“I am a good player because I win at least 50% of my games.”
“I have seldom lost because my win percentage is about 60% all the time…”
“My buddy is great at this game, he rarely loses.”
“A good player should win at least 50% of his games if he is playing an opponent of equal skills…”
Now these boasts are not generated by some 12 or 13 year kids (Lord forbids I’ll have those schmucks running my shops) but instead said by adults range any where between the age of 20 till 45 in my shop. After viewing a similar topic in a forum that I frequent currently, I decide to sit down and analysis the likelihood of such happening.
I decided to use inferential statistics rather actual statistics to solve the issue. The reason is a simple one. It will push the possibilities to infinite to consider every aspects of the game as a variable and an equal likely outcomes by using actual statistics, and the final findings will still have little significances on the issue of discussion here. IS, on the other hand, would allow me to better analyze the situation by only identify a few key elements as key variables while assuming the rest a constant.
It has been awhile since I did hypothesis testing since college, but I’ll see if my higher education had pay off here. 
I’m going to establish a few common grounds here. First, I’ll use 40K as the common game system since that was the original discussion of the topic. Then I’ll assume that all variables in questions are constant unless the discussed issue in each testing (players skills, dice, etc.) And last but not least I’ll focus on the common belief that “a player should win at least 50% of his games in 40K.”
First off, let’s set up the null hypothesis, for those of you who are not familiar to the term, feel free to do a quick google/wikipedia search. It is really a fancy term for “the common belief”. We are first going to analyze the likelihood to obtain a win between players of similar skill level.
H0: The likelihood to receive a win between two players of equal skills in a game of 40K should be at least 50%.
The alternative is then,
H1: The likelihood to receive a win between two players of equal skills in a game of 40K is not at least 50%.
Let’s use a simple matrix then. We shall analyze the following variables.
The first variable that we shall consider is the importance of a dice in the game. Most of the 40K gamers should agree that a good dice distribution for one player when paired against bad dice distribution for the other player will end a win for the player with the better dice distribution. Alternatively, if both players dice distribution are about the same, then the most likelihood outcome of the game would be a draw.
Notation wise I shall use the following:
PL = Player. OP = Opponent. GD = Good dice distribution. BD = Bad dice distribution.
So,
OP/GD OP/BD PL/GD Draw Win PL/BD Loss Draw
As you can see, the likelihood of getting a win is only 1/4 of the times. Thus I’ll reject H0 in favor of H1 when the variable in question is dice distribution.
Next I’ll analyze player lists, another common aspect that many players consider an important fact for one’s victory. It is generally accepted that a player with better, more tournament quality list will win against a player with a fluff based, nothing min/max list.
Notation wise I shall use the following:
PL = Player. OP = Opponent. GL = Good List. BL = List.
So,
OP/GL OP/BL PL/GL Draw Win PL/BL Loss Draw
As you can see, the likely hood to win is again at 1/4. Let’s reject H0 in favor of H1 again, shall we not?
Now for my last testing, I’ll consider both the dice and the player’s list. For argument’s sake, let’s consider it an equal outcome when a player with GD/BL versus a player with BD/GL. Since we’ve established notations prior, it should be.
OP/GD/GL OP/BD/GL OP/GD/BL OP/BD/BL PL/GD/GL Draw Win Win Win PL/BD/GL Loss Draw Draw Win PL/GD/BL Loss Draw Draw Win PL/BD/BL Loss Loss Loss Draw
What you know, the liklihood of winning increased to 5/16 instead of 1/4. But it still not as close as to what the H0 would indicate. Again we’ll reject H0 in favor of H1. Thus,
H1: The likelihood to receive a win between two players of equal skills in a game of 40K is not at least 50%.
Now I’ve finished the initial testing, here are something that came to my mind.
- Is a “good player” a player that was good? or “lucky” as a result of match ups?
- What is a “good player” then? A player that has above 50%? 40%? 30%?
- Or is a player a good player when he wins majority of his games with a bad list and equally bad dice distribution?
Since none of these questions can’t be answered without proper discussion or testing, I shall categorize it along with the rest of my observations – a phenomenon I considered “Failhammer”.
Yes!
Your inference is good until you reach your last matrix. There, you have too many variables in too few slots. You are now n=3 axis of possibilities and should properly use matrices to come to a conclusion.
Or just say “good ’nuff” and drive on.
:}
Pretty good overall.
I’ll check it again later. I wrote it this morning before heading to my divorce trial in relief of some stress.
><
Zen