Achieving the Highest Possible Elo Rating
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914751487934464 |
|---|---|
| author | Shah, Rikhav |
| author_facet | Shah, Rikhav |
| contents | Elo rating systems measure the approximate skill of each competitor in a game or sport. A competitor's rating increases when they win and decreases when they lose. Increasing one's rating can be difficult work; one must hone their skills and consistently beat the competition. Alternatively, with enough money you can rig the outcome of games to boost your rating. This paper poses a natural question for Elo rating systems: say you manage to get together $n$ people (including yourself) and acquire enough money to rig $k$ games. How high can you get your rating, asymptotically in $k$? In this setting, the people you gathered aren't very interested in the game, and will only play if you pay them to. This paper resolves the question for $n=2$ up to constant additive error, and provide close upper and lower bounds for all other $n$, including for $n$ growing arbitrarily with $k$. There is a phase transition at $n=k^{1/3}$: there is a huge increase in the highest possible Elo rating from $n=2$ to $n=k^{1/3}$, but (depending on the particular Elo system used) little-to-no increase for any higher $n$. Past the transition point $n>k^{1/3}$, the highest possible Elo is at least $Θ(k^{1/3})$. The corresponding upper bound depends on the particular system used, but for the standard Elo system, is $Θ(k^{1/3}\log(k)^{1/3})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_14567 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Achieving the Highest Possible Elo Rating Shah, Rikhav Combinatorics Computer Science and Game Theory Elo rating systems measure the approximate skill of each competitor in a game or sport. A competitor's rating increases when they win and decreases when they lose. Increasing one's rating can be difficult work; one must hone their skills and consistently beat the competition. Alternatively, with enough money you can rig the outcome of games to boost your rating. This paper poses a natural question for Elo rating systems: say you manage to get together $n$ people (including yourself) and acquire enough money to rig $k$ games. How high can you get your rating, asymptotically in $k$? In this setting, the people you gathered aren't very interested in the game, and will only play if you pay them to. This paper resolves the question for $n=2$ up to constant additive error, and provide close upper and lower bounds for all other $n$, including for $n$ growing arbitrarily with $k$. There is a phase transition at $n=k^{1/3}$: there is a huge increase in the highest possible Elo rating from $n=2$ to $n=k^{1/3}$, but (depending on the particular Elo system used) little-to-no increase for any higher $n$. Past the transition point $n>k^{1/3}$, the highest possible Elo is at least $Θ(k^{1/3})$. The corresponding upper bound depends on the particular system used, but for the standard Elo system, is $Θ(k^{1/3}\log(k)^{1/3})$. |
| title | Achieving the Highest Possible Elo Rating |
| topic | Combinatorics Computer Science and Game Theory |
| url | https://arxiv.org/abs/2203.14567 |