Stats

Other Games SotM Game Engine
1

Hi all,

     I love the community stats page, so I thought I would calculate the statistics to help put things in perspective. 

 

This is a binomial stat calculation assuming a 2/3 win percentage. It would be more accurate to use the exact win % for each hero, villain and environment, but I am to lazy.

So in general the formula comes to:

% error = square root(2/9/N) x 100%

 

where N is the number of games for that hero, villain, or environment.

 

So for 100 games which is about where most heroes are we get 4.7%.

 

for 40 games which is where most villains are at we get 7.5%.

 

to get 2% error we need 500 games for each hero, villain, or environment.

 

to get 1% error we need 2000 games for each hero, villain, or environment.

 

so we can say a little bit about the heroes, but I think the stats are still to low to say much about the villains.

 

2

Erm...so...erm...what is it you're working out, exactly?

3

 

Ooh, yeah, this looks fun. Statistical analysis, I choose you!

Mean victory rate is 65.75%, in 511 games. Legacy is 78.45% with 116 games, Tempest is 75.61% with 123 games, Tachyon 74.79 with 119, Young Legacy 74.79 with 31, Visionary 72.58 with 124, Expat 60.36 with 111, Wraith 60.34 with 116, Bunker 60.05 with 119, Ab-Zero 60 with 105 and Fixer 60 with 100.

Jesus, I've forgotten how to do this... Okay, so we have a mean of 0.6575, standard deviation of... 0.475? I think?* And n=511. Then we're comparing that to:

Legacy: ![\bar{x}](upload://qdnzMvxDMowwvWP91QGyflAa8ch.png)=0.7845, S=0.413, n=116, so Z = [0.7845 - 0.6575/Root(0.413^2/116 + 0.475^2/511)] = 2.9045

Tempest: ![\bar{x}](upload://qdnzMvxDMowwvWP91QGyflAa8ch.png)=0.7561, S=0.431, n=123, so Z = [0.7561 - 0.6575/Root(0.431^2/123 + 0.475^2/511)] = 2.2318

Tachyon: ![\bar{x}](upload://qdnzMvxDMowwvWP91QGyflAa8ch.png)=0.7479, S=0.436, n=119, so Z = 2.0020

Young Legacy: ![\bar{x}](upload://qdnzMvxDMowwvWP91QGyflAa8ch.png)=0.7479, S=0.434, n=31, so Z = 1.1198

Visionary: ![\bar{x}](upload://qdnzMvxDMowwvWP91QGyflAa8ch.png)=0.7258, S=0.447, n=124, so Z = 1.5074

Expatriette: ![\bar{x}](upload://qdnzMvxDMowwvWP91QGyflAa8ch.png)=0.6036, S=0.491, n=111, so Z = -1.0543

Wraith: ![\bar{x}](upload://qdnzMvxDMowwvWP91QGyflAa8ch.png)=0.6034, S=0.491, n=116, so Z = -1.0777

Bunker: ![\bar{x}](upload://qdnzMvxDMowwvWP91QGyflAa8ch.png)=0.6005, S=0.497, n=119, so Z = -1.1361

Absolute Zero: ![\bar{x}](upload://qdnzMvxDMowwvWP91QGyflAa8ch.png)=0.6, S=0.492, n=105, so Z = -1.0971

Mr. Fixer: ![\bar{x}](upload://qdnzMvxDMowwvWP91QGyflAa8ch.png)=0.6, S=0.492, n=100, so Z = -1.0748

So, to put those Z-values in perspective: any value above 1.6449 (or below -1.6449) has a less than 5% chance of occurring if everything was perfectly equal. So statistically, Legacy, Tempest and Tachyon may be overpowered (or at least other factors result in them winning more games than the average), but none of the heroes at the bottom are statistically underpowered... The chances of Fixer's figure or worse coming up on a perfectly average hero is 14%.

 

*My formula for the curious, though it's probably wrong: S^2 = [Sum(x^2) - n(mean^2)]/[n - 1].

4

 Blue your formula looks good. 

 

I agree that legacy looks overpowered, but that is about the only significant stat yet.

 

My purpose is just to say that we need a lot more stats, before we can say anything about balance, so play more and record you results.

 

edit: Blue are your S's missing a zero? I could be wrong, but I agree with you Z's.

 

5

I ... -believe- ... what this is about (correct me if im wrong, but my math and statistics are waaaay behind me) is finding the necessary # of games to give accurate represenatation of which heroes are better and which are worse. Am i right?

 

and the second bit is about which are higher than the average wins (not average, mean I guess) or mean sstatitistcs and are overperforming in comparision and which are under performing. (by an exact numerical value than just a strict comparison - in other words, in comparison to others Legacy is overperforming by about 1.something)

6

Yes, Blue is assuming that all heroes are equal, and the Legacy result is significantly different from average to suggest that he is better then the average hero.

 

Some people, myself included, are using the statistics report to say things like fixer is the worst hero. My point is tocaution people, we don't know yet. We need more data.

 

About the only statistically significant result is that Legacy is good. The villain stats in particular are still so low it is difficult to say anything except that the Chairman is tougher the Gloomweaver. 

 

 

7

Yes, we need more data to make any statiscally valid statement. The temptation is to look at the values and try to interpret them "intuitively", but statistical analysis only can tell if, for instance Legacy really wins more often than other heroes, or if his apparent success can be attributed to an imperfect distribution of results.

I am impatiently waiting for when we will hit enough results to begin extracting datas with a very low chance of misrepresentation !

8

also its folly to believe all heroes are created equal. it’s been stated this is not the case - and in any case this is a cooperative game, because it wouldn’t be unfair to any player if x hero was significantly more over powered than any other because we aren’t competing

that said were pushing almost 800 games with a week to go. Awesome!

9

This is absolutely fantastic. I am way excited about stats :)

10

It's okay to be 'excited', but 'way excited' ? hrm. sounds a little dirty :wink:

 

 

11

Like those "more than happy" weirdos?  :slightly_smiling_face:

12

I'm more than happy to be a weirdo. ;P

13

In this case is the value of x either 1 or 0 in all cases (for win or loss)? 

Are you using x-bar or mu when you say mean?  Since these are your sample std devs it should be the x-bar value.  I'm guessing so as I just ran Legacy myself and got the exact same value for s.

I thought the z-score of the sampling distribution was just (x-bar - mu)/(sqrt(s^2/n)) which essentially means I'm not sure where the + 0.475^2/511 portion of the denominator is coming from.  This makes quite a difference in the results as all the z-scores would have a larger magnatude.

Could we also do this as a Chi-square test where we assume they are all the same and then calculate the whether the variation is significant enough to say that they are not?  I think that would work but whats the point since we already know that the heros were not all created to be equal and that doesn't identify anything about the specific individuals.

14

Edit: Ok I looked it up and you seem to be correct, its just that for large enough N that part is often ignored and dropped from the equation.

15

Well, this Saturday i have a game-long day. i mean a day-long gaming session 9ewiter works :D).

I will be playiong a lot of games, different hero/villain combinations, and so expect tos ee a lot of new data. I'll even take count to the number of rounds it takes!

 

Regards,

 

Your friendly-neighbourhood Me.