Damn, Ryan beat me to it. Yes, that was a hypothesis of mine ~4 years ago, but as we recorded more and more observations, we realized luck was normalized to roll, not to game. Ryan might've even commented in chatbox about it, perhaps... sorry, long time ago.

While we've got Ryan's attention, can you please confirm/deny/no comment on those crazy-bad luck accounts? None of us really care any more, it's so far back in kdice history now... did you design a rudimentary targeted roll-tweaker? I swear we were measuring several standard deviations away from the norm.

Louis, not that I am an expert in stats, but yes, we had to take two graduate-level courses for the phd. And medical physics is mostly all physics, no medical. I spent years designing and implementing Monte Carlo code, which is based completely on stats. Hence my choice of screen name btw.

@jurgen: "Someone can reinforce that theory by sitting 100 games and never attacking. The luck% for that account should be about 50,7%."

Either that or just check whether the att:def ratio negatively correlates with luck if you take a large enough sample. But if you check the top fives of the "most aggressive this month" and "most defensive this month" lists, it seems to condtradict your assumption.

Federer in particular plays a heckload of games every month, his att:def ratio is consistently over 80:20 every month since February and he still has OK luck. OTOH, it's true that he usually flags out very early so he might not be a good example. (Need to check a larger sample...)

Month Rank Score Games PPG Kills Dom Att:Def Luck 1st 2nd 3rd 4th 5th 6th 7th
August 2015 1 932nd 0â?? 473 -52 1 13 % 84 : 16 50.7 % 0% 0% 0% 1% 26% 19% 53%
July 2015 2 484th 0â?? 1326 -50 3 16 % 87 : 13 49.6 % 0% 0% 0% 1% 22% 19% 57%
June 2015 2 509th 0â?? 1329 -50 3 15 % 86 : 14 49.6 % 0% 0% 0% 1% 24% 20% 53%
May 2015 2 329th 0â?? 1123 -50 3 14 % 85 : 15 50.4 % 0% 0% 0% 0% 22% 21% 54%
April 2015 2 189th 0â?? 965 -49 11 16 % 85 : 15 50.1 % 0% 0% 0% 2% 23% 21% 52%
March 2015 2 607th 0â?? 1223 -50 8 15 % 84 : 16 50.6 % 0% 0% 0% 1% 25% 20% 52%
February 2015 2 218th 0â?? 1314 -50 5 16 % 85 : 15 50.2 % 0% 0% 0% 1% 19% 20% 58%

@monte: That really was easily trolled, but thanks for the explanation ;-) I happen to have been using MC-simulation myself, including the coding.

Back on topic, Federer would have been my example too. His luck is above average and he's more or less only attacking which means, he should be below by theory since he doesn't benefit from defending draws.

Very much to the basics, I think luck should be based on a per dice level. Any dice showing above 3.5 is lucky, any dice below is unlucky. If you like you can number degrees of luck/unluck depending on the distance to the expected value. Given random rolls this should average to 50. Any other measure is semantics and thus not computable. Even a loss might turn out somehow positiv in some cases so that that roll actually was lucky.

I like kakku's map quite a lot. You can see your offense/defense average per dice and can clearly say if it is above or below 3.5. That's showing quite nicely if you are lucky or not - of course others might have more luck.

A bit more about the correlations: I pasted the aggressiveness and luck stats from last months top100 onto a spreadsheet to see if there is any negative correlation between the two.*

At first, it seemed that there was, but it was only due to three outlier guys who only played 1 game during the entire month (ArnasBro, DonnieScribles and gtzlat). After removing them from the sample, I was left with r=0.032, which basically means there's no linear correlation.

(*Technical info: to get the aggressiveness stat, I just used the digits before the colon in the att:def ratio)

maybe federer get's some extra luck because Ryan built in some extra luck for players with a low win% (just feeding the paranoia here :D)

thanks for doing some research on this

This is pure speculation but the reason federer's luck is boosted up is because he plays to maximise his number of attacks. So he goes for obvious +1 rolls and only does -1 or even rolls when it's the only move left.

Also he's not giving people the chance to kill or attack him when he's weakened by spreading out. Being killed means you lose defends, meaning lower luck. So he's denying people the lowering of his luck after his turn. Other people only flag out say 50% of the time, while in the other 50% of the time they get killed and lose some luck%

Well - losing a defend let's say 8v1 is not unlucky but very expected. If you rolled a 6 with that 1 dice you would have been very lucky indeed, although you lost. That's one point where these stats are without any meaning. Losses can occur even though you roll 6 with all the dice you got - and then you certainly have not been unlucky, just outnumbered.

totally agree

that's why I have been suggesting to add the average dice roll stat for years

It's not perfect either but (to me) knowing you rolled 3,8 on average in a 20 round game is far more interesting than seeing I had a 51% or 49% luck stat.

I also think that there needs to be a seperate luck stat for first 3 rounds of a game. If your luck sucks at the start you only have a small chance to win or come back. If you can survive the start and manage to fight for say 12 more rounds, you might end up with a 52% luck game.

Well, then again, deciding if you had a shot to come back or not is semantics. Finding a rule to cover that is difficult. Losing that 8v6 in turn 10 might be more lethal than losing 4v2 in 1st turn - you never know.

Give the average roll per dice and monthz as one measure and accumulate the difference of the rolls to 3.5 as another measure. You might discuss normalizing the difference by the number of games and, if you like, turns. Doing that on a monthly base you see who really rolls too low. Maybe these stats should only become available after a certain number of games to make fiddling with it with just 1 game played not possible.

Seeing those number I so hope it would totally even out for all.