The RD floor was reduced from 60 to 50, to stabilize ratings of frequent players.
We're using a rating system which has many similarities to Glicko-2:
http://www.glicko.net/glicko/glicko2.pdfIf you read Glickman's paper, it doesn't have an RD floor; theoretically, ratings provide the greatest predictive accuracy if the RD floor is zero. Which immediately raises the question: what if I improve at the game?
The key difference between Glicko and Glicko-2 is a volatility term to keep track of (within a rating period) whether a player's level of performance is consistent (and if so, RD decreases slower). So if you're an improving player, your rating volatility should be high, causing RD to slowly decrease; conversely, a player who isn't improving or worsening will have a low volatility and a low RD. All that said, RD slowly increases over time to account for uncertainty due to player inactivity.
Ratings should have predictive accuracy. Having random ratings doesn't make sense. (As I again reread
http://www.glicko.net/glicko/glicko2.pdf I think the RD >= 30 in Glicko-1 is unnecessary in Glicko-2 because the volatility term already accounts for improving or declining players. However this raises a question about Glicko-based systems with undefined rating periods and whether volatility terms are stable.
Thanks to gcp for this analysis/simulation:
github.com/ornicar/lila/pull/4034#issuecomment-433472996Because the RD(phi) increase is applied after every game instead of every rating period, Glicko-2 has much higher RDs by default, causing the ratings to flobber about much more. Empirically, on lichess the majority of players never go below RD=60, there's maybe a dozen or so in my entire dataset (mostly because they managed to get non-default lower volatility, which is also very rare).
After removing the RD >=60 limitation, or putting it to >= 30 (as recommended in the Glicko-1 paper), the prediction performance of this pull (Glicko-2 + sigma scaling over time, aka Lickgo-2) beats Glicko-1 and it's a strong improvement over the current Glicko-2 ratings.
Limiting the RD to 30 or not limiting at all seems to make very little difference [in terms of predictive accuracy]. In general it will grow quickly unless the player is playing a ton of games, in which case their rating is constantly adjusted anyway. So the limit probably just isn't necessary at all.
Glicko 1 prediction rate 56.591%, MSE=0.2250
Glicko 1 (no RD cap) prediction rate 56.618%, MSE=0.2250
Ligcko 2 prediction rate 55.483%, MSE=0.2269
Lickgo-2 (no RD cap) prediction rate 56.729%, MSE=0.2248
lichess prediction rate 55.122%
So, if the minimum RD gets lowered to 30, or removed entirely, it would clearly improve the accuracy of lichess ratings.
