Put simply, a variable is said to take an asymptotic value of zero if it gets increasingly close to zero with time, but never reaches the actual figure at any point of time. So, if one were to build a suitable model which plotted records in sporting events along with the time (from the advent of the event) when they were achieved, one could get an estimate of what the all-time best performances can be.
In 2002, using world record data on 100m run from 1964-2002, the author and his collaborator Professor Jean-francois Angers of the University of Montreal, Canada, tried to find out the answer to this question, using a methodology called the regres- sion spline model (the details of which are best avoided in a mainstream newspaper). We obtained the values of the possible world record in men’s 100m at 2020.
The findings were published as a research paper in 2002 in the Brazilian Journal of Probability and Statistics (volume 16, pages 25-38). In that study, we obtained the world record value of 2020 as 9.57 seconds, and that in 2100 to be 8.79 seconds. Today, at the beginning of 2019, we are surprisingly close to the predicted world record value for 2020; the present value of this record is 9.58 seconds!
Let us come back to the question of best cricket scores in tests and ODIS. An asymptotic value of what the best test and ODI scores can be estimated by fitting a
(See Chart 1)
mathematical model (the Shifted Exponential Model has been used here) along with a large number for the time-period of the sport. If one were to take months as the unit of time for tests and ODIS, we are currently in the 1535th and 577th month. The asymptotic value can be found by assuming the number of months to be a million. These calculations give us the value of 417 and 301 for test and ODIS respectively. (
Does that mean that nobody will ever score a 500 or a 450 ever in a test inning? Not necessarily. We should remember that we are dealing with champions here. In statistical language, we call them “outliers”, who are not explainable by the standard rules that are applicable to billions of common people. If that happens, the poor
statistician might need to recalculate the asymptotic highest test score or asymptotic 100m world record afresh.