Tournament Statistics Project


#1

Hey guys

This is my announcement for a project I am doing on the side that is related to fighting games. A while back a conversation on SRK sparked my interest in the idea of “How does my chance of winning a round propagate through sets and tournaments?” This originally got started as “If I have a 4-6 match up how does that effect my chance of winning a 2 out of 3 set? A 3 out of 5?” In my first attempt at this problem I tried to derive a formula to deal with it, but found the math got too big too fast. I was able to get some useful results however which you can find at this link:

I realized I couldn’t actually find this answer for a tournament of any significant size (A 4 man bracket was already difficult to do). So to solve this I have actually written a piece of computer code that simulates a tournament using a Monte Carlo style algorithm. I know that sounds difficult, but the idea is actually very simple. Set up a bracket, run the matches according to set probabilities, determine the winner, send the winner/loser to the next round, and record the results.

A match is simulated on the computer rather simply. Let’s say I have a match against another player and in a long set I would win 60% of my matches against that player. The computer will simulate each game in a standard tournament set by selecting a random number between 0 and 1. If that number is less than .6 I win, if not I lose. We simply repeat this till someone wins the set. Then the rest of the program works exactly how a tournament would, advance the winner and knock out the loser.

With this you can sample thousands of tournament scenarios which allows you to figure out how different factors effect chances of winning.

Here are some of the factors I intend on testing

  1. If I have win rate of x% how does that effect my chance of winning an entire tournament?
  2. If there is a top player in my bracket how does that effect my chances?
  3. If I have a bye in the first round how does that improve my chances?

I’ll be posting some of my results as I finish them.


#2

I thought about statistics and applying it to tournaments but there’s always human error so I don’t know if the data would reveal anything significant or be reliable. It’s a lot like LSR models in football. Tons of variables that aren’t exactly quanitifiable. Who’s to say Justin Wong just happens to have an off night and doesn’t make it out of pools?
One thing I would like to know is the amount of players. Does the size of a tournament change outcomes? And I’d base it more off of local players because I feel like using players that travel consistently to regional tournaments introduces a random variable (the top-player variable if you will)… But I don’t do a lot of stats work and read “Monte Carlo,” style and “wrote code” and was like “fuck it…” But I can speak a little Econ and do understand a bit about Game Theory matrices… If that gives me credibility.


#3

Probability includes human error. When we talk about something like an 8-2 match up we are saying if character A always plays perfectly then character B should lose, but because humans control it there is always a random factor. I could muck up my spacing and get Ultraed/Supered/etc. That’s why there is still a small chance of the disadvantaged character to win. Likewise if we are talking about J-Wong having an off day it’s the same deal. It’s measured by probability.

That’s the whole idea of probability is that you can’t know all the variables so you look at the overall statistical trend.

I actually have that included. My code is generalized to allow me to adjust the bracket to whatever size I want. I can do as small as a 2 man or as large as a 1024 man bracket. It was frankly the hardest part of writing it was making it so the bracket management scales with the size of the bracket.

The study would be more general although you could apply the code to a specific case if you knew the values to input.

So for instance if I want to simulate a player like J-Wong in the bracket I wouldn’t use specifically J-Wong’s data I would vary the chance of me beating him to collect the whole range and see what the effect would be since J-Wong statistically has to be somewhere between 0% and 100% (Most likely between 90% and 100% for most players lol).

So for example let’s say our top player has a 90% chance of winning a single round in a match against everyone. Over the course of hundreds of simulations eventually you will find one case where that top player loses, but the overall trend will be that top player will win much more than he loses.


#4

First post in the series. More to come