[Patch 3.03: Quinn] General Discussion - Page 148

On March 15 2013 05:14 onlywonderboy wrote:

BO2 would be ideal but BO1 is OK.

On March 15 2013 00:48 zulu_nation8 wrote:
let's just make it so that nothing in the game is ever frustrating or obnoxious, everyone will always win lane and there's nothing "dumb" like manaless champions, free crit, stealth, or anything that makes the game remotely challenging. After all you paid for skins so you deserve to be good at the game, and the only reason everyone is not diamond is because of dumb mechanics in the game that apparently everyone aside from you has figured out how to play against.

On March 15 2013 03:18 zulu_nation8 wrote:


majority of fights is decided by who has more gold + xp, when that's even, then it's just up to skill, better initiation is a factor but not as often the deciding one as most would think.

On March 15 2013 03:45 TheYango wrote:
LoL takes advantage of the law of large numbers too though. It's not like a single crit or dodge determines the outcome of a game. In the case where you got crit in a level 1 or 2 engage, that doesn't equate a lost game unless you and your team make a long series of misplays after that fact.

The effect of these things is spread out over the course of the entire game.

On March 15 2013 07:15 Goumindong wrote:


The short answer is that this is incorrect. While a LLN will apply to critical strikes themselves (specifically Markov's iirc) in that the sample average of critical strikes will converge to the average of critical strike rates it is not true that this will have zero impact of the game. This should not come as a surprise because this is the reason that riot nerfed crit in materies and normalized crit rates.

The reason it doesn't is tied up in time series statistical concepts but can actually be explained fairly simply. We can think of most games as a sequence of random variables with the value of each of the last random variables mattering into the value of the next random variable.

I.E. X_2= Z + Beta*X_1 + error | Z is all non-random factors(skill/abilities/the actions you take in team fights etc), X is the outcome of a fight measured say in gold, error is any randomness like crit.

If we look at this system we can apply some form of LLN's if Beta < 1. The reason for this is that if Beta < 1 its possible that E(X_2) = E(X_1). When this is the case we can also do something kind of interesting by using "lag operators". Which means that its possible to write the value for X_t as the infinite sum of the previous error terms (and previous Z's in this case).

What matters in our case is that the infinite sum of the previous error terms is finite if Beta<1. Additionally the coefficient for each previous error term can be written as Beta^i where i is the number of terms back the error is. I.E. the closer Beta gets to 1, the more persistence that we have in the system. If Beta = 1 then the system is not stable, the persistence is permanent and our LLN's don't apply to the system.

In league, Beta is at least 1. We know this because if you win a team fight at level 1 and are up 100 gold. Even if that 1500 gold had no effect on whether or not you won the next team fight you would still have 1500 more gold at the end of the next team fight regardless of the outcome. Or, another way to say it is that the expected value of the gold difference at the end of the game goes up by at least exactly the value of a team fight result.

And who ever told you that you were never going to use math in your everyday life.
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A more interesting thing is whether or not critical strikes can be predicted by skilled enough players due to Riots critical strike normalization procedure. If it can then none of it holds because critical strikes are no longer random in terms of tournament plays.

Also note that this does not determine the relative value of the non-error portion of the system as compared to the error portion. While it is certain that the random portion is persistent for league and this invalidates the LLN for the purposes of the game it may be the case that the random portion is simply so small as compared to the non-random portion that the non-random portion doesn't matter. I.E. as the standard deviation of the error term divided by Z -> 0 is equivalent to the error term being zero.

E.G. If for instance crits only did +10% damage an attack we could easily see how they may not have much of an impact on the outcome of a fight

All of that being said, I am not sure its possible to create a system in which ADC's are relevant without the third multiplicative DPS source, so if you're going to remove the randomness of crit (which is not bad) you have to also keep in the game an auto attack only multiplicative damage source of roughly equal strength if you want to keep auto attack based ADC's relevant.

On March 15 2013 07:30 NeoIllusions wrote:


What a beast of a write-up. 20 games is nothing to scoff at. X_X
Thanks to everyone involved: writers, editors, and artists.
For TeamLiquid~

On March 15 2013 07:38 thenexusp wrote:

You make me go to reddit to find the link to the writeup

I see what you did there

On March 15 2013 07:52 Complete wrote:
Yes...Yes it does.

On March 15 2013 07:42 xes wrote:

"real math" statistics doesn't get any harder than calculus/analysis/set theory (e.g. invoking Zorn's Lemma to prove something about convergence)

Function analysis is way cooler B-)