# Why do you see peaks on the elo distribution?

I was observing the elo distribution in Lichess and noticed peaks around rounded numbers elos ratings for medium to high rated players. This is consistent in Bullet, Blitz, Rapid games and not so much in Classical. I would have expected to observe a smooth curve.

Does anyone have an explication for this phenomenom?

My own explanation is that people tend to play until they get a nice number and stop for a while. I know I do this sometimes. In Classical playing to many games is not an option because obvious reasons and so the curve is smoother.

• It's also possible that people try harder (and thus win more) when they're about to drop below a nice number- i.e. someone rated 1710 would really like to stay at least 1700 so they can call themselves a "1700 lichess player" Jun 26, 2021 at 3:09
• And the same effect also probably happens for the 1690 player who would really love to cross the 1700 mark Jun 26, 2021 at 3:10
• small samples, probably Jun 26, 2021 at 21:46
• If this distribution happened on an exam, it would show cheating. Jun 27, 2021 at 0:42
• @David I belive this is not a small sample problem This is obtained from the Lichess players. In rapid there are more than 30 000 players with 2000 or grater elo. Jun 28, 2021 at 14:27

This is because Lichess is plotting the curve, taking 25 rating points as a unit. That's why you can see coordinates on X-axis 25 points apart.

Now, let's understand the concept with an example. Say, Lichess is using Floor(25) to plot the graph. So, If your rating is 1979, it will consider your rating to the multiple of 25 you have just passed (i.e., 1975). Let's say, you have lost a game and your rating has gone down to 1972, then it will consider you in the 1950 tier.

Now the obvious question is Why?

As you can see, this is a frequency plot (Non-cumulative). Now, assume that you take the unit of your plot as 1 (instead of 25). Also assume, the number of the players as follow:

Rating No. of Players
1900 37
1901 23
1902 3
1903 7
1904 17
1905 32
1906 33

Now, if you plot the above imaginary data, it will be very hard to understand the trend of the rating due to numerous peaks and crests. That's why, a good practice will be to form a normalized group or say a rating range first (Like in this case, 1900-1925) and then plot the graph taking the range as a unit. In this way, you can visualize the data better.

Now, you as well as another person in the comments have already pointed out that people always try to achieve a milestone (i.e., 1500,1600,1700,...) and halts playing for a couple of days to keep their rating in that milestone. That's why You can see the micro peaks tend to happen in the first quarter (i.e., 1500-1525, 1600-1625, 1700-1725, and so on). This milestone mentality is common in amateur players (1600-2100). Absolute novice (<1200) or absolute strong (>2300) players play regularly. That's why micro-peak is not common in those regions.

Last but not least, you may ask whether we can make the graph smoother (Something like in chess.com).

The answer is YES. You have to use moving-average for that. But, that doesn't reflect the trend of the mid-tier milestone-mentality. I think that's why lichess sticks to this plot for better insights into the rating distribution.

• To help more this theory it could be possible that lichess uses round(25) instead of floor(25). This way we also include people who stop after they got bellow the round number. I know I do that too. Jul 12, 2021 at 13:02