EPTDustin Browder Calculates Balance, Overturns Mathematics
5x +3y = 20
x = ?
For thousands of years, certain mathematical truths have been considered incontrovertible. One of these supposed truths was that it is impossible to solve for two independent variables from a single dependent variable. In other words, in order to solve a linear system with two unknowns, it was necessary to have at least two equations. However, it seems one of the minds at Blizzard has finally overcome this problem, and overturned the foundations of mathematics as we know them.
The breakthrough occured when Blizzard's balance team for the popular video game Starcraft 2: Wings of Liberty, tried to solve one such equation. Most of the development team immediately dismissed the problem as impossible to solve, citing the long-standing principles of mathematics. However, that didn't dissuade one man...
![[image loading]](http://i.imgur.com/224pi.png)
Dustin Browder has a Bachelor's Degree in English Literature from the prestigious UCLA.
I sat down with the mind behind this incredible feat for in depth look at how he reached the solution to the problem which has stumped mathematicians for millennia.
Browder - "Well, you see, we were trying to come up with an equation to calculate the balance of the races in our game, Starcraft 2. The only data we really had was the win and loss statistics of the millions of players worldwide, and we had to find a way to calculate the balance of the game from these game results.
"Unfortunately, we have a matchmaking system which pits players of equal strength against each other, so the statistics eventually revert to 50%. To overcome this fact, we decided to take into account each player's skill at the game, in order to determine which race was winning a disproportionate amount of games based upon player skill.
"This is where we encountered another problem. We couldn't calculate the relative skill of each race without knowing the balance of the races. The skill of each player was unknown, and the balance of the game was unknown. We couldn't solve for the balance without knowing the skill, and we couldn't solve for the skill without knowing the balance. This means we had two unknowns, and only equation, based on the win ratios for each race. To put it simplistically, the equation we had was something like this:"
Relative Player Skill * Relative Race Balance = Win Ratio
"Now, I was told again and again that it was impossible to solve for two independent variables given only the win/loss statistics, but I was determined to find an answer.
"My solution was rather innovative, genius really... One day, while I was sitting at home, poking a needle into my reaper doll, it suddenly hit me like a ton of bricks! What if we just ignored one variable temporarily, solved the equation, and then substituted the result back into the original equation?"
![[image loading]](http://i.imgur.com/Ib2kj.jpg)
The solution was elegant in its simplicity, and yet incredibly effective. Here is an example of the process at work, taking the sample equation above:
5x + 3y = 20 ---> 5x = 20 ---> x = 4
5(4) + 3y = 20 ---> 20 + 3y = 20 ---> y = 0
And shazam. Just like that, thousands of years of work by mathematicians and scientists was turned on its head. When the evidence was presented to Dr. Noam Elkies, head of Mathematics at Harvard University, he responded with dismay.
![[image loading]](http://i.imgur.com/HRdc6.jpg)
Dr. Noam Elkies - "You trollin' me, dawg?"
Browder - "This is how I solved the problem of figuring out both player skill and game balance from individual game statistics. I ignored balance in the equation and calculated each player's relative skill. Then I plugged skill back into the equation. Incredibly, we discovered that imbalance was practically zero; in other words, the game was nearly perfectly balanced, give or take a few percent.
"When I came to the rest of the team and told them of my solution, they couldn't believe it. They just sat there with their mouths hanging open, staring at me. Eventually they got over the shock of my accomplishment and started getting to work, running the numbers."
Blizzard Developer - "Look, I'm only talking to you on conditions of anonymity. He came to us with this 'solution' to the problem, and well, we just didn't know what to say. I mean, our jobs were on the line... So we got to work trying to mask what was actually being done by making an equation as complicated looking as possible, to confuse the general public."
![[image loading]](http://i.imgur.com/JOoZz.png)
However, not everyone was convinced by Browder's achievement. A few notable pros have made comments critiquing Blizzard's claims of balance.
![[image loading]](http://i.imgur.com/XYfoK.jpg)
Greg 'IdrA' Fields - "He's just retarded. The whole thing is fucking stupid.
"You can't determine skill from game stats. Otherwise I'd have a perfect record against Cruncher. The only way to determine skill is to watch people play the game."
Sen - "You see!?! YOU SEE!?!?!"
From here, Browder feels he has no where to go but up. Recently, he has turned his attention to more advanced mathematical theorems. His next project is to solve the problem of division by zero.
Browder - "I had this idea, see, that if we define the quantity zero times infinity as one, then the math all seems to work out. Once you divide by zero, the zeroes cancel out."
For now, however, this brilliant mind is still a lead game developer at Blizzard, and the hero of millions around the globe.
![[image loading]](http://i.imgur.com/Ep9YI.png)
