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Date of registration
: Mar 21st 2013
Platform: PC
Location: __main__, Finland
Reputation modifier: 16
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Variables  Correlation & P + time+kd  0.135 (p <<< 0.01) time+spm  0.266 (p <<< 0.01) time+kpm  0.246 (p <<< 0.01) rank+kd  0.244 (p <<< 0.01) rank+spm  0.688 (p <<< 0.01) rank+kpm  0.524 (p <<< 0.01)  kd+spm  0.336 (p <<< 0.01) kd+kpm  0.371 (p <<< 0.01) spm+kpm  0.709 (p <<< 0.01) 
Alright I am not too sure if there's a good or special method of creating nice product of all these, but I got correlation of 0.507 against rank and 0.236 against gameplay time when I calculated the variable like this:
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1 kd/median(kd) + spm/median(spm) + kpm/median(kpm)
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Variables  Correlation (rho) & P + time+kd  0.367 (p <<< 0.01) time+spm  0.427 (p <<< 0.01) time+kpm  0.323 (p <<< 0.01) rank+kd  0.567 (p <<< 0.01) rank+spm  0.734 (p <<< 0.01) rank+kpm  0.540 (p <<< 0.01)  kd+spm  0.704 (p <<< 0.01) kd+kpm  0.831 (p <<< 0.01) spm+kpm  0.718 (p <<< 0.01) 
Quoted
Alright, I calculated log(kd) and did correlation tests against that (This time I assume I should use person's, because log(kd) is almost normally distributed?). I get 0.547 against rank and 0.303 against gameplaytime.
As for doing product with summing and z values I get following (again, I assume pearson's is the one we should use because of normal distribution of product?):
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1 2 3 4 Test  vs. Rank  vs. Time ++ Pearson's  0.654  0.303 Spearman's 0.664  0.396
This post has been edited 7 times, last edit by "Miffyli" (Apr 10th 2014, 6:28pm)
Date of registration
: Apr 12th 2013
Platform: PC
Location: Guilin Peaks, Finland
Reputation modifier: 14
"Playtime/Rank doesn't tell how good player is"
Date of registration
: Mar 21st 2013
Platform: PC
Location: __main__, Finland
Reputation modifier: 16
Could you plot the distribution of ranks? The apparent lack of highbutnotmaxrank players speaks for a segregation of the playerbase to occasional/casual/dropout and hardcore gamers.
As to confounders, time is of course confounded by the fact that prior experience is not accounted for. Rank on the other hand is essentially the product of time and SPM, and there not a variable independent of SPM (=> high correlation between dependent variables is like a tautology).
Date of registration
: Mar 21st 2013
Platform: PC
Location: __main__, Finland
Reputation modifier: 16
You could also test using the product of KDR, KPM, and SPM as a skill metric to see if that gives a stronger correlation with the investment metric (time, rank).
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kd/median(kd) + spm/median(spm) + kpm/median(kpm) 
What (if any) light does this shine on the acual ingame "Skill" stat. I know we've got the formula somewhere. From my experience, it tends to vary quite a bit. I imagine gamemode and similar factors have a fairly significant effect.
Date of registration
: Mar 21st 2013
Platform: PC
Location: __main__, Finland
Reputation modifier: 16
Awesome work!
Could you possibly show the distribution of the other variables(time,kd, spm,etc)? The rank histogram was very useful, clearly shows what is "normal".
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SPM: 0.0000 328.0347 451.9802 619.1244 3232.8914 KPM: 0.0000 0.414393 0.5730724 0.7577548 3.0480124 Time(h): 0.0000 69.12722 128.91722 212.84333 1240.09444 
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