didn't feel totally right.
Thanks in advance - Hugh
One "bonus" type you might want to consider is having the score being based on their highest scores, with decaying after the highest.
So, for example (with a $5\%$ decay rate), let's say you have a player that played $5$ games with scores of $1,1,\frac{2}{3},\frac{1}{3},0$. Then, you could calculate that player's total ranked score as $1+0.95\cdot1+(0.95)^2\cdot\frac{2}{3}+(0.95)^3\cdot\frac{1}{3}+(0.95)^4\cdot0\approx2.84$ points. This scheme rewards playing more games, while still being somewhat fair to players with a better record. You can then adjust the decay rate to make the system suit your needs.