Arena for lucky games

[grojaky]

Games like Dominos are quite strategic, but with a clear part of luck; I have won 62% of my games, I think it is fair to say that between a "pro" and a "newbie" the odds will be around 2/3 and 1/3. Sometimes you lose and you just can't fight (and of course the opposite).
When you reach 1700 or 1800 points, you're happy to play against high ranked players, but when you play against players below 1500, you hardly win 5 points but you may lose more than 30 points in a row (so more than 5 games to revocer).
Any thoughts on making this bit more balanced?
1- limit the number of lost points for a set of games (for example with luck >= 4)
2- match only against players within 200 points (probably not great cause it limits potential number of opoonents)
ELO system is great and should be kept imho, but could maybe be adapted for Arena mode.

[Strode]

There are several issues with Elo at BGA, most involving its use in multi-player games (it was designed for Chess).

The fact that you don't have much to gain when you play someone much lower rated than you is by design.

limit the number of lost points for a set of games (for example with luck >= 4)

I would not favor adjustments for games with a lot of luck. Someone would need to judge how much luck each game has (trust me, we don't agree on this). The luck ratings on BGA are not standardized, and a lot of games are rated 3 only because it's the default.

match only against players within 200 points

Would you have favored this when you were lower rated, rising up the ranks? It would have been much harder for you to get to 1700 to begin with.

I would argue that a game with a lot of luck shouldn't have a wide range of Elo scores to begin with, so let's not try to help people persevere their higher ratings (which may have been obtained partly thanks to luck).

The solution is to not take Elo too seriously for games with luck (or perhaps for any games at BGA).

[grojaky]

Agree that it's not easy to rate luck scale.
I'm not challenging nor taking too seriously (I think) the ELO system, I'm more questioning the ELO ranking for the arena.
The ELO is reflecting your level normally, indeed extremely adapted to chess when you're 99.99% sure to win when gap is big so you win little and may lose a lot.

In this season 3 players were 3 fighting between 1790 and 1800 and eventually 2 lost and cannot challenge again. I mean they could have if they had played high ranked players, but 1 loss against someone at 1400 can just not be recovered.
So what happens is that first player stops playing for the season, unless someone overtakes him, in which case either he wins a game and gets back first or falls from the cliff and loses 40 points
I find this a bit frustrating, if you have the chance to play against high-ranked players you can come back with 2-3 victory streak, if you play against low-ranked players you need more than 10 wins in a row which is by nature of the game extremely unlikely.

Agree best solution is not to play against similar arena rankings, better option would probably be to balance differently arena points for some games. Meaning still boosting bit earned points even when gap is high. In fact by definition ELO is deisgned with probability of win between 2 players, I just think that probability is correct on BGA for complex 2p games but quite incorrect for some dice games for example.

Know it's not easy, probably won't be done anyway but still wanted to share on this

[buv3x]

I do agree, that Elo rating while good by itself is not an ideal solution for Arena, albeit maybe for slightly different reasons. That being said, I can't think of a better solution, that is practical for BGA.

So here are my thoughts. Ratings in general and Elo rating specifically are designed to evaluate player's strength at a given point of time, and it achieves it by essentially having a recency weight on your performance (Elo is not usually viewed as an average performance, weighted by a recency of games, but you can look at it that way; it's a bit harder to figure out the weights, but I've done a little research on this topic, and I'll use a bit of it later). That means your last game is X time more influential on your rating as, say, your tenth to last game.
This is not, however, what your would expect from an event, with the goal of deciding the best players over a certain period. It's like a world cup format in most of the sports, pick any you want. They tend to have the same weight of the stages over the whole period, or at least if some stages have bigger weights, that's not directly related to the recency of a stage or/and the difference is not overwhelming. With Elo arena format it's more like a stage 1 giving 3 World Cup points for a winner, while the last stage giving 100.
The analogy might be a bit to abstract, so here are some numbers (I hope I'll follow through with a more detailed post at some point later). Let's say we have a game with a players' rating distribution with a standard deviation = 100. For arena with a mean being ~1500 that would mean about 2.2% of the players have a rating > 1700 (2σ), and about 0.1% > 1800 (3σ). So it does look similar to a provided example. If you play 100 Arena games of this game (randomly getting your players) and you are an average level player (around 1500), then first 50 games would have a cumulative effect on your rating of about 6.5%, while the last 50 games will affect it by the remaining 93.5%. It is a little different for a 1700 player, first 50 games would amount for 12%, last 50 for 88%. I know, I throw the numbers seemingly out of nowhere, so I'll try to write an explanation later. But essentially, the point is, there is not much point in the beginning of the arena. If you play enough games, however you played your first games practically speaking doesn't matter. And that is for me, why Elo is not an ideal option for an Arena.

[kostinen]

It seems possible to me to estimate the luck factor of a game.
A simple method: take the average elo of the 10% of the best players in the "basic" ranking. The higher this average elo is, the less luck is important in this game.
At the start of a new season, we can take this luck factor into account to slow down or accelerate the gain/loss of points for the season. This factor is applied for the whole season. For new games, it is enough to apply a medium default factor (like today)