abraker wrote:
Blastix Riotz +DT seems a little weird for 500k and 600k, double difficulty. I am going to guess not enough data points.
The data in Blastix Riots +DT is lacking. By what we can see in the data, it seems only the best players can achieve more than 500k score in the beatmap, but there aren't many scores set by the best players, so we can't be certain that the difficulty estimation is accurate. The difficulty rating for 700k score or better is very extrapolated, so it may not be accurate at all. The best player that has set a score in the beatmap is [Crz]Player (which is rated as the player who sets good scores in the most difficult maps, but it's not the player who consistently sets the best scores), and he was still far from getting a 600k score or better.
The scale of difficulty is set so the skill of the players in the data follow a gamma distribution with mean 3 and standard deviation 1.5. So a value of 3 is something the "average" of the players in the data is expected to be able to do (which is still quite an achievement since the data is mostly composed of the best players in the game), a value of 5 is roughly something only the top 10% is expected to be able to, while 10.71 is something that goes a bit beyond what any player could do consistently.
The scale is not actually something of importance regarding calculations. If you can define what "double the amount of difficulty" means, maybe I could set the scale according to that definition.
abraker wrote:
This makes me think, since you have been working with the data for sometime now, how many data points do you typically need for the results to be accurate or at least make sense?
The more scores from players that struggle for a certain goal, the more confident we can be the difficulty estimation for that goal is accurate.
Usually, about 20 scores in the same score range is the bare minimum to be confident about the estimation, but having above 200 or even 1000 plays is much better. Some popular maps have 1000+ scores in total in the data, but still have few scores in some score ranges (for example, despite AiAe [MX] being the most popular map, few players in the data have less than 700k score on it).