How to estimate your FIDE rating (conversion formula inside)

In this forum post, I develop a formula which can be used to convert your Lichess ratings into an estimate of your over-the-board FIDE rating.


FIDE Rating = 187 + Lichess Classical Rating X 0.38 + Lichess Blitz Rating X 0.48

Read on for details.

# Intro

A lot of Liches members play online, but not in organized FIDE-rated tournaments. We know that Lichess ratings are not accurate measures of "real" over-the-board ratings. This raises two questions:

1. What is the relationship between Lichess and FIDE ratings?
2. Can you use Lichess ratings to estimate an over-the-board FIDE ratings?


1. The relationship is strong.
2. Yes, you can!

# Data

Some Lichess players choose to disclose their FIDE ratings in their user profiles. We can compare those self-reported FIDE ratings to users' Lichess ratings to assess the relationship between the two measures of performance.

To do this systematically, I downloaded the user profiles of all registered Lichess players with at least 50 blitz or 50 classical games played. The dataset I constructed includes over 300,000 accounts, about 1% of which include information about FIDE rating. This gives us a sample of about 3,000 players for which we can make FIDE vs. Lichess comparisons.

# Descriptive statistics

The picture at this link shows the relationship between FIDE and Lichess ratings:

The FIDE measure is imperfect: It is self-reported, and several users obviously make things up (3000? Really?).

Nevertheless, on the whole, the relationship between users' observed Lichess ratings and their self-reported FIDE rating is strikingly regular. The central cloud in the two panels of this Figure is relatively tight, and it slopes upward.

Since there are many (fake) outliers, summarizing these data using the average would be misleading. We use the median instead:

* A typical (median) user's FIDE rating tends to be 78 points lower than her Lichess Blitz rating
* A typical (median) user's FIDE rating tends to be 169 points lower than her Lichess Classical rating

# Lichess vs. FIDE conversion formula

To produce a Lichess-to-FIDE conversion formula, I estimated a linear regression model of FIDE rating on Blitz and Classical ratings. Before estimating the model, I excluded extreme outliers and ratings calculated on the basis of less than 50 games.

Here's the conversion formula that this approach produces:

FIDE = 187 + Lichess Classical X 0.38 + Lichess Blitz X 0.48

For example, my current Classical rating on Lichess is 1848, and my current Blitz rating on Lichess is 1577. As a result, my estimated FIDE rating is:

1646 = 187 + 1848 X 0.38 + 1577 X 0.48

How accurate is this formula? Honestly, I'm not too sure. The results seem a bit sensitive to the strategy used to eliminate outliers and fake FIDE reports. Still, this seems like a reasonable attempt to make sense of a large data set. I don't think there's anything out there that approaches this effort in terms of scope or quality of data comparison.

My advice: Treat this as a good "informed guess."
Does it help at all to strip out the obvious fakes, like the people who put down 3000 for their FIDE rating? Or, really, anyone claiming a 2500+ FIDE rating with less than 2000 lichess rating, etc.
Right now, what I do is (a) calculate the FIDE-Lichess gap for each player, (b) calculate the standard deviation of that gap, and (c) drop all observations where the FIDE-Lichess gap is over 2 standard deviations away from the sample median.

With that approach, all the obvious fakes that your criteria would drop out drop out.

I played around with other ways to drop ridiculous observations. It did make some difference, but not a ton. For instance, the current formula says I'm a 1646 player, other approaches produced outcomes like 1685 or 1620. Not nothing, but not a huge deal either.
On top of what you suggested, I would also remove the data that lies perfectly on a number that's a multiple of 500[or maybe even 100 if you have enough data] (1000, 1500, etc...), because more than likely it's player estimated and regression would likely be less accurate. Even with these removed points, you should still have more than enough data for it to be statistically significant. After the pruning, I would assume that your Pearson's correlation coefficient will increase.
@KHeartz Good idea!

After pruning multiples of 500, I get the following amended formula:

fide = 163.29 + classical * 0.38 + blitz * 0.49

For me, the result is 1637 instead of 1646, so not a huge difference.
This seems wrong. My Classical is 700 Points Higher than my FIDE. My Blitz is 600 points higher than my FIDE.

There are extreme examples too.
pavpavinkalesi 's blitz is 900 points higher than his FIDE.

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