Analysis of CS:GO Win-rates · smabie

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12 Jun 2020

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This post is going to be a little different from usual; instead of<br>markets, we're going to look at a video game, namely, Counter-Strike:<br>Global<br>Offensive<br>(CS:GO). CS:GO, like most great games, is easy to learn but deceptively<br>hard to master. For those at are unfamiliar with the game, we'll give a<br>quick overview below.

CS:GO is a competitive zero-sum game in which two teams of 5 players<br>each try to win rounds. The first team to 16 points wins the game. The<br>game is asymmetric as there are two distinct sides: the terrorists<br>(T-side) and counter-terrorists (CT-side). After 15 rounds, each team<br>switches sides. The goal of the T-side is to either eliminate all CT<br>players or to plant a bomb and have it explode before the CT-side can<br>defuse it; the CT-side wins the round if kill all the players on the<br>T-side before the bomb is planted, if they defuse the bomb, or if time<br>runs out on the round. this asymmetric rule-set implies that the CT-side<br>can lose a round even if they kill all the opposing players, while the T<br>side cannot lose if they eliminate all CT players.

In order to get a better idea of the structure of the game, let's look<br>at a top-down perspective of one of the most famous and iconic maps,<br>Dust2:

T-side starts the game in T-spawn and must plant their bomb at one of<br>two locations: B-site or A-site, designated by the red areas on the map.<br>the CTs start off in CT spawn and must try and defend these two sites.<br>If T-side manages to break the CT defenses and plant the bomb, the<br>remaining players on CT try and retake the bombsite (either A or B) and<br>defuse the bomb before it explodes.

Because of the asymmetric nature of the game, I thought it would be<br>interesting to analyze how much a kill effects the game for each side.<br>To start off with, we'll first look at the situation where the number<br>of players on each side is equal.

Even Match-ups

First up, let's look at the so-called even match-up, where there are an<br>equal number of players on each team: 5v5, 4v4, etc. Using over 400,000<br>rounds of match data from mid-2018 (click<br>here<br>for the original dataset), we aggregate all rounds with even match-ups<br>and the side that wins. From this, we can calculate a cumulative win<br>probability for each match-up:

From the above graph, it's seems that the T-side enjoys a significant<br>advantage. Even when the match starts, the CT-side has a less than 50%<br>of winning the round and as trades are made (a situation where each team<br>loses a player), the advantage the T-side has only goes up. But is this<br>significant? Let's look at a table of CT-side win rates and their<br>associated p-value:

CT win rate<br>p-value<br>players

0.48729<br>2.67482e-55

0.469768<br>1.17974e-151

0.455098<br>3.84482e-237

0.439982<br>1.52963e-319

0.430299<br>2.35914e-282

It's clear from the minuscule magnitude of the p-values that we can<br>reject the null hypothesis, namely that each even match-up is fair: a<br>50% chance of each side winning the round.

All Match-ups

Now that we've established that even when each side has the same number<br>of players the T-side has an advantage, let's consider all the possible<br>combinations. Clearly a situation when 5 CTs are up against 4 Ts is not<br>a fair fight (We might assume that CTs have the advantage), but unfair<br>is it? After crunching the number for each permutation, we get the<br>following graph:

Interesting! When the CTs have close to the number of players as T-side,<br>the first kills make the most difference. A 5v5 for the CT side gives<br>them a 48% chance of victory, but netting the first kill shifts the odds<br>considerably to 68%. When the difference is large, the final kills have<br>the highest percentage chance, as the chance of the CT-side winning is<br>so low to start off with. Below is a graph of the exact figures:

1 CT<br>2 CT<br>3 CT<br>4 CT<br>5 CT<br># T alive

0.00218907<br>0.0227307<br>0.106122<br>0.274956<br>0.487288

0.00689667<br>0.0682988<br>0.235994<br>0.469768<br>0.683482

0.0287596<br>0.187184<br>0.455091<br>0.70026<br>0.858241

0.123364<br>0.439972<br>0.732706<br>0.893306<br>0.961373

0.430299<br>0.7915<br>0.941975<br>0.985024<br>0.9967

0.906434<br>0.989945<br>0.998562<br>0.999731<br>0.999873

Conclusions

I know little about professional CS:GO strategy and the data isn't<br>taken from professional games, but we can quickly infer a couple things<br>from the data:

T-side wants to trade down as much as possible, CT never wants to<br>trade.

CT-side needs to be play very conservative, maximizing the number of<br>players on their team that are alive.

T-side wants to play in a very aggressive style in order to take map<br>control and trade.

Anyways, this has been a fun little post to write, I hope you enjoyed<br>it! Click here to view the<br>GitHub project.

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