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.
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!