As I look on websites like LOLKing and at your own post game information, I don't see a way to quantify a player's ability to teamfight well.
Granted, this usually depends on a couple of things:
Ability to focus champions
Prior teamfight gold+items
While I think that it would be impossible to come up with a perfect rating system for teamfighting ability, I believe that I might have an algorithm to help with the lack of discrimination concerning a player's ability to focus champions.
Only (lulz) care about stats with any of the following qualifiers:
highest gold gained,
most damage dealt to enemy champions,
most 1v1 fights won (or 1v1-5 fights won, using the "out of combat" buff logic present on guinsoo's rageblade),
a kill to assist ratio,
a kills to death ratio,
an assist to deaths ratio,
least magic resist (or armor/magic resist in a range of user provided values),
targets with user indicated items,
highest amount of a certain kind of damage within a certain specified time (user defined burst damage).
These are obviously stats that people care about when choosing what targets to focus. Note that these are only stats about the target; IMO, everyone should be focusing the primary damage dealers (carries, usually) all the time in a teamfight. I may be wrong about this, but Riot, you might want to do some research as to determining what strategy is best for winning teamfights before you shut this target-focused idea down.
As for a specific algorithm that would use any of the above listed stats ton determine a player's teamfighting ability, I would recommend starting somewhere with calculating the total number of teamfights (a teamfight would be counted using the out of combat buff from guinsoo's rageblade or having attacked a champion in the last 20 seconds more than 4 times with at least 2 other teammates in a range of 1400), and then dividing the total amount of damage (physical, magic and true) against the target with the highest amount of gold gained at the time when the teamfight started.
Alternatively, you could divide the damage done against the initial target over the course of an entire game's worth of teamfights by the total damage done to champions for the entire game, regardless of teamfights.
The larger algorithm would ideally work well with a series of columns corresponding to relevant information:
- Teamfight number
- Champion played
- Target champion name
- Start time of teamfight
- Total gold gained by target at start of teamfight
- Total damage done against target
- Total damage done in teamfight
- Result of teamfight