Why Brian Lara and Usain Bolt records will fall

KOLKATA :In August 1884, Australia’s Billy Murdoch became the first batsman to score a double hundred in a test match. It was 46 years later that Andy Sandham from England became the first player to score a triple century in this format of the game. It took another 74 years before Brian Lara reached an individual score of 400 while batting against England at Antigua Recreation Ground, St John’s.

So, will we ever get to see a batsman cross the 500 figure in test cricket?

The same question can be posed vis-à-vis other sports as well. Exceptionally gifted sportspersons will keep pushing to improve existing records. But this pursuit of excellence will hit an upper limit of human performance at some point.

For example, people will never be able to run 100 metres in a second.

Is it possible to predict what these limits will be?

Mathematical models around the concept of asymptotic values can help us answer this question.

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 regression 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! (See Chart 1)

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 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. (Chart 2)

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.