MNb, 

Please note the time between my last message and this one. 

According to Wikpedia, 

in 1914 there were 5 GMs

in 1950 there were 27 GMs

in 1972 there were 88 GMs

in 2005 there were over 900 GMs.

Ostap, that is certainly true.

During the Cultural Revolution in China, all things western were considered to be capitalist and were duly destroyed.  It's only been in the last two decades or so that chess has really taken off  there.  Chess has also become very popular in India since Anand's ascent.

Smyslov_Fan wrote on 07/14/06 at 05:12:22:


This is just theory. Valuable theory, but only theory. Is this confirmed by the facts? Before drawing any conclusion someone really should do the counting I suggested in my previous post (I am too lazy for it).
Then we must settle the problem of interpretation (eg in 1950 there were considerably less active chess players in the world than now, or not?)
Before I have seen results, I do not immediately accept the assumption, that the number of GM's is an exponential function of time.

Smyslov_Fan wrote on 07/14/06 at 14:03:30:

You're using a bit of a flawed argument. The amount of GM's as compared to other disciplines doesnt say anything about the difficulty to obtain the title. There are various other factors involved. Ie I know a couple of youngsters who decided to not pursue the IM title in favour of their education. Iirc he still got his IM results anyway.

Smyslov_Fan wrote on 07/14/06 at 05:12:22:


I think we are more or less in agreement on the economics analogy.  But I would argue that the pushing out of the demand curve resulting from the breakdown of the Soviet Union and the rise of China and India, is the equivalent to the removal of an artificial restriction, so that what we have now is much closer to the model of a competitive market than we had before.  It may be easier to get the GM title in the sense that there are more opportunities to play in tournaments and get qualifying norms and ratings but - at the risk of repeating myself - that doesn't necessarily mean you don't have to play as well to make those performances.

Incidentally (and this probably belongs more in the original thread) I'm not sure I understand your criteria for qualification for the GM title.  Do you have to be in the top 0.3 per cent (or whatever )consistently?  Or is just once enough? And can you lose the title as well if you drop below a certain rating (or percentile)?

Personally I would welcome that: insofar as I have an issue with the GM situation now, it's that you get people who play well enough for a short time to earn their GM title but then they stop playing regularly and it all goes to pot.  But they still write books and sell them on the basis that they are a GM.  Serious chess players will also take into account how strong the players in question are (by looking at their rating and recent performances for example).  But lower down the scale of club players, people will be duped into thinking that these guys are the elite when in fact they are possibly not even as strong as a rising young IM.  I think you should have to, say, make at least one GM norm every two years to keep the title.

Smyslov_Fan wrote on 07/14/06 at 05:13:04:

I was just trying to distract you from thinking about the French Defense!  

Of course, digesting your detailed response will distract me as well...  

Anyway, 

Factors that affect supply at every point of the P/Q graph are said to "shift" the supply curve.  Same with Demand.

One example of shifting supply is to add more suppliers.  In the chessic sense, this is adding players from new markets.  (The problem with the chess analogy is that the product supplied, professional chess players, is also the consumer.  It makes things a bit confusing.)

By adding new quantities of chess players, the price (rating) of each player will change depending on the quality of the new product.  When the Soviet Union broke down, the United States and western Europe saw a tremendous influx of talented players who wanted to make a living.  This affected the DEMAND side of the equation more than it did the supply side.   

Demand for products (prizes) skyrocketed, but the supply was stable and unable to reach demand.  This meant that the value of prizes went through the roof, while ratings for all competitors also went up.  Soon, these foreign players were gaining titles that were unattainable in the Soviet Union and adding to the ratings pool for everyone.   

The real inflation of rating, that is, the addition of ratings points to the pool of available ratings, occurred mostly after 1990.  New markets opened up, including China and India (Hi, Castlerock!).  This increased the volume or ratings even more.  This was not a simple arithmatic increase, it was exponential (or at least close to it).   

The number of GMs skyrocketed, not just from the new markets but also from the older established markets because there were more chances to gain ratings.  It is this multiplying effect that caused the true ratings inflation of the last 15 years or so.

Keano argues that the rating inflation is fine, but rating inflation devalues the product.  In this case, the title of GM.  It is now easier than ever before to become a GM, and there are those, myself included, who would like to fix that.

My solution is to tie the title to a percentile of the FIDE population that can demonstrate its superiority over the average FIDE member.  (There is a problem with my previous description of the FIDE population in that it isn't a "standard normal distribution."  It is so heavily skewed to the top that it can be described as only half a standard normal population, with the lower half not even being members.  The numbers I cited were accurate for this type of population as well, though.)   

A GM should be at around the 97.7%ile (2z) of the FIDE membership.  An IM could be at the 95th %ile (or 90th) or whatever the FIDE board suggests, and the FM at the 80th%ile  There will still be an increase in numbers compared to the number of GMs before 1990, but it won't be any easier than before 1990 because the way of measuring will be tied to percentile, and the ratings will not be prone to inflation.

Ok, let me try to tackle Supply and Demand in kind of the same way I do for my students.

Let's say I'm going to show a movie on Friday during class and lunch.   I will be selling pizzas for the people attending.  I ask who wants pizza.  35 hands go up.  Then I ask how many slices each.  I get about 100 slices.  Each pizza has 8 slices, so I would have to buy 14 pizzas.  Then I say that I'm not going to be able to afford 14 pizzas unless you pay for your own.  How many would be willing to buy pizza at $.10?  Everyone is still in.  Then I say, show me the money.  Because demand is not just about wanting the pizza, it's also about being able to pay for it.  I do the same for $.25 and say that still won't cover my costs.  Each pizza will cost me about $10. $.50, and now fewer people want to spend money on pizza.  Say, the demand has gone down from 100 slices to 80.  When I get to $1.00 a slice, I get about 50 slices, when I go to $2.00 a slice, I have about 5 people still interested.  

The T-chart would look something like:

D (demand)



That's the demand curve.  Now my real price per pizza is only $5, but I didn't tell them that.  I need to make about $.65 a slice to cover my costs.  When the demand reaches my acceptable limits of supply, we'll come to a fair cost.  I ask them what the demand would be for $.75 a slice.  The Q (quantity) = 70 That is, I make $52.50 and I get two slices of my own. My actual cost is $45 plus tip to the driver, $5, equalling $50.  I make a profit of $2.50 and lunch.  The students are happy because it's still cheaper than cafeteria lunch and they get to eat in class.  I'm happy because I don't lose money.

The Supply Curve looks very simple:



I draw these figures on the board as I do it.  I explain that the supply curve marks the price for every quantity.  As the quantity goes up, so does the price.

Demand is just the opposite.  As the price goes down, the quantity goes up.

Where those two curves meet is the point of sale, known as the point of Equilibrium.

The Supply and Demand graph shows a snapshot of the supply and demand at one moment in time.  The only factors that change this curve are price and quantity.  

There are factors that will affect all quantities at all prices, and they will shift the supply or demand curve.  These are inflationary, deflationary, or neutral in nature, but they change the S + D over time.