Determining a fair overall winner in a fencing competition

Question

For a (friendly) fencing competition I'm trying to setup some (new) rules. Since this is an internal competition between members of the club there is no requirement to be present at all the match days.

For the scoring on the day I am thinking of using the pool system so we have some matches. This seems like a fair option and is not what I am trying to figure out.

However since we have 10 match days in a year I am trying to get a fair system (and relative simple to understand) to determine the overall winner.

The current system is that each competition day you get 1 to 8 points (depending on the pool ranking) or 0 points if you weren't there. For the overall winner the 3 lowest scores are removed and the rest is summed.

Although this seems quite fair I'm not sure this is the "best" way of determining the overall winner. I am trying to optimize for presence so I would prefer that someone who is present at all the days and becomes 3rd each time would win over someone who is only present 5 times and becomes first each time. (In the current system the one who is present only half the time would win).

Are there any better methods out there?

From the "similar questions" I did find this (somewhat) related question. Fair system to score players between friend games Although there are some suggestions to use I think rankade is way too complex, jogabo is down and the rest is optimized for soccer instead of fencing.

Answer 1

The general rule is that if you want to favour consistent performances over a few exceptional performances, you want a "flat" points structure where the ratio between places is relatively small.

For example, if you have a "spiky" structure where first place gets you 9 points, second place 3 points and third place 1 point (i.e. a ratio of 9:1 between first and third place), then you're going to favour people who do very well in one tournament and win it, rather than someone who consistently comes third in every tournament. An extreme example of this would be just to count wins, effectively setting the ratio to infinity.

On the other hand, a flat structure where first place gets you 10 points, second place 9 points, third place 8 points and so on down to 10th place (i.e. a ratio of 1.25:1 between first and third place) means that you favour the consistent performers, and it doesn't matter so much exactly which position they come in. An extreme (and probably silly) example of this would be just to count number of tournaments entered, effectively setting the ratio to 1.