Hindustan Times (Delhi) - - METRO - (Atanu Biswas is a pro­fes­sor of statis­tics at ISI, Kolkata)

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

Chart 2)

statis­ti­cian might need to re­cal­cu­late the as­ymp­totic high­est test score or as­ymp­totic 100m world record afresh.

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