One of the frustrations of counter strike player statistics is that players are frequently under-equipped compared to their opponents and teammates but their raw stats don’t reflect this. Also sometimes a strong player is on a team that struggles and as a result their team plays a lot of Eco rounds. That player is at a disadvantage statistically through no fault of their own.
Some players hog the budget or have the luxury of playing a role that allows them to more frequently survive rounds, carrying their kit over to the next. In a one sided match players frequently sit on a budget advantage I wanted to look at developing a statistic that accounted for the value of equipment players carried into rounds and how that affected their performance.
To measure the performance though I needed a single performance statistic that would make sense and be easily understandable, and that had a clear relationship to a player’s share of eco expenditure.
My candidate stats were:
- Net Kills per Round, (kills – deaths)/rounds. This is a fairly straightforward stat that is heavily optimised to the single individually measurable stat that correlates well to the round win – kills. It also incorporates the damage getting killed does to your team’s chances. It rewards play taken to a maximum point of aggression while also taking care of a player’s own life.
- Raw Net Kills. Largely used as a reference point to check that correlating net kills per round improved the accuracy of the study.
- Average Damage per Round. This is something that is often cited as a particularly fair stat, as it still allows players who have a dangerous role in the team to still acquire positive stats. In my studies though I haven’t found it to correlate as strongly to winning as kill statistics.
- Kill/Death ratio. Anyone who has spent time with game statistics know that these ratios can be very misleading as they interact very badly with time, essentially rewarding camping play and baiting your own team. However that also makes them an excellent part of a study, because if a ratio is the best match something has potentially gone wrong.
The study set is a very broad base of games across a wide variety of competitions and levels, creating thousands and thousands of performances. For each game the total expenditure for both teams was calculated and compared to the potential metrics identified above to find relationships between eco share and individual stats.
Just be completely clear, when I talk about Eco Share, I’m talking about all the players in the server, not just the players on one team. If you’re hogging your team’s budget then players are expected to do well, but if the opposition is stacked then we have to make adjustments to performance expectations as well.
Net Kills per Round (NKR) had the best correlation with Eco Share, at 0.723 when ADR only correlated at 0.569. NKR was significantly better than raw Net Kills which was expected and had to be confirmed. KD also correlated well with Eco Share (better than ADR) but not as well as NKR.
So having established that player NKR has a significant relationship with a player’s Eco Share, the next step was to create a model. Something to remember is that a model is essentially predictive in nature, so it will never correlate as well as the correlations taken only from the historical data.
What immediately became obvious from visualising the data was that a simple linear relationship wouldn’t cover the variations, so a 3 degree polynomial regression gave me a pretty solid match – correlation to model of 0.5325 r2.
Translated into English this means it’s not perfect, but clearly has meaning. It produces an S shaped curve which indicates the initial budget differences are of key importance and there is a diminishing return for bigger use of the budget. So going from 10% to 12% of the overall budget should produce a bigger jump in performance than going from 14% to 16%.
This shows the trend as well as the general shape of the prediction made. Deviations from the trend line are things I’m putting down to skill, luck and good or bad form and being on the team with less overall money. There are a few problems with this, and as with everything I’ve had to make some trade-offs when it comes to presenting the data.
Firstly it doesn’t deal that well with pistol rounds. It’s rare for players to have much disparity in their Eco Share in those rounds and there is a slight bias in the model to a positive score, and there aren’t very many pistol rounds in comparison to most other types of round so in a single map or even match there often isn’t enough variation to produce a refined number.
It also seems that AWP players at a top level are more deadly than my general model predicts, so successful snipers appear to get rewarded more strongly than perhaps is justified.
I wanted to keep this simple so even if you don’t understand what is going on mathematically you can visualise that as a player spends more in comparison to everyone else in the game their performance is expected to go up. I am aware of some more refined possibilities, but they start to become hard to understand both mathematically and conceptually.
For the future there are still many possibilities for improvement. Having used a very large study set to create this baseline statistic there are some weaknesses in how it applies to elite level players, and there are some other complications to do with how the Eco considerations have two sides – the value of the equipment and the potential of them to earn more money which this study doesn’t take into account.
Overall the problem of the perfect model of player performance has only had it’s surfaced scratched by this study, but there are plenty more ideas in the works.