ChiefPointThief wrote: ↑16 April 2024, 09:38
Can you give an actual example of 2 players using your system? Is their strength being calculated at the time the game occurred or by what their rank is at the end of the season? All games are calculated at the end of the season?
Hi, for implementation I think the easier way would be to compute the strength of your opponent when the match occurred. I would be keen to freeze rankings during an Arena, but on a 3 month period it is a little bit too much and would lead to unfair outcomes.
The formula could be updated after every game, as long as we keep track of games and % of wins on every level.
Let's make a simple example of a small arena between players A,B,C,D,E.
A and B start as low players, C and D as medium players and E as a top player.
They play 10 games against each other, A always lose, B beats C 60%, D beats C 80% of time and D beats B 60% of time. E beats B 80% of time, C 90% of time and D 80% of time
After this initial period they played a minimum amount of games and we have the following situation:
A vs low - 10 games 0 wins
A vs med - 20 games 0 wins
A vs high - 10 games 0 wins
A current score = 5 * 0 + 3 * 0 + 1 * 0 = 0 (considering as factors 5,3,1 for your wins against top, medium, low)
B vs low - 10 games 10 wins
B vs med - 20 games 10 wins
B vs high - 10 games 2 wins
B current score = 5 *0.2 + 3* 0.5 + 1*1 = 3.5
C vs low - 20 games 14 wins
C vs med - 10 games 2 wins
C vs high - 10 games 1 wins
C current score = 5 *0.1 + 3* 0.2 + 1*0.7 = 1.8
D vs low - 20 games 16 wins
D vs med - 10 games 8 wins
D vs high - 10 games 2 wins
D current score = 5 *0.2 + 3* 0.8 + 1*0.8 = 4.3
E vs low - 20 games 18 wins
E vs med - 20 games 17 wins
E vs high - 0 games 0 wins
E current score = 3* 0.85 + 1*0.9 = 3.45
At this point we could extract some situations. A and C are clearly underperforming, hence their last position in rankings. B and D have done pretty solid, winning games during the whole season both in their level and on higher levels.
Even if E has been the best performer, it could be considered that he has been farming, that's why he is not leading, even though that will be for a short period. E is penalized for not playing anyone on top level, however if B and D keep playing at a consistent win rate, they will increase level and E will compute games against top players, and if he keeps that win rate he will easily win the tournament.
Clearly to avoid the problem of E being exploited, low, medium and top levels should be defined in a way that ensures that players will play many games against each level.
Note that some big points are being avoided:
1 - Order of wins only matter when there is a player changing ranking, but in general WL and LW are equal
2 - Players B/D are not incentivized to stop playing, as their "Top Player" score is quite low and will easily be surpassed
3 - Farming against player A won't produce much extra points as the wins against low players have a limit on points awarded
Just a rough idea of how it could be
Thank you
