ELO on luck based games

[Archisian]

It's not calculated in integer form. It's calculated as a non-integer real number and displayed in integer form.

Ah, okay. Got that mixed-up.

[Archisian]

So, perhaps a summary of Elo would be helpful here:

Starting with some basic assumptions:
1) Both plays have completed 21 games.
2) Neither player forfeits or quits unless it is a concession at or above 50% game progression, which has no effect on the Elo results
3) Neither player has won 3 or more consecutive games against the opponent.
4) Both players are at or above 120 Elo
5) The game is PvP (meaning, 2-players).

Elo facts:

1) The Elo gained by one player will be exactly the same as the Elo lost by the other player. That's how the formula works.

2) If both players have identical Elo ratings (regardless of what those Elo ratings actually are), the winner will gain 10 Elo and the loser will lose 10 Elo.

3) The greater the Elo disparity, the greater (or lower) this result will be. For example, if the Elo differential is 100, and the higher Elo player wins, that player gains 7.2 and the opponent loses 7.2. If the lower Elo player wins, that player gains 12.8 and the opponent loses 12.8. Notice those two values add up to 20. That's not an accident. That's the result of the Elo formula and the standard k-factor of 20.

4) If Elo differential is:

200, then the numbers would be 4.8 and 15.2
300, then the numbers would be 3.0 and 17.0
400, then the numbers would be 1.8 and 18.2
500, then the numbers would be 1.1 and 18.9

5) MEANING: Yes, you gain a much bigger Elo reward for beating a much higher rated player than you do for beating a much lower rated player. Obviously.

6) That being said, winning against high rated players is one way to progressively gain Elo. It can also be accomplished by beating low-rated players. In the game "Earth", I have been successful at both methods. (I play Arena, so I have no filter controls over the Elo of my opponents). SO, yeah, if I lose a game, I sometimes need to win 6 or 7 or 8 games to get that Elo back. That's fine with me, because, well, I'm a top 5 player, and I should be able to win those 6-8 games for each loss. If I couldn't do that, I wouldn't have nor deserve a top 5 rating.

7) Someone said "Elo [in some circumstances] should be zero-sum". In fact, it IS zer0-sum. The Elo gained by one player equals the Elo lost by the opponent. (Assuming the above 4 assumptions are true.)

8) Players who complain about this situation are simply not good enough to maintain the Elo they believe they are capable of maintaining. Or, the game has too much luck for anyone to achieve and maintain those Elos. Spades is a high-skill game, yet, nobody is good enough to reach a 500 Elo rating. In Spades, the margins are too narrow, the nuances too nuanced, among other factors. That said, generally speaking, the 300+ Elo spades players are very good, and the 150- Elo players are not.


___________

Going back to the 4 listed assumptions and why they matter:

1) A player who has not yet completed 21 games will have a k-factor of 40 or 60, and thus will appear to be gaining or losing 2x or 3x as much Elo as expected based on the formula. This is not a bad thing. The goal of these higher k factors (for a player's first 11 games and first 21 games) are designed to get a player's Elo to the appropriate level faster rather than slower.

2) When a player forfeits or quits, TWO things happen that skew overall Elo. First, the winner only gets partial Elo, based on game progression percentage, which will make it seem as though the results are wrong, because you might see one player take -9 while the winner takes +4. As explained in the posts prior to this one. Second, the player who quits or forfeits gets hit with an extra -10 Elo penalty (regardless of what either player's Elo was.) SO, forfeits and abandoned games really wreak havoc with the overall Elo system, and contribute to it not being zer0-sum all the time.

3) TO prevent multi-account Elo dumping, a player who wins 3 or more consecutive games against the same opponent will be assigned an Elo decay that starts at 10% and gets increasingly higher. This can make it seem as though the results are "wrong", and it WILL also contribute to Elo not being zero-sum. (This is a bad policy especially in Arena where we don't even get to choose our opponents.)

4) Players can never lose Elo when they are below 100 Elo. This can have the same effects as listed above; the results might seem "wrong", and it will not be zero sum. (I personally think this is a completely absurd feature.) Also, a player who reaches 100 Elo will never go below 100. SO, that player could lose 40 games in a row without losing ANY Elo, then win one game and go up to anywhere from 101 to 120. This is also a really silly feature, further skewing Elos and making it not zero-sum overall. That is why some sites start players at 1500 Elo as the default Elo. That 1500 Elo should, in theory, mean "exactly average". A player at 2000 would be 500 above average (expert level, to some extent equivalent to a 500 ELo here on BGA). Starting everyone at 1500 allows players to go below 1500 when they lose, which makes sense. That way, Elo would in fact be zero-sum. If two 1500 players play, the winner will be at 1510 and the loser at 1490. But, here, if two 50 ELo players play, the winner will increase, but the lower will remain at 50 Elo. Losing a game but not losing any Elo makes no sense.


5) All sorts of silly and difficult-to-comprehend things happen with Elo in 3+ player games. It took a lengthy thread involving numerous experienced players and some developers to reverse-engineer the convoluted formulas for games of different player counts above 2p.


Bottom line: If you want to reach high Elos and continue to increase Elo, you need to win games. And avoid losing games. To suggest it's impossible to gain ELo by playing lower rated players, that's just false. Look at my game results for "Earth". Or Pente.

This was a great explanation. I completely understand it now. Thanks a lot.

[BarnardsStar]

4) If Elo differential is:

200, then the numbers would be 4.8 and 15.2
300, then the numbers would be 3.0 and 17.0
400, then the numbers would be 1.8 and 18.2
500, then the numbers would be 1.1 and 18.9

Agree with Archisian, fantastic explanation.

I wanted to provide a bit of context on where these numbers come from. Elo is set up—indeed, it is defined so that a difference of 400 means the higher-Elo player in a 1-on-1 game is 10x as likely to win as the lower-Elo player. Note that when we say one side is y times as likely to win, it means their absolute likelihoods are y/(y+1) vs 1/(y+1).

For any differential X, the higher player is 10^(X/400) times as likely to win a the lower player (so that is the “y” above). The ratio of the Elo won/lost by the two players is proportional to that number, so by way of example, at a difference of 200 the higher player is 3.1623x as likely to win as the lower player, so the two values are k/4.1623 and 3.1623k/4.1623. When k is 20, that’s 4.81 and 15.19.

(3.1623 being 10^(200/400) = 10^(1/2) = √10).

[FrankJones]

The BGA FAQ pretty much explains all of this.

[BananaHarambe]

The 1500 starting rating makes the most sense logically, but is not popular with weaker than average players which is why I think it was scrapped. It is upsetting to start at 1500 and keep dropping in rating to 1300, 1100, triple digit 900s. It is objectively estimating your skill level, but feels bad to be lower than the starting position.

Other websites have reported players making new accounts when their rating gets too low which is why they implement a similar system of starting at the floor Elo and working up to remove the incentive to make a new account.

Instead of having the weakest players all tank into triple digit Elo where they could more accurately find suitable matches we got the BGA system which clusters weak and new players together around 100 Elo. Weakest players get stuck at 100 Elo and can't drop further while their opponents farm Elo off them, which adds Elo into the system and pushes player ratings up. Anyone that gets stuck at the 100 Elo floor multiple games and is always stuck in the 100-120 Elo range is in the weakest skill bracket, but blends in closer with everyone else to avoid hurt feelings. Checking player stats like win rate can give a more detailed picture.

It feels less bad to hover between 100-120 Elo than it does to tank from 1500s to triple digits.

[BarnardsStar]

I’d think the answer to that would be to hide the actual Elo values. Its primary rationale, on a site like this, is simply to match people up with players of their level. If you can’t see the values then you can’t get upset about them.

Maybe you show the values above a certain threshold… like more than 2 standard deviations above 1500. Or even 1 stdev. Something like that for the competitive types, but most people don’t need the actual number. Just pair me with players +/- 100 of me.

[ChiefPointThief]

There is no money involved, nothing to lose or gain but ELO and maybe pride? Its not a big deal. The system isnt perfect and it would be near impossible to adapt the ELO for each individual game.

Dont worry about ELO and just enjoy the game.

Face palm. Always one of these comments. Also it isnt impossible to adjust the win probabilities to consider luck factor. Actually it is rather simple.

Just don't worry about Elo for luck-based games.

It's less complicated that way. Plus, we'll never all agree as to which games count as luck-based and to what extent.

Don't worry about site crashes, Don't worry about bugs, Don't worry about new games being added etc etc etc. You can apply this to literally every topic.

Actually in another luck based related thread luck factor ratings were pulled from games on another site that lets the community rate games. Those ratings were more on point than bga ratings which are set by the dev. Same thing could be done here.

Avoid playing Arena, because in Arena, you cannot filter by Elo.
Play non-arena games and set an Elo filter to avoid being matched against players with very low Elo, because in a high luck game, you don't want to be playing against players rated lower than you are.

This doesn't solve the problem at all. We've been through this Frank! (Although this tip can be helpful)

Elo is reflecting win probability. If there is a high luck factor, there is not much difference in win probabilities between players, hence players tend to have similar Elos.

Except the win probabilities are inaccurate for high luck games. Creating false elos. Thus it isnt even properly reflecting win probabilities. Which brings players closer to the same level than they should be and results in more skilled players inevitably falling below weaker players because the math is off.

I’d think the answer to that would be to hide the actual Elo values. Its primary rationale, on a site like this, is simply to match people up with players of their level.

Its been stated multiple times in this thread that the purpose of elo is for matchmaking which is not true for this site. Elo is used to determine prestige on this site. Your profile is ranked by xp and where you rank all time on the xp list is posted on the home page. The majority of xp is gained from placement on the all time elo list and arena seasons. So if the gaming site is going to crown players based on these things then it should actually attempt to enhance its rating system which has clear flaws.

[dschingis27]

Elo is reflecting win probability. If there is a high luck factor, there is not much difference in win probabilities between players, hence players tend to have similar Elos.

Except the win probabilities are inaccurate for high luck games. Creating false elos.

What are you talking about? The "win probabilities are inauccurate"? Are you one of these "the site is not random" sceptics?

I can agree on the following two things:

(1) The Elos are inaccurate for high luck games because they rely so heavily on a too small number of recent games rather than a large enough sample of games to be meaningful. Hence the win probabilities calculated from those Elos are often inaccurate, that is true, maybe you meant that. But it is clear to me that it is the Elos that are inaccurate first, creating wrongly calculated win probabilities, and not the other way around like you wrote it. It doesn't start with wrong probabilities, it starts with too small sample sizes being used for Elo. The inaccurate Elos would resolve themselves if they would simply reduce the K factor by a lot.

(2) Elo is often not the best measure for skill, particularly in high luck games. In high luck games, small differences in win percentage can reflect highly different skill level, this is not reflected in Elo, that is true. Still, Elo is a model that can describe win probabilities, it's just that we shouldn't use Elo to measure our skill against each other, better things are available indeed.

[FrankJones]

Games with more luck are inherently going to have player Elos more tightly bunched, because higher luck means the better player is going to win less often than in pure-skill games.

In the short run, anyway. In the long run, with enough games played, the better players will have higher Elos than the weaker players.

[Strode]

Just don't worry about Elo for luck-based games.

It's less complicated that way. Plus, we'll never all agree as to which games count as luck-based and to what extent.

Don't worry about site crashes, Don't worry about bugs, Don't worry about new games being added etc etc etc. You can apply this to literally every topic.

There's far more reason to worry about site crashes and bugs than about Elo in luck-based games.

Elo was designed for a no luck game (Chess). The more luck a game has, the less meaningful Elo is, and the less you should care about it.