I've learned quite a few things about TF2 stats over the last few years which have never seen the light of day and which nobody else uses. I'm gonna dump this knowledge before the game is completely dead in the occasional thread.
The first one is a stat that deals with a couple of outstanding problems with kill and damage stats. Currently the commonly used 2 are a variation on a ratio like KD or KAD, and the damage output stat DPM. Both of these have problems, the ratio stats can be enormously inflated by passive play. Take the following two example players:
Kills Deaths KD
Plyr A 15 5 3
Plyr B 3 1 3
Clearly Player A has had a far bigger impact on the game here but the cowardly Player B who hid the whole game and just picked off a few players has exactly the same KD suggesting they have achieved something equally important. This is an extreme example, and for the most part players in competitive matches don't tend to do this, but when compiling event statistics there are always less effective players that pop up near the top because they play conservatively.
Because players tend not to milk their KD too hard though, it does make it a pretty good stat to compare to because it's fairly strong as a win/loss indicator. If something happened like players being made aware that they were being ranked on KD in some way then they might start to try to distort it.
Similarly with DPM a player that religiously spams chokes and corners will pick up a ton of extra damage that doesn't really contribute anything particularly significant to their team, and probably helps their opponents build uber. A player that only causes damage when taking fights has more meaningful damage stats, and the crossbow means that damage built up from spamming almost never sticks.
My goal was to find something that had more relevance to the result, a performance stat that had a clear mathematical correlation to the final result. The first attempt was moderately successful, taking the logic that high damage meant that a player was being more aggressive (even spamming chokes requires a player to be positioned slightly riskily) then combining that with KD would produce something useful.
Attempt 1: DPM * KD
This was OK, there's a tendency to favour heal heavy spamming pockets and demos that build up damage, but if they're not winning fights they're also punished hard. Similarly it also sidelines scouts a little because their damage stats tend not to be competitive with the spamming classes. It also has a reasonable correlation to games won and lost. The problem with this isn't really that it's particularly inaccurate, it's that it's conceptual basis doesn't describe a game winning advantage. Damage is something that happens by playing the game, and it's being modified to link it to something relevant.
Returning to basic concepts, most games have 3 elements to consider when modelling them - material, position and time. In TF2 5cp or koth material is largely dominant, having more players is almost always a big deal, and time and positional considerations only decisively trump those in niche situations. And also we don't have stats for positional considerations from logs, so there's nothing we can do for that anyway.
So if we're thinking about material, how does that manifest itself in TF2? Teams are denied material (players, any charged up abilities over time like uber and banners, etc) by players being killed and sent to the spawn queue. So we're really looking for a player stat that reflects how much extra time on the field they generated for their team with a player advantage in the game, and this is kills. Because their own frag counts against their team, it's a net frags statistic.
Net Frags per minute: (Kills - Deaths) / Time Played
This looks extremely simple, almost childishly so, but the simple +/- approach creates something that links more clearly to in-game advantages than the other ratios and secondary activity stats do, and has a stronger link to wins and losses.
So if we return to our example players
Kills Deaths Net Kills
Plyr A 15 5 +10
Plyr B 3 1 +2
Player A's vast additional contribution to the game is now reflected here. Making the stat per minute makes it possible to compare time spent off classing, and compare from game to game, and it is very simple to read. Statistically it correlates with win loss the best from the candidate stats including KD.
It has some obvious weaknesses. It's susceptible to kill stealing, there are some situations where it's right to die, and a player that baits out their team can still inflate their personal stats at their team's expense. However it doesn't promote meaningless spam or passive play, in fact it promotes finding the maximum point of aggression you can without compromising survivability and working with your team. It also tends to reward scouts which seems right as they're broadly considered the most powerful class in 6v6.
If we look at a real world example http://logs.tf/1739763 pot8o is on +12 whereas YppY is on +8, they're only separated by 0.2 in KD but pot8o is a clear 50% ahead on Net Kills. Given pot8o was doing this from the low heals flank scout position it's a creditable performance. Much of it may have been cleanup work from the sacrifice of others but if he doesn't hit those shots then they lose the game. He also had a solid stint on sniper.
When looking at logs and considering the net kills (and per minute when looking at class breakdowns) I've found it does help to throw a new light on things and provides a solid link to the in-game advantages a player achieved.