Chess Ratings Distribution

I was struck by a recent forum post which pointed to the fact that there are not that many Grand Masters. Any chess player probably knows that, but what surprised me was just how few there actually are.

Using the FIDE Advanced Search facility and excluding inactive players, there are currently (August 2015) 1,212 GMs. With around 600 million people playing chess, that is an incredibly small proportion that obtain the highest title. What’s more, 487 of those 1,212 currently have a rating under 2500, leaving only 725 active GMs with a GM qualifying rating of 2500 or more.

This prompted me to look a bit more closely at the latest English Chess Federation (ECF) data (see download link on the Database page). The July 2015 list contains 13,822 players, of which 18 have a grade of 0 and 2,851 have no grade. Taking those out leaves 10,953 players. Unfortunately this includes players who have an ECF grade, but are not English or not based in England. For example the top 3 graded players are Anish Giri, Vladimir Kramnik and Hikaru Nakamura. Other notables in the top 20 or so are Anand, Wei Yi and Topalov. I left these in, because although I recognise the players I listed as not being English, I certainly can’t identify all the non-English players in the database. So the data is predominantly on English players, but not exclusively.

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There are 460 females (5% of classified players), 8,690 males (95%) and 1,803 unclassified.

Before I talk about other statistics, a note on the ECF to Elo translation. The calculation of ECF x 7.5 + 700 = Elo is not perfect. The lowest ECF grade of 1 translates to 707.5 Elo; I suspect players in single digit ECF grades are below 700 Elo in reality. It also does not translate well at the highest levels; comparing the ECF translated grade with the FIDE grade, those over about 2400 Elo seem to have a higher ECF translated grade. I checked A-rated grades (played at least 30 games in the past 12 months) who have FIDE ratings, and invariably their FIDE grade is below their translated ECF grade. It appears to normalise at about 2300.

On to some basic statistics. The mode and median are both 129 (1668) and the average is 130 (1675). The 25th percentile is 101 (1458) and the 75th percentile 159 (1893). So a 1900 grade puts you in the top 25%.

Excluding the top and bottom 2.5% from the population (just a rough cut-out of outliers), barely changes the results; mode and median remain the same, average drops slightly to 1672, the 25th percentile increases to 1465 and the 75th percentile drops to 1878.

The distribution appears normal; I didn’t do any tests, but the graph below is broadly normal, as you’d expect, albeit there is some noise around the median.


So what to make of all of this? Well the average rating of around 1675 (130 ECF) seems about right, considering a) this data is not all chess players, it is people who register with the ECF and play in rated OTB club games or tournaments, and b) there are clearly some players at the top end who are not club players, but taking out the outliers makes little difference to the statistics.

It is surprising how far away in absolute terms the 75th percentile is from the maximum. It seems to show that getting to 1900 is great (top 25%), but to get to Master level is a whole other story – the tail is very flat.

My own current (Aug 2015) rating (108) puts me on the uphill side of that curve, so there is a lot of work to do. But at least I am out of the bottom quartile!

8 thoughts on “Chess Ratings Distribution

  • 5th August 2015 at 3:01 pm

    I really don’t understand all of these conversions. I certainly do understand the math itself, but the population statistics, themselves, don’t make any sense to me. I have read that the mean and mode among active American players’ USCF rating is right at about 1520. I am also told that there is a 50-100 difference between USCF ratings and FIDE’s elo ratings, i.e., a FIDE player of 1800 is more like 1850-1900 in USCF rating. Then, people I know go to play in FIDE tournaments in Europe and earn ratings hundreds of points above their USCF rating (one USCF rated 1400 acquires a 1670 FIDE rating and another 1400 acquires a 1700+ FIDE rating). I have to bow out of these conversations about comparing ratings between rating pools, whether USCF, ECF, FIDE, or I really don’t think it can be done. Looking at the numbers is fun, but I don’t think there is anything to be learned.

  • 5th August 2015 at 3:20 pm

    Hi David. In terms of conversions between ratings, I think you are right. A few things though: 1) The purpose of the post wasn’t to talk about conversion. I would have liked to do the analysis with FIDE data to avoid the conversion issue, but could not easily find it. The post with ECF data would have been incomplete without giving Elo comparisons for the ECF ratings, because anyone not familiar with the ECF grading system would get no value from it. 2) I think FIDE is the one that matters. If you want an international title, then you have to play in FIDE rated tournaments and your title (bar a few exceptions) follows your FIDE grade; 3) Although there are conversion problems, if you know your rating within a defined population (so ECF for me at the moment), then at least you can see where in the population you fit.
    As you say, it is only a bit of fun and I certainly wouldn’t read too much into it.

  • 5th August 2015 at 4:07 pm

    sometimes i’m amazed that they are ANY grandmasters. seeing how much improvement someone needs to do – and what dedication they need to pursue an obvious gift.

    lets put it in context. (and make it a little personal). I am 42. all my life I have considered myself a “good chess player”… by that I mean that when people find out I’m interested in chess- and they want to play me. I usually ended up winning most of those games.

    yet by USCF (which is comparable to FIDE at amateur levels)- I am/was about 1200.

    this is “good” by the perspective of the average guy who knows chess, but certainly NOT by the average tournament player that has taken the time to get use to “standard” time controls where a game can last for hours not just a few minutes (why do you TAKE so long goes the impatient beginner).

    if we accept that 400 elo is about the gap where the better play reliably beats the heck of someone. your average english tournament player clearly beats the heck of me (and other patzer tyro’s!)…

    but of course this is just the average. to be average; then means to really start participating in tournaments- day (and often days long) with for some a considerable investment in time and effort and traveling. — as much as I obsess on chess (and I truly do)- its TOO much for me. so there is clearly a barrier to just being a competitor.

    but- we have not considered yet what it takes to bring the game to the next level? is it tactics, endgames, endless review of your own game and those of masters?? well- yes all that and probably more.
    and even more than all that – YOUTH. with its endless time, freebom from distractions, tons of parental support.

    so a subset of your curve with potential. now they need to battle their emotional insecurity, raging hormones, the sting of losing- and play better players and after a big effort Again expand to the point at which they can consistantly beat the heck of the average player. and still they are 2000 ELO. the “expert”.

    good. yes.I’m not exactly sure where they are in the curve but in the USA just a few people in an entire state of millions.

    this is the next barrier. IMHO. to get better means travel. it means playing even higher competition. for parents the gets really expensive. and after much investment… one wonders how they continue to travel to far-away places, and train in a competition where very subtle play with pawns make for the win deep in an endgame. if I knew someone on this level perhaps I’d understand the logistics of it.

    as it is, I think its a testimony to the dedication of many past chess players and enthusiasts that beyond expert- which I think is near the top of most countries curves. that there are TWO full 400 gaps to the world champion. yes, incredible talents- but apparently incredible support for people with extraordinary gifts. IMHO.

    • 5th August 2015 at 4:23 pm

      Hi Jason. It sounds like the set-up in the USA is one of playing in tournaments if you want a rating. In the UK most people play club chess for the main contribution to their rating, plus tournaments as and when it suits. For example I only play in tournaments that are close by, so that I don’t have to stay over. That may be about 5 available to me (of 5 games each, typically one game Friday evening, two on Saturday and two on Sunday), but I only play in one or two. The reason is that Sep – Apr I get a weekly rated game of club chess. I never drive more than a few miles and in fact I walk the 1.5 mile to my local club most of the time. I can see how, if you need to travel vast distances to get to tournaments as your only option for rated chess, it would be a real obstacle. And you’re right, being old with limited time is not a great recipe for success. Won’t stop me trying though!

      • 5th August 2015 at 8:59 pm

        I don’t honestly know if people can play lots of rated games at chess club in the USA. my take on it, was that some people don’t in the hopes of showing up at some tournament with tons of skills – so that they can “GAME” and Under xxxx amatuer prize.

        these kind of thinking had gone to such lengths that uscf, actually prevents people from deliberately losing rating (they create a ‘floor’ – you can’t sink any lower) to “sandbag” a prize reserved to low-rated players.

        as for me. I will simply play the best chess I can online. its not as nice and social as a “chess club” would be. but in keeps the game alive for me.
        I am very excited to think that one of these days one of us OLDER patzers are going to take up the challenge and actually gain real ELO. I don’t see why this impossible. yes time is an issue. perhaps aches and pains make us a little athletic than the normal 20 year old-in-peak physical shape. but I like to think that with the age- comes a little maturity and patience that helps to offset perhaps a little of the mental quickness that the youth might have. other issues we can work on.

        if Korchnoi can be a gm AFTER a stroke…. why Can’t someone rise to expert strength (or better) from the ‘club level’ with time, determination and passion. and more personally why not me? (or you!?)

        accept no limitations!…. I look forward to reading of your accomplishments.

  • 5th August 2015 at 4:14 pm

    I’ll quickly add that I don’t mean to imply that improvement is only for the young. BUT. there’s no denying that youth is a huge advantage (chess improvement wise).

    as a whole, working adults don’t rise dramatically in rating.

    I think few people who haven’t gone to some OTB tournaments and really sought out better players understand just HOW good- even an expert is.

    then they go on about how much they want to be a GM. lol.
    Pipe Dreams. is the american expression.

  • 15th October 2015 at 9:18 am

    Interesting post. My understanding of these statistics is that it is a pain to find good players to learn from, or practice (when reaching a certain level of course, let’s say 180 in ECF or something like 2000 in FIDE).
    Excuse my poor question but how do you find FIDE rated tournaments agenda ?

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