Monday, 4 May 2015

Men vs. Women - Who Plays Better?

It’s been a looooong time since our last blog but the long-planned article is finally there. And as it seems just on time as it coincides with the verbal exchange between Nigel Short and some female chess players. Purely coincidence. So here comes the analysis of the much debated battle of the sexes, carried out on the 64 squares of the chess board. Who carries away the victory?

Before I start, let me be clear that this is by no means a sexist article with no intent to offend anyone. We only take a neutral point of the analysis of the available ratings data by FIDE. No matter which side walks away with the attribute of being the better chess player (on average), this post does not make any gender better than the other. Let’s also acknowledge the fact that men and women ARE different in many ways. Fact. And even some voices might want to convince you otherwise there is no negativity around the term "different" and instead let’s see it from a positive angle: Differences make the world a more interesting place.

That preamble out of the way, let’s get started.

As I did previously, data from the FIDE ratings list (April 2015) have been condensed to give a clearer view. The April list had well over 200,000 registered players and was filtered down to exclude:
  • Inactive players;
  • Players with no year of birth given (to allow an analysis of age too);
  • Players with a K-factor of greater than 20 (to exclude players with less than 30 games played)
I’m aware that the last exclusion of the list is unfair to serious players with not enough games yet, but it should help the analysis to exclude players with a short-lived interest, perhaps skewing the statistics. In other words, let’s only consider players who compete for some time already and represent a more “typical” chess player.  This still leaves us with a list of 61,294 players which is a good sample size for most statistical purposes.

First argument on the table (without looking at data): There has never been a female world chess champion. True, but it should also be pointed out that when such title was first up for grabs at the end of the 19th century, women were mostly socially disadvantaged. Thus, for quite some time there was only a tiny likelihood that a woman could achieve this prestigious title. Times are changing and we should see in the next few decades whether or not a woman can manage to achieve the number One spot.

As for the numbers, the first thing which jumps into the eye is the ratio of male to female players: There are 16 (plus a bit) men per female player! Taking a purist standpoint and ignoring people’s personalities and gender specific attributes, this fact alone makes a male world champion much more likely than a female one, simply by means of chance, if you were to pick a world champion randomly. Another rather interesting fact is that FIDE-registered men come from 163 different countries, while women’s nationalities account for only 123; there are no female players, at least not FIDE registered ones, from 40 countries. The number one culprit on this list is – although strictly speaking not a country – Faroe Islands with 54 men vs. no women. Leaving the Faroe islands aside, and considering only “real” countries (no offence to Faroese players), we have Libya with 48 males. That said, all players from those 40 countries add up to only 350 players. While you could argue that discrimination against women is in place in some of those 40 countries, the number of men isn't great either making a world chess champion from one of those countries a dwindling small possibility, purely looking at numbers and not at individuals.

Next thing to do is to process all the data and take a look at some graphs. A picture can say more than a thousand numbers. The below two plots show the number of male / female players within a range of 10 ELO points; in other words, we look at the number of players who have a rating of 1000 to 1010 points, 1010 to 1020 points and so on. As statistical textbooks would tell you, you end up with a bell-shaped curve, also called Gauss distribution. It’s not perfect but it can be seen. Data for women show many spikes and more irregularities but that can be contributed to the rather small sample size of just above 3,500 players vs. over 57,000 for the male category.

Nice, but how does this compare to each other? To avoid a graph full of clutter, I plotted only the Gauss curves for both categories (see below). The y-axis (height of plot) is normalised so the two categories can be easily compared rather than comparing the tiny 3,500 sample size with the massive 57,000. What can be read from this plot is that men achieve a higher average performance with an mean rating of 1960 points. Women are not too far off with an average of 1891 points, only lagging 69 points behind men. However, female players show a slightly broader distribution (best seen by the lower peak), meaning that there are more players who do perform better or worse than the average player (in simplistic terms). Looking at the two plots above again, it appears that the Gauss distribution might not be the best fit as in both cases it seems the curve is slightly over-representing lower-than-average values and being close to the data to the right (above average).

Now what do we get if we consider age? In my previous article, we looked already how your future looks like as a chess player as time goes on. The argument is not different here, except we split the two categories up. We find a clear pattern here: At any age, rated male chess players outperform their female counterparts by 27 to 182 points (ignoring the 95+ age category where no women are present). See below plot. The interesting fact here is that women seem to achieve their peak performance later than men. After the peak in a male’s life, a gradual decline follows, until you hit 80. (And then 100!) But women seem to fight back against their rating decline once they start their fifties and then again in their seventies. Whether this effect is true is debatable as there is only a very small sample size in those age groups for women. There are more 85-90 year old men in the list than 50-55 years old women. The lesson learnt from here: As a young energetic guy, don’t underestimate your senior female opponent in her thirties!

Let’s conclude here: Whether you like it or not, in the arena of competitive chess play, men do perform slightly better than women. (If you call this a sexist statement then ask yourself what you would say if it were “women play better chess than men”). Again, this is not an argument in form of “X is more intelligent than Y” and our analysis here does not take into account a person’s individuality. A good chess player can’t be characterised with one attribute only like strategy but other factors like emotions come into play too. While men may excel in some areas, women do better in others. Who knows, the Number One place may soon be filled by a female chess player – at least our analysis won’t exclude this possibility. And this would trigger yet another debate over this old question of who is the better chess player and why. But let's leave those discussions to others and we better get back to more important things :-)

Thanks for reading and Happy Chess!

Lion Chess Ltd.

Monday, 8 December 2014

Lion Chess showing off a New Face

Our website got a bit... outdated shall we say. So we brought in a professional website designer to give our website the needed facelift. The site remained its structure and functionality but its design got greatly improved and we are sure you will agree with us. And on time for the Christmas season!

Below is a screenshot of our new site and we hope you like the new look, presented on a subtle tartan pattern to connect to our presence in Scotland! Please come and enjoy!

Monday, 2 June 2014

Age vs. ELO

Age vs. ELO - Your battle against time

Following my recent blog of what your chances are to beat Carlsen (or any other elite player), I was wondering about the importance of age in chess. Of course, it’s never too late to play chess and it’s good for your mental fitness at any age, but when can you expect to reach your peak? It’s also an interesting question to look into to find out what Anand’s chances are to take the world champion title back from Carlsen in November, with Anand being nearly twice Carlsen’s age. That said, FIDE needs to get this match organised first…
I wasn’t sure whether this question can be answered easily. Of course you can look into the FIDE Top-100 list and make an analysis of the age distribution. But we would deal with only 100 players, all of whom are professionals and their life gravitates around chess. Not uninteresting itself but it doesn’t necessarily answer the question of when most of us reach their peak performance in chess. (And for those statistically inclined you will agree that 100 samples does not give a good statistics either). And then… I found a list of all(?) FIDE registered players. 179,221 players in total, as of May 2014. A dream for every statistician (and no, I’m not one). That should allow for some good analysis – in fact, I will have to split the analysis into several articles since you probably want to play a game too.

Let me first recall some far-distanced memories from school (I was once young too). In psychology class, we learnt that intelligence peaks when you are around 18 to 19. Intelligence should not be mixed up with wisdom which increases with age. Without going too much into citing definitions, you can broadly define intelligence as the ability to solve problems and wisdom as the ability to recall information from memory. Brain memory that is, not the memory in google’s server farms. Since chess training and performance relies quite heavily on learnt patterns, openings, tactics, strategy, etc., pure intelligence alone won’t make a great player. In fact, most elite players wouldn’t classify themselves as geniuses but they all studied hard to be where they are.
Before we start our analysis, let me first define and justify some assumptions made. To answer our question of how your (chess) skills improve with age as accurately as possible, the list with its 179,000+ names was filtered down in the following way:
  1. All entries with year of birth “0000” were deleted (without a valid year of birth, no analysis can be done);
  2. Inactive players were excluded from the analysis (an inactive player could carry a high ELO rating into the old age and therefore skews the statistics; as good as Kasparov is, he won’t be a 2800+ player at the age of 95 anymore);
  3. The list separates male and female players, but our analysis does not make a difference between the sexes – that’s stuff for an other article;
  4. The ages given are within one year and might not reflect the true age of a player. The age was simply calculated by subtracting the player’s birth year from 2014, for example 2014 – 1970 = 44 years. This shall be good enough for us; after all, your chess won’t improve or degrade the day following your birthday;
  5. Only players with a K-factor (used in the calculation of ELO ratings) of less than 30 are included. A K-factor of 30 is used for players who haven’t played 30 rated games yet. No discrimination against serious newcomers here, but we want to ensure only serious players are included in this analysis, as short-term enthusiasts could distort the picture;
After filtering the list down to meet the above criteria, we are left with almost 71,000 players which is still a respectable sample size. That’s enough of preambles now, let’s look at the results!
The first plot shows you the average ELO rating in various 5-years age bands. The strong blue line gives the average rating, and the two thin lines above and below are the minimum and maximum ratings found per age category. As seen in the chart, the peak performance in chess is reached when you are in your late twenties. Probably not an unexpected result as this is the time when your intelligence is still near its maximum level and you had enough time to soak in lots of chess theory and gained enough playing experience. Once you hit your thirties, performance is slowly but gradually decreasing. Again, no surprise.

But what’s the jump in the rating once you are close to 100 years you may wonder? I’m afraid it’s not enlightenment – at least not in chess – but this jump by almost 200 points is down to the very small sample size: Only 2 players fall into this category. It would have been better to merge all 86+ players into an 86 and over category but I felt it’s a nice demonstration that you can still play good chess at an old age.
You may wish to ignore the bottom line as it could indicate players who don’t take their play very serious.
More of interest is the maximum rating found in each age group. The shape follows quite closely the average performance of players. Our respect goes to the 90+ year old player who still plays at a performance of over 2300 points!
Next thing is to have a look at the age distribution of active players, again divided in age bands of 5 years: 

My expectation was to see the usual bell-shaped Gaussian distribution, maybe with a longer tail towards higher age; in other words you only have a few young and old players and a single peak somewhere in between. Thus, I was surprised by the plot above: (Competitive) chess is most popular amongst teenagers! Then, the interest seems to wane until it peaks a second time when players go into their forties and early fifties. As to the why of this shape, I can only theorise and I welcome any better or alternative explanations:
As a teenager, you get quickly enthusiastic about new leisure activities. You are also likely to be competitive (remember that unrated players and players with only a few played games are not included in the stats here). Apart from the lack of physical activity in chess, the game is great for teenagers as they usually have quite some spare time and not much of a financial investment is needed. Out of school, college or university, the hardships of life struck: You have a job, perhaps start a family and suddenly you don’t have as much time to play chess as you had before. And trust me, young children don’t like to see you deeply concentrated over a chessboard…
As you get older, it appears you have more time again – children getting more independent, you might divert more of your time towards chess rather than other sports, etc. Following the second peak the number of players goes down and down… and never peaks again. I expected to see another minor peak once people enter their retirement but I guess your competitiveness fades away and you prefer having friendly games with your pals. Finally, I believe the vanishing number of FIDE rated players at the far right side of the chart does not need any further explanation…
I believe this article got long enough. Thanks for reading that far Smile. Before concluding, I show you one more plot without any further explanation as it's not much more as a summary of what has been discussed already above. This last chart plots each of the nearly 71,000 players in terms of their age and ELO rating. Where can you find yourself?

To go back to our first paragraph: Can Anand beat Carlsen in the match for the world chess champion title? His age is not on his side, but his experience of a long career is. The beauty of statistics is often not found in the average but in the outliers and it would be great to see if 44-year old Anand can prove that you don’t have to be a youngster to be at the top. In case you find yourself at the wrong side of the age curve (a nicer way to express “you are old”) do not despair: You could always be the exception to the rule – by being the statistical outlier you are confirming the validity of the theory Wink. Thank you.
Happy Chess,

Monday, 5 May 2014

You can beat Carlsen. Statistically.

The well-followed Shamkir chess tournament is over and it’s no surprise to see Carlsen walking out as the winner. However, he failed to collect the necessary points to break the ELO 2900 barrier and on the FIDE ratings list of May he gained just one extra point.

Looking at the Shamkir tournament results, I was surprised to see Radjabov’s achievement: Although the lowest rated player in the A-class, he performed best against Carlsen who is rated nearly 170 points higher than him. Yet Radjabov came out at fourth place.

This strong play of Radjabov made me wonder what the likelihoods are to win against a 2882 player and so I played around with the calculation of ELO rating numbers.

Unfortunately, the possibility of a draw in chess makes a statement of what your winning chances against your opponent are hard, if not impossible. Radjabov’s likelihood of winning a game against Carlsen were mathematically 28%. Or you could say he had a 0% chance of winning, 56% of drawing and 44% of losing. Or anything in between… A draw counts as half a win and half a loss in the system and that makes it tricky to give likelihoods for wins (if that’s possible at all). I leave those details to the more skilled mathematicians.

Many chess enthusiasts are eagerly looking forward for the re-match Carlsen vs. Anand. So what are Anand’s chances then to win (a single game) against Carlsen? With their current ratings (May 2014), the calculation predicts a 36% chance. Statistically that is and neglecting the possibility of a draw.

Since we are dealing with a mathematical model here and not the real world, we can of course ask what are YOUR chances to beat Carlsen in a game of chess? Again, we ignore draws here but you can easily extend this by remembering that a draw counts as half a win and half a loss. The following tables gives your chances of winning against a 2882 player (choose the closest match for your rating):

Your rating<12501300135014001450150015501600
Winning Chance<0.01%0.011%0.015%0.02%0.03%0.04%0.05%0.06%

Your rating16501700175018001850190019502000
Winning Chance0.08%0.11%0.15%0.20%0.26%0.35%0.5%0.6%

Your rating20502100215022002250230023502400
Winning Chance0.8%1.1%1.5%1.9%2.6%3.4%4.5%5.9%

Your rating24502500255026002650270027502800
Winning Chance7.7%10%13%16%21%26%32%38%

Because a picture tells more than a thousand numbers, I also plotted the results graphically. The coloured dots mark three selected players, and in brackets are their current ranks as per May 2014 FIDE list. The plot stops at Carlsen’s own rating of 2882 who has a 50/50 chance of winning against himself – should he ever step up to the challenge or being bored of everyone else…

ELO curve and winning chances against Carlsen

Next time you experience a series of defeats, don’t be disheartened: Mathematics tell you that you will eventually win against anyone, even an elite-player like Carlsen. Statistically. Perhaps one game in 20 years if you play a game a day… At least that’s the path to victory and a high self-esteem if you are a statistician (no offence intended, I respect this profession). The better advice for the real world is the old and well-known formula: training, study and practice. Lots of it. And statistically speaking, training gives you the highest likelihood of winning too. Enough number crunching for now, so let's go back to chess ;-)

Happy Chess,
Lion Chess Logo

Thursday, 24 April 2014

Is ELO 2900 here?

Carlsen is only 10.8 points away to break the ELO 2900 barrier as the first chess player in history. (The top performing computer chess engines are well above the 3000 mark but that’s a different story and the numbers are skewed and don’t allow a direct comparison).

In order to achieve the feat of a 2900+ rating, Carlsen would have to gather 8.5 points out of 10 at the Shamkir 2014 tournament (see the Article Carlsen also beats Nakamura in Shamkir). An other way to put it is that Carlsen has to defeat the three highest ranked players after him, which would put him at the 2900 mark. Not an easy task but certainly possible as Carlsen seems unstoppable at the moment.

What are your thoughts: Do you think he will become the first player to breach the 2900 mark? Or will someone stop his meteoric rise in the last moment?

But due to the inflation of ELO ratings, it certainly won’t stop the debate of who the greatest player of all time is and this discussion will surely continue…

Happy Chess,

Lion Chess's First Post - Our Introduction

A warm Hello to everyone and thank you for taking your time reading our first article. This first post provides an introduction to who we are and what we do, and I spare you the typical marketing phrases.

Lion Chess Limited is an online retailer of quality chess products, located in the beautiful seaside town of Largs in Scotland (see image). Lion Chess was founded in 2013 by Guenther Wurmbauer (that’s me) a chess enthusiast for many years – albeit his chess skills should be better by now but they are slowly improving. Although we need to make money in order to survive, we are not selling you chess products for the sake of selling you something but we value high quality and fine craftsmanship to satisfy your expectations of what a good chess set should be like. Holding a finely crafted knight from a luxury chess set in your hands is a rewarding experience and reminds you of why you are running a chess retail business, which is not the easiest business to run.

So what makes me to start yet another chess supply business in what seems to be a saturated market? Some years ago, I obtained permission from my wife to buy a luxury chess board from the outlet section of a chess shop (since it is now a competitor I’m sure you understand why I can’t tell you its name). Then I only missed luxury pieces to fit this beautifully crafted board, even though it had some minor defects – as you would expect from an outlet item. Since my wife wouldn’t allow me to start collecting luxury chessmen, one way out of my misery was to start my own chess business. And so it was done. (And an other part of me was probably jealous of seeing the fun my wife had running her own business while I had to leave going to work each day). Now I have plenty of chess pieces to admire, yet no high-end ones to play with as they are up for sale…

Are we any good you may ask? It’s a fair question to ask about every newly established business. And it’s a question we invite you to answer yourself. What can be said however is that we don’t claim to have reached perfection but we work hard towards this unreachable goal. As the saying goes: The journey is the reward. Things can go wrong and they do; not everything is our fault but we believe it shouldn’t be you who has to deal with any issues. Whether the courier damages your newly acquired chess set or the postal service is losing your parcel you long for – we will deal with it since we want you to enjoy chess and our products. After all, life is hard enough already.

Even though it’s nice to see money trickling into your bank account (bills need to be paid at the end of the day), it’s your positive reviews and (constructive) feedback which keeps us going each day. It always makes our day to hear of another happy customer and that makes us work even harder. We are looking forward welcoming you on our site and hope you enjoy it. Thank you for reading.

Happy Chess,