Pace — adjusting EPM to better characterize playstyle
Problem: winning gunfights increases your engagements per minute separate from your inherent pace
tl;dr: Engagements per minute can be misleading when slow players have high KDs because it will always be faster to stay alive and get a second kill than to die, respawn, and die again. To adjust:
Pace = EPM - (extra kills per min * 0.3)
The pace is a crucial stat for context when comparing players in Cod. We think of some players as slow players, others fast, oftentimes by their gun choice. AR players are usually slower, subs run-and-gun. I find myself using engagements per minute (EPM) as a proxy for how fast a player is playing, and I see many others do the same. This makes sense intuitively; the more engagements a player gets in, the faster he must be playing. But there is an inconsistency in the logic of EPM: players do not have equal control over all the gunfights they get into.
An Example
Consider the fastest player imaginable. He sprints around and losses every gunfight. He is fast, so he averages 10s between spawn and first engagement. Assuming he plays a 10-minute game with 5s respawns, this speed demon would end the game 0–40.
- EPM = 4.0
Now consider a player who goes only 75% as fast — that is, he averages 15s to first engagement off spawn and wins 50% of his gunfights. This example gets slightly trickier because we must assume some time between engagements after gunfights that he wins. This example could be infinitely complex, considering the chances of a player winning each subsequent gunfight as >0% but getting smaller every time. We can use some LAG scrim data to pick a reasonable trade attempt time: 3s.
For simplicity's sake, let’s say our slower player wins 0% of these trade gunfights (he always gets traded after kills). I’m sure there’s a way to calculate this slow player's expected engagements mathematically. Still, I can just run 5,000 simulations and get an estimate of this player’s average EPM in the same game.
- EPM = 4.1
In fact, this year, plus-minus in a game has correlated with EPM, explaining 22% of EPM variance (R² = 0.22). Here’s a graph that shows exactly what I think is wrong with EPM as a measure of player speed: Winning gunfights increases your EPM separate from your inherent speed.
How can we fix this?
Keep in mind that the inverse is also true: NOT getting into trade engagements decreases your EPM relative to your actual pace. The “average” EPM player is getting into some amount of trade engagements every game, so dying more will limit that number, making you seem slower. We need to account for extra kills and excess deaths relative to average because, as I’ve suggested, secondary engagements are more so dictated by the trading team.
With this perspective, I propose a new stat, “Pace,” that aims to account for the extra engagements after the first kill and remove their influence on EPM.
Pace=EPM -(PMPM*0.3)
Where PMPM = plus-minus per minute.
We can actually look at some early data from this year, CDL 2021, to see how Pace compares to EPM. The CDL has also provided (with no context) “average speed” as a boxscore stat, although I am still unsure what it means. We can use speed as another check of Pace. Speed should correlate more strongly with Pace than traditional EPM.
In the following correlation table, we can see that Pace achieves both better correlation with measured game-speed and less correlation with plus-minus.
A few notes
- While Control games obviously have a slower overall pace, the relationship’s slope (+0.3 EPM/1 PMPM) is similar in both cases.
- Speed, the new stat from Activision, should be the new standard for comparing players’ paces. But, until the stat is explained and widely available, I believe my Pace is a suitable alternative.
- I calculated game duration used for EPM, PMPM, and all other rate stats by using boxscore time alive per player + deaths because Activision has not released actual game durations for any games this season (yes, you can see it in the post-game scoreboard, but not on our stats portal) :(
