# Ivars Peterson's MathTrek

June 3, 2002

## Setting Records Randomly

A wide variety of factors can influence the winning time of a race. For a given event over the course of a year, for example, the results may depend on the quality of the runners, the race location, weather conditions, and so on.

In a 1985 article in the Journal of the American Statistical Association, statisticians Peter Tryfos and Russell Blackmore of York University sought to forecast future record performances on the basis of observed past records in a given event. They chose to view such athletic records as realizations of a random process, reflecting uncertainties in the many factors that influence any given result.

This approach "may be applied to all types of athletic competition—not just running—and at all levels for which records are kept," Tryfos and Blackmore remarked.

One crucial assumption concerns the period of time over which the distributions of winning times (in races) or distances (in field events) are considered to be approximately the same. "That hereditary, nutritional, training, and other factors have caused these distributions to change drastically over time cannot be disputed," the statisticians conceded. "Today's athletes on the whole appear to be much better than those of 100 years ago."

"What is not clear is how far in the past the line should be drawn," they continued. "The period chosen need not be the same for all events."

On the basis of their statistical analysis of record performances in six running events from 1968 to 1982, the statisticians made forecasts of what the world record would be in each event in 1997. Here's how they did.

### Actual and Forecast World Records for Men in Six Running Events (in seconds)

 Event 1982 (Record) 1997 (Forecast) 1997 (Record) Current Record 1,000 m 132.18 131.32 132.18 (1981) 131.96 (1999) 1 mile 227.33 226.57 224.39 (1993) 223.13 (1999) 5,000 m 780.42 777.21 759.74 (1997) 759.36 (1998) 10,000 m 1,642.4 1,638.6 1,587.85 (1997) 1,582.75 (1998) 20,000 m 3,444.2 3,433.9 3,415.6 (1991) 3,415.6 (1991) Marathon 7,693 7,671 7,610 (1988) 7,538 (2002)

Interestingly, with one exception, the forecasts fell short of actual records. The results for 1000 meters reflected the singular performance of runner Sebastian Coe, whose remarkable 1981 feat wasn't surpassed until 1999.

In the May 30 Nature, Daniel Gembris, John G. Taylor, and Dieter Suter returned to the question of what contribution chance makes in athletic endeavors.

The researchers applied their method of statistical analysis to the top performances of men in 22 track and field events during the German championships of 1973 to 1996. Data for the years 1973 to 1984 served as a reference period from which they predicted the best result for the period 1985 to 1996.

In distinguishing between effects that stem from better training and equipment and those that stem from elements of chance, the researchers concluded that in 18 of the events in their sample, improvements in records were no better than those predicted by chance.

In four cases, "the results achieved are better than the predictions, indicating systematic improvement," Gembris and his colleagues reported.

A comparable analysis of annual best results worldwide (rather than just successive world records, as in the 1985 study) revealed that record-breaking results in seven out of 19 events could be attributed to some sort of systematic shift in performance rather than merely chance.

In the other cases, the records appeared to reflect random variation rather than true improvements in performance.

Intriguingly, the new study also hinted that athletes in a number of events have neared some sort of physical limit. Record-breaking occurs in such small increments that chance factors loom large.

References:

Gembris, D., J.G. Taylor, and D. Suter. 2002. Trends and random fluctuations in athletics. Nature 417(May 30):506. Abstract available at http://dx.doi.org/10.1038/417506a.

Tryfos, P., and R. Blackmore. 1985. Forecasting records. Journal of the American Statistical Association 80(March):46-50.

Data on record performances in track events can be found at http://www.runnersworld.com/home/0,1300,1-141,00.html.