Xavori, on 28 November 2017 - 12:38 PM, said:
Dude, I know Law of Large Numbers and Gamblers Fallacy. I'm not attributing anything to anything. That's the point. You're the one trying to attribute meaning to the leaderboard in spite of acknowledging it's based on random numbers that you can't know anything about.
If you want to apply the Law of Large Numbers...well...what's your range of numbers? You have to have one because you cannot have an expected value without a known range. And you've already acknowledged that PSR is garbage, and the matchmaker is garbage...soooooo.....???
It's interesting, isn't it that when you bring up TrueSkill, I point out that it specifically invalidates your desire to read meaning into wins and win/loss ration because it's ultimately designed to move w/l ration to 1 (side note: 1 is the expected value so the law of large numbers says you'll eventually get there after you first get matches between equally skilled opponents as the norm.) So you give up on it and pull out The Law of Large Numbers.
And now I'm pointing out that you cannot apply the Law of Large Numbers because you don't have an expected value, you don't have a range of numbers to give you an idea of necessary sample size to be "large" and you don't even know if the player skill levels of MWO's current player base fits a normalized distribution. So guess what? The Law of Large Numbers does not apply.
Ya know, it's almost as if I've studied a whole bunch of mathematics....
I cannot stress enough that the leaderboard is garbage.
And the entire point of these discussions I keep having is that it doesn't have to be this way. PGI could easily implement any one of many player ranking systems that over time would produce quality matches which in turn would produce a quality leaderboard. But one of the most important features of such a leaderboard would be that W/L ratio, that stupid number you keep trying to magically assign meaning to in the current PSR/random matchmaker created leaderboard, would be utterly and completely meaningless for player skill because every single player, no matter what their actual skill in playing the game, would have a W/R ratio that of ~1.
Except it's not random. That's the whole point you refuse to get. Player skill is not an infinite curve. No human behavior is an infinite curve or truly random. It's not even that big a curve or that wide of a spread.
Page 14 in the link you provided for TrueSkill.
You also seem to absolutely and totally not understand how matchmakers and win/loss work. Neither Elo nor TrueSkill push a player to 1.0 w/l. That's why you have a matchmaker with a different ranking instead of just using win/loss.
It assigns you a value and then modifies that value based on who you played against - so beating a player who's better than you raises you a lot, someone who's your skill a tiny bit, someone less than you not at all. So your win/loss only every changes by 1 but your ranking changes by a variable number based on your team and the other team.
Now you're trying to use terms you clearly don't understand.
The population of MWO fits a normalized distribution - every group fits a normalized distribution, you normalize the distribution based on the group. Again, the link you posted to the TrueSkill breakdown discusses this and how it groups and distributes and assigns ranks.
LLN works with infinite variance, however your variance in this is absolutely finite. You are 1/12th of your team and you're playing against a team of 12 every match. There are 11 variables on your team and you can either treat the other team as one averaged variable or 12 individual variables coming to an average - the results are the same.
The value of each of those variables is ranked along whatever skill curve you want; as detailed as you want to get however they're going to fall within a set range.
Because this equation holds true for every player everyone is ranking along the same curve. Because win/loss is zero sum, as in every single match there are 12 wins and 12 losses, every single players win/loss is relative.
There is no magic here save that you really, really want to pretend that your win/loss is not a direct result of how well you play, just like every other players is. You want to believe that you have no measurable impact on it. You are arguing that because teams in QP are random you have 0 impact on your team.
Take 12. Divide it by 1. You get 8.333%. That is your impact, every single match, on your team. How much value your 8.333% adds and sways the probability of your win by is a reflection of how well you play on average.
Again, the math you're refusing to get here is 1/12 and that 8.333% > 0%. So all the leaderboard does, by principle of basic mathematics, is identify in a 0 sum environment what your relative 8.333% is approximately worth on average relative to everyone else.
If you have a 49% win/loss then someone else has to have a 51% win/loss. Because that match you were in had 12 wins and 12 losses.
How much you carry your 8.333% of your team influences how likely your team is to win. A person who disconnects every single match is not going to win as often as the comp tier player in top meta on average, right? One of them is contributing more to his team, every team he plays on, every match, right? His average wins will be higher.
This is what you refuse to get. The matchmaker needs based off win/loss. While the current matchmaker does a poor job of building teams of players with a relative skill level that influences the enjoyment of the matches for the players, not the reliability of the results. Good players will win more than bad players on average in a QP environment. They will have a higher win/loss. Every high win/loss is matched by a low win/loss. 12 v 12, 12 wins, 12 losses, it all has to sum to 0.
1/12. 8.333% > 0%. Your win/loss is a reflection of how good you are at helping your team win games. As such it's the only useful metric to use for building a matchmaker. Hence why Elo and TrueSkill use win/loss as the metric they use to create a score from.
Once again - if the results of the Leaderboard are random then they would have a random distribution. From +100 to 0.01 range of variance for each player every single month. Show me that in the leaderboard.
Edited by MischiefSC, 28 November 2017 - 01:14 PM.