Each game on BGA is already rated on a 0-5 scale for "luck." I propose that the K-factor used for Elo calculations ("all-time" and "arena") be determined in part by this luck rating, with more luck-based games having lower K-factors.
Why?
On BGA, your Elo rating for a game is an estimation of your true strength, which can be used to predict your win probability against a given opponent.
When you win or lose a rated game, you gain or lose Elo. How much Elo depends on the difference between your strength and your opponent's, and on your "K-factor."
Your K-factor is a number which basically answers the question: "how much weight should this most recent game have in estimating your true strength?" On BGA, I think your K-factor eventually settles to 20 for any given game, meaning that the most Elo you could gain or lose in a single game (against a single opponent) approaches 20.
A higher K-factor means that your Elo rating puts much more weight on your recent results, whereas a lower K-factor means that your rating considers a larger sample size of past games more evenly.
Putting much more weight on recent results is appropriate in combinatorial/pure strategy games, where your recent results are likely a reflection of your current strength. But to estimate the true strength of a "Can't Stop" player, you'd want an enormous sample size, right? You achieve this by lowering the K-factor.
For example, if you want to estimate the strength of a chess player, a handful of games might be sufficient, so you could have a relatively high K-factor. If you want to estimate the strength of a poker player, you might need to see them play for months, so you'd want a really low K-factor.
For low-luck games, the Elo system in place on BGA works relatively well. The highly rated players tend to be the strong players, and the arena seasons are typically won be the players who played the best.
For high-luck games, the highly rated players are often just those who went on a historic streak and then stopped playing, and the dynamics of arena are all about hunting for one big win-streak, and then camping your inflated Elo. This is the direct result of a poorly chosen K-factor, which is weighting recent games more than it should.
An example of what new K-factors might look like:
K = 4 for 5-luck games like Can't Stop
K = 7 for 4-luck games like Backgammon
K = 10 for 3-luck games like Wingspan
K = 14 for 2-luck games like Splendor
K = 17 for 1-luck games like Ark Nova
K = 20 for 0-luck games like Boop
Your K-factor would still start out higher and drop as you play more.
It might sound silly to think about only gaining or losing a couple Elo points at a time in games like Can't Stop, but if your Elo rating is just meant to be an estimation of your true strength, a single game really shouldn't change much.
Why?
On BGA, your Elo rating for a game is an estimation of your true strength, which can be used to predict your win probability against a given opponent.
When you win or lose a rated game, you gain or lose Elo. How much Elo depends on the difference between your strength and your opponent's, and on your "K-factor."
Your K-factor is a number which basically answers the question: "how much weight should this most recent game have in estimating your true strength?" On BGA, I think your K-factor eventually settles to 20 for any given game, meaning that the most Elo you could gain or lose in a single game (against a single opponent) approaches 20.
A higher K-factor means that your Elo rating puts much more weight on your recent results, whereas a lower K-factor means that your rating considers a larger sample size of past games more evenly.
Putting much more weight on recent results is appropriate in combinatorial/pure strategy games, where your recent results are likely a reflection of your current strength. But to estimate the true strength of a "Can't Stop" player, you'd want an enormous sample size, right? You achieve this by lowering the K-factor.
For example, if you want to estimate the strength of a chess player, a handful of games might be sufficient, so you could have a relatively high K-factor. If you want to estimate the strength of a poker player, you might need to see them play for months, so you'd want a really low K-factor.
For low-luck games, the Elo system in place on BGA works relatively well. The highly rated players tend to be the strong players, and the arena seasons are typically won be the players who played the best.
For high-luck games, the highly rated players are often just those who went on a historic streak and then stopped playing, and the dynamics of arena are all about hunting for one big win-streak, and then camping your inflated Elo. This is the direct result of a poorly chosen K-factor, which is weighting recent games more than it should.
An example of what new K-factors might look like:
K = 4 for 5-luck games like Can't Stop
K = 7 for 4-luck games like Backgammon
K = 10 for 3-luck games like Wingspan
K = 14 for 2-luck games like Splendor
K = 17 for 1-luck games like Ark Nova
K = 20 for 0-luck games like Boop
Your K-factor would still start out higher and drop as you play more.
It might sound silly to think about only gaining or losing a couple Elo points at a time in games like Can't Stop, but if your Elo rating is just meant to be an estimation of your true strength, a single game really shouldn't change much.
