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Rating penalty for letting time run out

As a way of inducing players to resign rather than let the clock run out, Lichess should consider introducing a rating penalty for a player that abandons their game. E.g. rather than lose 10 elo, they would lose 12. I don't believe the penalty has to be punitive to discourage this behaviour, and a small penalty won't be a significant issue for players with occasional internet problems.
Why would you reward players (make their future games and U1X00 arenas easier) for abandoning games?
Rating is just a tool to match you with players of similar strength, not a means of coercion.
@Frankie0909 no, it wouldn't, obviously.

You play a classical game, 20 minutes on each side:
"I'm just going to wait 20 minutes to lose more rating points"
Yeah...no.
@Toadofsky I think it's fair to say that most people wouldn't consider it a "reward" to have a lower rating. Rating is a matter of pride since it's used as a metric of skill. I don't think anyone has said "well, at least my rating is much lower" after a losing streak.

If rating loss was a reward, players would just challenge bots and resign after two moves. To my knowledge this has never been an issue.
@FireBreathingDragon If the rating penalty is small the effects on matchmaking will be small while still discouraging game abandonment.
The problem is that rating is not a privilege that can be taken away for bad behaviour. It is a metric of likelihood to win, so changing the rating for bad behaviour is distorting information. Also, if the rating penalty is small, it won't matter much to the player anyway. Is 1748 any different than 1750, for example? (OK, I know that 1998 is different from 2000 but let's be realistic here :D)
@VulcanForge Regarding the first point: a possible workaround could be to have a "visible" rating that's used for matchmaking, access to tournaments, displayed on profiles, etc., and a "hidden" rating that's used for matchmaking. There a drawbacks to this beyond the complexity of implementing it though, so I'm not enthusiastically endorsing this idea.

For the second point: I think that a significant fraction of players who intentionally abandon games are doing so because there is no cost to themselves and so see no drawback to leaving the game as quickly as possible. The moment there is a penalty, that assessment changes. Psychologically, if a player is already upset by a loss, they effect of losing a greater-than-normal rating for that loss should weigh even more on them. This is my hypothesis at least.
#9 If you're going to separate the two concepts, might as well refer to them the same way as is done on other game servers: a skill score (rating) and a reputation/karma score.

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