A Mathematical View of Track and Field World Records

timer, stopwatch
(Image credit: Julian Liam | Creative Commons)

(ISNS) -- A mathematician has developed a new model that can estimate which track and field world records are the most likely to be broken.

Brian Godsey, a graduate student in mathematics at the Vienna University of Technology in Austria, recently published a paper including computations of the likelihood of record-setting performances in 48 different men's and women's track and field events during this calendar year.

Godsey's paper did not directly address the likelihood of an athlete setting a track and field world record at the 2012 London Olympics, but his analysis suggests that viewers should keep a close watch on the men's 110-meter hurdles and three women's events, the 5,000-meter and 3000-meter steeplechase races, as wells as the  hammer throw. There is a 95 percent chance that the women's steeplechase record will be broken this year, Godsey wrote in the Journal of Quantitative Analysis in Sports.

Godsey gives competitors a better-than-10 percent chance of besting the world record in 22 events during this calendar year, 18 of which will be contested at the Olympics. Numerous records, however, seem far out of reach.

This year, no woman has come within 5 seconds of the 3:50.46 record for the 1500-meter run, set in 1993 by Qu Yunxia of China. Godsey predicted a less than one one-hundredth of a percent chance of the record falling in 2012. Most of the event's top historical times are from the 1980s and 1990s. That's also true for numerous other events. Performances from the 1980s currently hold the record in 13 of the events Godsey reviewed.

Godsey was inspired to analyze track and field world records after watching Usain Bolt's 100-meter world record-setting 9.58 second performance at the 2009 world championships in Berlin.

"I thought, 'Can I possibly prove that it's either the most or one of the most impressive records at the moment or in history?'" said Godsey.

It's easy to define performance in a single event, but it's less intuitive to compare results from events of different distances, or to compare throws and jumps to running events.

Godsey approached the issue by graphing each event's best performances of all time and analyzing both the numerical results and how recently the performances took place.

A mathematical model computes the likelihood that a record-setting performance will happen soon.

"The model that I used is able to predict how many people run faster than a certain time, or what the expected longest throw is in the javelin," said Godsey.

Encouraging Data

As Godsey was developing his model in the fall of 2011, he found that it indicated something that seemed unlikely.  Calculations suggested that the record in the men's marathon was very likely to be broken. And on September 25, it was, by Kenyan runner Patrick Makau. In October it was almost broken again by countryman Wilson Kipsang Kiprotich.

"That gave me some confidence in my methods," Godsey wrote in an email.

Godsey based the published calculations on performances through October 1, 2011.

"What I do like about the paper is, relative to things even I've done, or others have done, is it's based on much more data," said Scott Berry, a statistician at Berry Consultants. "I think that creates more reliable answers."

Berry expressed minor reservations about the probabilities Godsey calculated.

"It would be difficult for me to take to the bank the [women's 3000-meter] steeplechase number of 95 percent," said Berry. He added that the ordering of records, from least likely to most likely to fall, was "probably pretty well trusted."

Other Performance Factors

There are numerous elements that contribute to a track-and-field world record's time or measurement.

Technology and rules are both factors. It's possible or even likely that performance-enhancing drugs are a factor. And of course, there are the athletes themselves.

"Performance, in athletic terms, tends to go up. People are always trying to get better, they don't try to get worse," said Steve Haake, director of the Centre for Sports Engineering Research at Sheffield Hallam University, in the U.K. "So if they do get worse, there's some kind of intervention in place that's stopping them being as good as they were."

Haake pointed to two major changes that substantially affected world records in the past. The javelin's center of gravity was moved in the 1980s, which reduced performance immediately. Automated timing, introduced in the 1970s, removed the roughly 0.2 second clock-starting-delay that followed the firing of starting guns, changing the progression of sprint world records.

Haake's research examined the last 100 years of data to search for trends among top athletes' performances. He found that the rate of improvement is slowing down.

"We're seeing this underlying leveling off, we're seeing that in all sports," said Haake.

One factor that's difficult to isolate is the impact of performance-enhancing drugs on world-records, including many that stand today.

"There are some sports, allegedly, where you think some of those [past] performances are enhanced through drugs use," said Haake.

"We know that some of them did it," said Godsey. "Some of these records are almost certainly tainted."

But it is unlikely that drugs are the largest factor in why performances improve or decline.

Population Effects

Berry's research into world records in track and field, swimming and speed skating showed that a majority of the increase in athletic performance seen over about the last 100 years is the product of a larger world population -- and the greater number of elite talents that naturally come with it.

"Suppose humans do not get better; a human is a human is a human whether it's 90 years ago or now," said Berry. "All I do is increase the number of them, according to the population at the time… I looked at how well that predicted, purely on the changing population, the changing world records."

Berry found that, depending on the event, about 68-95 percent of the variability in world records over time could be explained by the changing population.

Are the track and field competitors likely to take down any records when competition begins this weekend? We'll have to watch the events to find out.

Godsey suggested that one race to watch will be the men's 800-meter run, in which Kenyan Olympian David Rudisha holds the world record of 1:41.01. In an email, Godsey noted that "[Rudisha will] have to run over a half second faster than his best time this season, but I think the fans believe he can do it." He added that he thinks the chance of a new record in the race has improved from the 16 percent figure he calculated in the paper.

And weird things are known to happen when the starting gun goes off. In an early July race in Paris, the top six finishers in a men's 5000-meter race recorded the six fastest times in the event since 2006, Godsey said.

Inside Science News Service is supported by the American Institute of Physics.