Elo, DotA, stacking and player level

[redwolverine]

Suggestion: adding a new variable to the !sd command's output in DotA games (it's the only map I play here).

Note: the explanation below is probably a bit unclear, especially to people who are not familiar with maths, if there is anything that I forgot to add, seems wrong or needs to be explained better I will try my best to do so, just ask

To have an idea of the other players level we get to see their elo, as well as some other data, my suggestion is to add another variable, so that we can get a better idea of a player's level and can find more balanced games (or stack better xD).

For now I've come up with this:

We can already know players W/L and elo, so if we take the equation
Wx-Ly=K
where W=amount of wins, L=amount of losses, x=average elo per win, y= average elo per loss, K=elo - 1000
and also the equation
x+y=30
because the amount of elo you stand to lose, plus the amount of elo you stand to win adds up to 30.

These two equations have a single solution for (x,y). From this solution, we can know wether someone usually plays stacked games, balanced games or difficult games. We could then add (x,y) to the !sd commands output, or add a variable S:
S=x-y or S=x+y

But I think we could go further, the way elo works you get points according to the games expected outcome, so for a balanced Dota game in Ent you win 15 and lose 15. Now if (and this is 100% my assumption) the way elo is assigned at ent is (20,10)=(elo won, elo lost) means that (66%,33%)=(probability of defeat, probability of victory).

If that is how it works (if it's different it could still be adjusted), then
Ev=y/30 is the expected victory probablity (the probability that you win a game) according to elo.
We can also easily find:
Wp=W/(W+L) which is the win percentage that comes from dividing wins by the amount of games (wins plus losses).
Now if we take
Of=Wp-Ev
we get the offset, which is the difference between a player's win percentage and his expected win probability.
If Of>0 it means that the player usually contributes to his team and helps get a win even if a loss was expected, and if Of<0 it means he is a bad player that will make a theoretically superior (accordint to elo) team lose.
The larger the absolute value |Of| the better/worse the player will be. It might even be possible to add an average offset for each team.

If you are interested in adding this feature, I can write a C or C++ implementation for it so that the person dealing with it has an easier time adding it, even if you use a different programming language it should be very similar.

The reason why I would like this to be added is so that we can have a better idea of all the players level and can play more balanced games.

[nabo.]

First, elo win or loss is determined from difference of avg elo of both teams out of a 30 factor.

Second, u defined variable y as avg elo per loss. Yet, ur y value from Ev=y/30 is the probability of victory.

Third, after 2.2k elo ppl get different elo wins. I am not sure about exact calculation, but between 2200-2400 elo u get like 1/2 elo win and 2400+ get like 1/3 elo win. So higher the elo...less elo u win or lose from a game compared to others.

Fourth, Of value does not mean u stack or not.... An expected value is a weighted avg of possible values. I dont even know why ur trying to measure stacking when stacking does not determine someone's wins. If im in a team of 2700elo+900elox4 vs 1200 elox5 on other team... Does tat mean Our team is stacked? There r smurfs snipers etc...times like now when there r very little ppl who r actually good therefore less competitive esp. At pub games...stats earned nowadays dont mean too much. It is easy to make skewed stats nowadays. If ur team has high avg elo u will earn less elo n if ur team has elo avg u will earn lots elo... System itself seems simple n fair.

Elo n stats r approx values tat approximately represent a player's skill within his game pool. U play games n others can judge whether ur good or not. How u play in a particular one game impacting ur team's play or win outcome is wat actually matters...

Unless ur suggesting a more accurate stats system considering dota mechanics n individual+team play...dont see the point.

If u guys think few more number values will more accurately show u someone''s ability...by all means

[redwolverine]

First, elo win or loss is determined from difference of avg elo of both teams out of a 30 factor.

Yes, elo is determined like this:
Ra'=Ra+K(Sa-Ea)
Ra'= new rating, Ra=old rating, K is the factor, Ea is the expected score and Sa is the actual score
As you said in ent K=30, Sa is 1 for a win and 0 for a loss, do you know the exact formula for Ea used in ent?

Second, u defined variable y as avg elo per loss. Yet, ur y value from Ev=y/30 is the probability of victory.

I did say I was assuming that

Now if (and this is 100% my assumption) the way elo is assigned at ent is (20,10)=(elo won, elo lost) means that (66%,33%)=(probability of defeat, probability of victory).

which would defienetely be a very unusual way of distributing elo, but it made for an easy example of how to relate average elo per win to an hypothetical (average) expected win percentage.

Stats will still skew over

True, all rating systems are flawed, but that doesn't mean we can't discuss how they are flawed. The elo rating system was originally meant to be used in 1v1 games, and it was designed with that in mind.

For example, player A has (W/L)=(30/10) and elo 1300, player B has (W/L)=(10/60) and elo 1300. Both players have the same elo, so which of the two is the best player?
1)Maybe player B is better, he has 1300 elo and an 85% win percentage.
2)Maybe player A is better, because even though he has a lower win percentage of 75%, he has the same elo, meaning he won more elo with less wins, in other words a higher elo per win average.

Which hypotheses is right (if any)? I assumed 2 is a better choice, because any low rated player can make a new account and start giving away elo. Ofc as you said a good player can also do the same and take elo from weaker players, i just went with the assumption that low rated players (and maphackers) do so more than high rated players.

The point i was trying to make is that by finding the average elo per win (and per loss) we can determine an (average) expected win percentage, because the amount of elo on the line is determined according to the expected outcome of a game. And by comparing it to the actual win percentage we can see wether a player wins more than expected or loses more than expected according to elo.

Fourth, Of value does not mean u stack or not

Comparing an average expected win percentage (assuming it is possible) and comparing it to an actual win percentage, can show how well the rating system in use is working. If a player wins more than is expected, then he is a better player than his rate suggests, if he loses more he is a worse player. Higher Of means that a player won games he was expected to lose, stackers play games where winning is more probable, that is why a high Of could mean that you do not stack.

Even if it doesn't help find stackers, having a way to see if someone is rated above or below his level would be nice. I can dream xD

Also thx nabo. for taking the time to read through my rant and point out all the mistakes

[redwolverine]

it's been a week since the first post and there doesn't seem to be any interest this so I guess you can just move it to the archive now, I'll just add a one last rant (shorter than the two though)

1) To rate players faster, players can win/lose double the usual elo for the first 10 games or so. They do this with chess players and it seems to work pretty well. The idea is to allow new players to get close to their real rank faster. Would also help a bit with pro players getting new accounts, even if it only takes 30 seconds to get a new account, having to do it more often will definetly be a pain.
This change would also be very easy to implement

2) Originally elo was designed so that (1 person = 1 rank = 1account) so that as you play more games you get closer to your true level, it never took into account that someone could have two ranks (as in having two accounts). It should be possible to compare new players stats to other players with more games to see their real level. Regardless of the amount of games other stats, other stats like W/L ratio, K/D ratio, elo progression, etc might be similar.

I'll leave it at that so feel free to archive the topic =D

[aRt)Y]

Thanks for your engagement.