# Effect of Purchase Decisions on the Winning Probability [CS:GO]

Hey. I work at GOSU.AI, a company that studies CS:GO and Dota2 related data and develops tools to help players improve their skillz. In my recent article I offered some performance metrics related to the flashbang usage statistics. Today I would like to focus on economical decisions and how they affect your chances of winning the match.

I describe a data-driven approach that allows you to compare different purchase strategies based on a statistical evidence from 6000 recent HLTV.org demos.

Let’s start with the most simple case and consider one single round. Both teams have some equipment each round. Here is a diagram that shows probability for Terrorists to win the round based just on both teams equipment value at the round start:

There are about 93k rounds in total in dataset. For each round met I store CT/T equipment value and round winner. I split each dimension into categories like “3000-6000”, “6000-9000” etc. Given that I could calculate CT winning probability for each cell directly.

Note that I decided to blur the down-left corner because those situations are very rare and there are not enough statistics for them. Also, theoretically, a few warmup rounds may leak into the dataset:

Moreover, I could formulate a question like “if Terrorist have a 21k+ buy, how would CTs chances change depending on their equipment value?”

Okay, so now we’ve got a model that predicts single round winner based on the money input. In reality game is a sequence of connected rounds where the past ones affect the future rounds directly.

Let’s get back to the first question from the article. The score is 14-14 and you’ve got 2800\$ on your account plus 1900\$ in case of losing. Your captain takes a timeout to make a decision on how to spend the money.

For the brevity let’s assume that your enemies have got enough money to have a 21k+ buy in all of the rounds left. In case of 15-15 its overtime with 50% chances of winning. Let’s compare two possible scenarios:

1. Full eco vs Full-buy, then

Pictures above show the possible outcomes and their chances. After making some ordinary math operations with those probabilities and assuming that overtime gives you 50% to win, resulting numbers are:

1. Win: 19%

Lose: 81%

1. Win: 35%

Lose: 65%

So eco+full_buy scenario may seem to be more conservative and wise decision but in fact double force-buy almost doubles your chances of winning! It seemed to be a bit counter-intuitive to me, but I think there is an explanation:

1. I assume there is a 34% chance of winning 2800 forcebuy. It’s an average estimate and may vary depending on current opponents and how the current game goes. However, I should say that I calculated the same number based on Krakow Major demos to double check and it shows 30-33%
2. Yes you are not in a best starting situation, but winning just 1 round gives you ability to go overtime and have an extra 50%.

Conclusion and future work

Today I showed you an approach that connects teams’ ammo equipment value in a single round with round winning probability. Since a game of CS is a sequence of rounds, it becomes available to see how economical decisions affect winning and measure the influence directly.

I took a very simple 14-14 case for the demonstration and already have some interesting finding. However, in order to become available to make more complex calculations there is a need to make a bit more complex model.

First of all, number of players who didn’t die in a round affects teams’ money. So the model should be able to predict not only the winner but also a number of players alive.

One more thing to incorporate is economical decisions simulation. It doesn’t seem to be very hard but would take some time to implement

Another way to improve my analysis is to be more specific on weapons choice. So instead of operating with money values one could work with different sets, say “5 ak” or “4 ak + awp” or “5 deagles”. I think that using clusterization to figure out the most common combinations should work well.

What is really inspiring me in that model is that it connects separate rounds into a continuous sequence of rounds. So for example taking many risky in-game decisions (say rush B every round) affects your money directly, as well as saving and not taking too much risk sometimes might significantly increase your chances.