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.

tldr:

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?

Answers:

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:

imgur.com/a/nWy4x

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 imgur.com/a/nWy4x 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."