Impact on ELO from limiting ratings of opponents

[laggercat]

I am curious about the impact on a player's ELO if they only play in games where there is a set minimum ELO rating.

Let me give a simple example.

Consider a game of pure luck - the entire game is that each player rolls a single dice once and the highest roll wins and lowest roll is last.

After each game ELO is adjusted in the usual way - ratings points 'move' to the winner and away from the loser, with the amount dependent on the relative ELO of the players before the game.

OK, so let's say that you play this game a few times (two player) and get lucky with a few wins in a row such that your ELO increases to 250.

At this point, you only play games that you host, setting the minimum ELO for players to 200. From that point on, your ELO will stay above 200, since the ratings points after each game will switch between the players but that will simply even out over time. Your average ELO will simply be the average ELO of you and your opponents, which will always be at least 200.

In time you have another lucky streak and your ELO rises to 300, and you set the minimum level of your opponents to 250. In this way you can 'ratchet' up your ELO over time simply by ensuring that you always play against people with a similarly high ELO.

Of course, you will need to wait longer and longer for a game because there will be fewer high ELO players, so the method will eventually reach a maximum, but I think it will work until that point.

Is there anything flawed in this logic? That is, for game with a high luck element, you can engineer a high ELO simply by restricting the ELO of your opponents, perhaps through a few steps as I've described.

[RicardoRix]

Interesting thought experiment. It seems to hold some logic, but no game is pure luck. You need to think how the skill and luck elements might interact.
ELO in this case is just measuring luck rather than skill.

You can go below 200 if you lose. Which should happen nearly 50% of the time starting from 200 and playing a single game. Then when you fall down a bracket and you could continue to sink down. I suppose you could argue you just need to rinse and repeat until it works.

[ExaltedAngel]

Consider a game of pure luck - the entire game is that each player rolls a single dice once and the highest roll wins and lowest roll is last.

In this case any match with an higher rated opponent has positive expected value and any match with a lower rated opponent has a negative expected value. This means that if you always play higher rated opponents (assuming you can find them) your Elo will tend to infinite long-term.
Of course this is not the case of real games, when skill is involved, even if little, it plays its part, but theorically it's right.

Your logic is good and this is why in games with high luck factor I tend to avoid playing way lower opponents.

This is also why games with higher skill factor have a "longer" distribution of Elo ratings (basically the pros have higher score, this is especially evident in arena)

[RobertBr]

I am curious about the impact on a player's ELO if they only play in games where there is a set minimum ELO rating.

Yes, this is absolutely a thing you should do. Its well known that avoiding playing opponents of lower Elo will in the long run boost your Elo and it is true regardless of the skill element. Top Chess players do almost exactly this, avoiding contexts in which they might be paired with players outside of the top bracket of grandmasters because they gain little and risk a lot in such games.
The effect is even greater on BGA when playing someone below 100 Elo as they might in fact be quite a strong player because they have played elsewhere first. But its not such a large effect as to make the system fatally flawed.

[Jellby]

At this point, you only play games that you host, setting the minimum ELO for players to 200. From that point on, your ELO will stay above 200, since the ratings points after each game will switch between the players but that will simply even out over time. Your average ELO will simply be the average ELO of you and your opponents, which will always be at least 200.

Hm.... I don't think so. If your are at 201, you play against a 250 player and lose, you'll probably lose more than 1 point, and will fall below 200.

If you only play against players below your ELO, it might be almost as you say, but when you're at 201, it may be difficult to find players below you and above 200 I say almost, because still, when you lose against a player who's only 1 point below you, you'll probably lose more than 1 point, so it's not true that your ELOs will switch. It is true that what you lose/gain is what your opponent gains/loses (except for possibly different K-factors), but that's not the same as switching ELOs.

[RicardoRix]

I am curious about the impact on a player's ELO if they only play in games where there is a set minimum ELO rating.

Yes, this is absolutely a thing you should do. Its well known that avoiding playing opponents of lower Elo will in the long run boost your Elo and it is true regardless of the skill element. Top Chess players do almost exactly this, avoiding contexts in which they might be paired with players outside of the top bracket of grandmasters because they gain little and risk a lot in such games.

There should be no ELO drift downwards in a skill only game.

If an ELO 400 plays a 200, then (for argument sake) the win ratio is 3:1. And a win will gain +5ELO, and a loss will be -15ELO. So it balances out.

[RobertBr]

I am curious about the impact on a player's ELO if they only play in games where there is a set minimum ELO rating.

Yes, this is absolutely a thing you should do. Its well known that avoiding playing opponents of lower Elo will in the long run boost your Elo and it is true regardless of the skill element. Top Chess players do almost exactly this, avoiding contexts in which they might be paired with players outside of the top bracket of grandmasters because they gain little and risk a lot in such games.

There should be no ELO drift downwards in a skill only game.

If an ELO 400 plays a 200, then (for argument sake) the win ratio is 3:1. And a win will gain +5ELO, and a loss will be -15ELO. So it balances out.

I can see why you think that because it is how Elo works in theory but it is not actually how it works in practice. So you are wrong in this case. When the Elo gap gets very large it no longer accurately reflects the ratio of winning and losing in part because these ratios do not always map well onto the smooth mathematical function that underpins the formula. As I explained but you did not understand on BGA the Elo is less likely to accurately reflect a players skill when Elo is low and the inaccuracy is likely to be an underestimate, so by excluding players lower than your own Elo will tend to boost your own Elo. In Chess, because this is a well known phenomena in Chess as I stated, the danger is with draws. A player can play for a draw shifting the odds in their favour and this makes playing down on Elo riskier than playing up.

[Silene]

I think the issue is that elo is not the true skill usually. someone's elo has a tendency to approach to their true skill-level, but in reality it will only be somewhere around that level. on low-luck-games it's usually closer than on high-luck games (although part of that will be balanced by different k-factor, but maybe not to all extent). so a player usually shifts between being overrated and being underrated.

When you play with overrated players, your expected gain/loss is better than when playing with underrated players. On higher elo, you find more players that are overrated while on lower elo, you find more players that are underrated (but the 2nd part partly evens out with players who are already good but haven't played much on BGA). That's why it's an advantage to prefer playing high-elo-players as RobertBr already pointed out. But yeah - it's also true, that the effect is not big enough to devaluate the system in general.

Oh well - in the mean time you said the same thing. I post it anyway but this is just describing the same thing in other words

[laggercat]

You can go below 200 if you lose. Which should happen nearly 50% of the time starting from 200 and playing a single game. Then when you fall down a bracket and you could continue to sink down. I suppose you could argue you just need to rinse and repeat until it works.

Thanks for the replies everyone!

I didn't explain this part very well. In a pure luck game, your ELO will converge to whatever the average ELO is of your opponents.

If you place a lower limit on the ELO of your opponents, then that average ELO of your opponents will simply be higher, increasing your long-run rating.

Now, BGA only allows restricting tables to ELO brackets, and won't let you host a game with a minimum ELO set higher than your own, so there is a chance you can fall below the bracket. However, if you restrict the table to ELO 200 and above, the average opponent will be much higher than 200 - I think its something like 270 - so unless you get very unlucky and sink below the 200 threshold, you will keep rising to that average.

Anyway, I'd like to look at some real-world data ... so, what game on BGA is the most determined by luck?

[RicardoRix]

Anyway, I'd like to look at some real-world data ... so, what game on BGA is the most determined by luck?

For what purpose? You could do programming simulations for your shake the dice game..?

My bet would be the pirate game.
https://boardgamearena.com/gamepanel?game=piratenkapern