# Bias in average age for grandmaster title qualification by age groups?

It has been known for quite some time that the youngest age at which chess players managed to qualify for the grandmaster title has significantly decreased since the 1950s, and there are currently almost 30 players who became grandmaster before their 15th birthday. However, there is a question on Chess Stack Exchange that asks, What is the average age to become a grandmaster?.

Someone posted an answer for which he (I assume it's a he) looked at six subsets of grandmasters and found the following results:

• For players born after 1945, the average is slightly above 26 years old.
• For players born after 1970, the average is slightly above 23 years old.
• For players born after 1975, the average is slightly above 22 years old.
• For players born after 1980, the average is 21 years old.
• For players born after 1985, the average is just shy of 20 years old.
• For players born after 1990, the average is 18.5 years old.

(It is not entirely clear to me whether, e.g. the first group contains all grandmasters born after 1945 (which makes it a superset of the next group) or only those born between 1945 and 1970 (age bands). I think it's the former and that my question applies in both cases.)

The issue is that players born after 1990 were younger than 26 when the answer was posted (July 2015), so it would be impossible to get an average "GM age" of 26. The youngest subset in the answer naturally cuts off anyone who was over 25, while the "older" subsets don't. Doesn't this skew or bias the results? (Is this a type of selection bias? I have no background in statistics, and reading several related Wikipedia entries did not help.) If yes, how should (or can) this be mitigated? In the "older" groups, should the calculation of the average for GM title qualification only consider players who got the title before the age of 26?

• +1 Because a careful consideration of this phenomenon usually involves the techniques and concepts of survival analysis, I have added the survival tag. Of course you're right to be suspicious: after all, since nobody born after 1990 could be older than 26, it's mathematically impossible for the mean age of that group to exceed 26--but perhaps in 80 years or so, people looking back at the data will discover that the mean age to become GM in this cohort was 50 years!
– whuber
Commented Dec 7, 2016 at 16:49
• There has been a question on a not completely unrelated matter (whether winners of Oscars live longer) stats.stackexchange.com/questions/166414/… but nobody answered it so your current intersting question may have everyone baffled too. Commented Dec 7, 2016 at 17:26
• It has been noted, from studies of inscriptions on gravestones, that recently people are dying at much younger ages (on average) than they used to!
– whuber
Commented Dec 7, 2016 at 17:31
• @mdewey Thanks for the link to Do Oscar winners live longer?. I had not seen it because I wasn't aware of survival analysis when I wrote my question. Commented Dec 7, 2016 at 17:38
• I think this is a issue of right censorship which does come about in survival analysis. Taking a completely different tact, suppose we take the youngest grandmaster in the time periods. Wouldn't this data give a better indication as to whether or not there is a downward trend? Commented Dec 7, 2016 at 20:49

I think the average age to attain GM title will continue to decrease due to the ratings inflation (discussed in chessbase.com) and other factors such as the increase in number of players who are awarded the title and perhaps even the Flynn effect. However, I do expect that the mean decrease to bottom out at some point as you aren't just born a GM. It requires some minimum amount of deliberate practice and I will go with the 10,000 hour rule as a guess. The year 1950 was when the GM title was first awarded to 27 players who were regarded as the best in the world at the time and were probably GM strength for decades before they were granted the title. Last I recall the GM title requires a minimum rating of 2500 ELO and requires scoring 3 GM norms by attaining required performance levels in FIDE sanctioned tournaments in games against other GMs. If there are more GMs there are greater opportunities to score such norms. It was much harder in the past to find tournaments in the US to obtain such norms. Other ways to get a GM title are to win certain national events and international events (for youngsters) such as the World Junior Open.

Wikipedia has the list of grandmasters as of November 2016.

Per the "simple approach" I calculated the mean per year and here is a graph showing average age of GMs by year as well as the number of GM titles awarded that year.

For the last 5 years:
Year Mean Age
----- ---------
2011: 23.786885
2012: 25.925000
2013: 23.086207
2014: 25.250000
2015: 22.194444

A simple approach with the given data is a different slicing of the data:

Take all chess grandmasters that become grandmaster in a given year (or 5 years bin or 10 years bin) and compute the average age of them. This kind of slicing will be more robust (it is not influenced by grandmasters from the future, but is is sensitive to other effects, mainly for the number of chess players trying to become grandmaster: When it is increasing over time, it will make the average lower over time). There is probably a kind of correction to this effect available.

• Thanks. I assume the number of players that aim for master & grandmaster titles has increased over time, but I don't have any data on this. That's a question for Chess SE ;-) (E.g. Why is there a craze of becoming chess grandmaster?.) Commented Dec 8, 2016 at 10:36