Small, note to Farah's great post.

for Warlight it's assumed to be 10 ELO points.

Not assumed. I think Fizzer has looked on the win rates of games and found 10 points to be appropriate.

That doesn't make it less of an assumption :p

@cloud7:
Not sure I understand what you mean. How does playing 5 games at a time affect things since it´s not like I finished them all at once? In the beginning I finished a few per day. So it was one victory, one rating update, one new opponent at a time, I assume.

For brainteasers I usually find it helpful to construct extreme corner cases:

Case 1: You play only 1 game at a time:
--> After each victory you get paired up with a slightly better opponent than the game before until after around 10 games or so you play against the very best.

Case 2: You start out by playing 100 games at a time:
--> You get paired up with the lowest ranked guys. If you win all games then the question is whether the ladder sees you as an unstoppable killing machine or as an average guy who manages to beat the AI 100 times in a row. I'm not quite into math as Farah, however I have looked over the whitepaper of the Bayesian ELO algorithm a while ago and remember that they claim to work better than the ordinary ELO algorithm by not seeing you as that unstoppable killing machine in this case. However no matter the ELO algorithm: Obviously beating up those 100 low ranked guys has to be worth less than 100 proper ladder steps against increasingly stronger opponents.

You get paired up with the lowest ranked guys. If you win all games then the question is whether the ladder sees you as an unstoppable killing machine or as an average guy who manages to beat the AI 100 times in a row. I'm not quite into math as Farah, however I have looked over the whitepaper of the Bayesian ELO algorithm a while ago and remember that they claim to work better than the ordinary ELO algorithm by not seeing you as that unstoppable killing machine in this case.

That is interesting. The claim that they work better than the ordinary ELO algorithm by not seeing you as that unstoppable killing machine is easily falsified on a small scale. Regular ELO takes your game result and calculates a new rating. The increase or decrease of that new rating is limited by a so-called k-factor. Usually, this is 32 or 16. Example:
Assume a base rating of 1500. You beat the best player on the ladder (for argument's sake, he's rated 3000). You get a 32 point increase, since that is the maximum. Your new rating is 1532

Bayesian ELO tries to estimate your rating while also assigning it two variance factors. This means the amount of rating points you can get or lose after a game is technically unlimited: your rating may go up or down indefinitely, but the variance factor tries to correct for that. Example:
Assume no base rating, as you haven't completed any games. BayesELO will give you one after your first game. You beat the best player on the ladder (and again, for argument's sake, he's rated 3000). You get a rating assigned of ~3200, depending on the rest of the ladder.

Continuing that argument, it means that regular ELO will severely underrate new good players, while BayesELO will severely overrate new good players.

But, at the bigger scale, BayesELO seems to do a rather good job. It's not necessarily better, but here's a rough example:

You win 10 games against a player who was initially rated 1500.

Regular ELO:
You gain 115 points. Your new rating is 1615.
Your opponent loses 115 points. His new rating is 1385
This 230 points of difference means the system believes you to have a 79% win-chance against this opponent.

Bayesian ELO:
You gain 180 points. Your new rating is 1680
Your opponent loses 180 points. His new rating is 1320
This 360 point difference means the system believes you to have an 88.8% win-chance against this opponent.


The biggest flaw of using Bayesian ELO on the ladder is not that it's a bad rating system. It's the way that it's implemented on Warlight. When someone gets ranked after 20 games, you have no idea whether the system has a decent amount of certainty in that player's rating. This is why people who do 'runs' get rewarded. A low amount of games consisting of mostly wins means they get a rating that is most likely not trusted. An easy way to fix this is to have a player ranked when their variance is below a certain value (and the BayesELO program gives you this information for free), instead of after a certain amount of games. That was probably the one of the better things with the TrueSkill algorithm on the RT-ladder.

TL;DR:
Regular ELO gets you to a 'truer' rating in a slower way, Bayesian ELO gets you to a rating that might or might not be very volatile in a faster way.

Edited 10/15/2019 17:10:14

@Norman

Case 2: You start out by playing 100 games at a time:
--> You get paired up with the lowest ranked guys.

Why does playing several matches at a time get you paired up with the lowest ranked players?

@Farah

This is why people who do 'runs' get rewarded. A low amount of games consisting of mostly wins means they get a rating that is most likely not trusted. An easy way to fix this is to have a player ranked when their variance is below a certain value (and the BayesELO program gives you this information for free), instead of after a certain amount of games.

How to get that information about the variance? Assuming it´s too much work for anyone to do casually, any guesses how big of a sampling of games would with a high probability significantly limit this variance?

Edited 10/16/2019 15:23:22

Cloud if the system has no information about you when you get 100 games at once, the average of your opponents will be significantly lower than when you only get 1 game, win it, and then the system gives you a 2nd game after knowing you beat your first opponent.

I assumed we weren´t talking about that anymore since in my previous response to Norman I mentioned I finished the games one at a time while playing 5 games. So it doesn´t matter whether you have 1 or 100 games at a time, as long as you finish them one by one? Or am I just missing something here?

For matchups, it matters how many wins you have before the game gets created. If you start with 2 games and win these, your next 3 opponents should be higher rated than the ones you get if you start with 5 opponents right off the bat

Wait.. next 3 opponents? So are you discussing a scenario where 2 games are played at first and then the maximum amount of games is increased?

Come on cloud7:

Let's say you start with 1600 ELO and always get paired up with players at around your ELO level. Victories against players with equal ELO are worth 100 points and victories against players with less equal are worth 10 points (just for the sake of argument):


Scenario 1: You play 1 game at a time:
- Game 1: Opponent has 1600 ELO and you move from 1600 to 1700 ELO
- Game 2: Opponent has 1700 ELO and you move from 1700 to 1800 ELO.
-->You have 1800 ELO after 2 games.

Scenario 2: You play 2 games at a time:
- Game 1+2: Both opponents have 1600 ELO and you move from 1600 to 1710 ELO.
--> You have 1710 ELO after 2 games.

Yes, in the scenario where multiple games are played at a time more games are played against the base level. This has been clear the whole time. That difference is still not that much though (you make it seem like it is with those numbers I assume you pulled out of your ass). So to return to the original point of our conversation, how is it so clear to you that the difference between my opponent list, and the player´s list I was comparing mine to, was the amount of games played at a time? (by the way, I´m fairly certain he had 5 games going on also). As a reminder, his 2nd game was against a 1700 rated player and he played only total of 2 games against lower than 1500. Mine 12th was against 1800 and 9 games against lower than 1500.

Edit: my 12th opponent was at the time in the 17 hundreds so he indeed is a good comparison.

Edited 10/16/2019 17:47:29

Yes, when I say "just for the sake of the argument" what I mean is that I pull it out of my ass.

This has been clear the whole time.
hm...

Also you have edited your posts, so I was never able to see which player you are comparing yourself to.

You haven´t been able to see which player I´m talking about since I haven´t written it here. I guess I could but there is a chance the player in question does not want his ladder record to be a part of a conversation on the forum. I send his nick to you in private mail though so you can take a look.

And why I believe he played 5 games at a time too then is because: he finished games quickly then, during August I remember seeing him playing 5 games at a time and because he is still playing 5 games at a time.

Edited 10/16/2019 20:40:13

@Norman: It´s been a week and you haven´t responded to me either here or in private so I assume you don´t want to open up your reasoning about what I asked.

he´s first opponents could have had there ratings rise after he played them

Sorry, I don't know why PlayYourBest in particularly has managed to climb way faster than you. All I wanted to say is that playing multiple simultaneous games decreases your climbing speed in terms of needed games. As for PlayYourBest I guess he got lucky to get paired into a then low ranked M'Hunter who was also climbing and thus kept making his victory more valuable.

Njord is most likely right.

It´s actually the other way around since from the first 5 opponents, one player has come down 300 points. The others are fairly even overall, some have risen a little, some have fallen a little.

"I guess he got lucky to get paired into a then low ranked M'Hunter who was also climbing and thus kept making his victory more valuable. "

Not sure who you mean. The two M'Hunters he played are about the same now as they were then.