DESC 656.33 Quantitative Methods for Business Operations

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DESC 656.33 Quantitative Methods for Business Operations

Data Analytics Paper

One Hundred Meter Sprint Analysis

August 11, 2021

Two million years ago, humans’ evolving brains demanded increased protein intake which created the necessity for a new type of hunting strategy. Fossil records indicate that humans first began utilizing running during persistence hunting by noting distinctive physical changes on the human anatomy (Owen, 2007). During a time before humans had access to weapons or projectiles, the ability to track down a kudu for miles into heat exhaustion became an invaluable asset that was the differentiator between survival and starvation. The Wikipedia definition cites that the typical distance ran during a persistence hunting chase down is approximately twenty-two miles which is strikingly close to the recreational modern version of the marathon. What began as a means of survival for our ancestors evolved into arguably the first human spectacle of sport, with a universal reverence for the fastest times achieved that has permeated throughout history.

Fast forward to approximately 776 BC and the first recorded running competitions take place in Olympia, Greece, at the legendary Stadion in the form of a one hundred ninety-five-meter sprint (Pilanis, Kasabalis, Mantzouranis, & Mavvidis 2012). In over two thousand years since the races at the Stadion, the universal standard for measuring human speed in competition has slightly changed from one hundred ninety-five meter sprint to now one hundred meters. While the measuring standard has remained relatively unchanged, the last century of track and field has seen exponential evolution in every facet of the sport: how results are measured, how athletes prepare, and even the athlete’s shoes and track surface.

The fascination with determining the answer to this age-old question is on display at the highest level every four years at the Olympics. A gold medal is one of the most sought-after sporting achievements, but a world record guarantees gold and simultaneously cements a special legacy for an athlete. Analyzing historical data of men’s gold medal times while considering athlete’s individual traits and environmental variables will provide insight into answering the ancient question. Below, Figure 1 maps the previous thirty Olympic men’s gold medal performing times demonstrating a horizontal trend with slow improvement. The trend line shown in orange represents the years of competition that utilized a dirt, grass, or cinder surface, while the blue designates the “modern” era and the implementation of synthetic track surface.

So, what is the human speed threshold for sprinting one hundred meters and how close are we to breaking it? Australian physiologist, Jeremy Richmond, predicts the threshold to be 9.27 seconds based on his studies of fast-twitch muscle fiber reaction times along with ground-foot contact time (Burfoot, 2020). A sprinter’s speed is produced through vertical application of force as the foot strikes the ground and an elite sprinter like Bolt’s foot is currently in contact with the ground for 0.8 milliseconds per stride (Burfoot, 2020). Richmond believes that increased efficiency in fast-twitch training will reduce the ground-foot contact time from 0.8 seconds to 0.7 milliseconds, making a 9.27 second time achievable (Burfoot, 2020).

Segmenting the population by timeframes allows us to focus on the most current and relevant data, and eliminate the impact of the slower times from 1896 to 1964 in our future predictions. We can assume that sprint times will not regress to the level of performance prior to 1964, and isolate only the current, more valuable trend. Figure 2 applies historical trend data from 1968-2021 to the Holt-Winters additive method optimized to project how long it will take to achieve Richmond’s predicted speed ceiling. When applying the 1968-2021 results to the Holt-Winters method, the model predicts we will steadily approach Richmond’s 9.27 second mark for the next century until it is finally achieved in the 2128 Olympics.

World-class sprinters come in a variety of shapes and sizes which has contributed to debate over the ideal sprinter prototype. Usain Bolt is commonly referred to as the most naturally gifted sprinter the world has ever seen as he was recognized as one of the most dominant athletes for over a decade. This is easily said looking at Bolt’s performance in retrospect, but there has never been physical specimen quite like Bolt. Weighing in at two hundred seven pounds and measuring a staggering six foot five inches, Bolt shattered the notion that short explosive runners were the ideal sprinting prototype.

In Olympic sprinting, the margin of error may be a one millisecond differential between silver and gold, and cementing one’s legacy in sporting record books. Given such a small margin of error, every contributing factor must be considered on race day. Certain environmental factors lend themselves to an athlete’s peak performance to include: the temperature of the air, the altitude at which the races take pace, and the wind. For example, after multiple world records were shattered in the 1968 Mexico City Olympics, the Olympic Committee decided the games would never be held at high altitude ever again. Wind is also always gauged and reported, and even factored in to revise the official meet times despite what the clock may read at the finish line. Tyson Gay thought he had the world record but was saddened that the 4.1mph wind assist nullified his performance. Wind is only factored in when assisting the athlete’s time, so a strong headwind may ruin world record hopes for an athlete on the cusp. Any wind reading that exceeds two meters per second or higher is not acceptable and must be adjusted per legal competition criteria.

In order to assess which individual and environmental characteristics are the most impactful in world record times, inputting the available data into a multiple regression model can help us predict which factors best translate to speed on the track. Figure 3 shows the top twenty  all-time performances with wind, location, age at the time of record, height, to assess if any contributing factors stand out as most impactful.

Adjusted R² states that this combination of independent variables (IVs) explains about 23% of the variability in top times. This model demonstrates how difficult it is to assess a sport as complex and unpredictable as Olympic sprinting, and reenforces that world record sprints come from a variety of athletes in different environments. Testing the significance of each IV provides insight into the most significant variables in our data set. T-test results state that athlete’s age (0.0273) is statistically significant, while height (0.143), wind (0.4734), and race location (0.6023) are not statistically significant. Additionally, there is no problem with collinearity between our IVs as none surpass the .7 indicator of strong correlation. With so much of the outcome depending on an athlete’s start reaction time, and foot to ground vertical force application, and ability to peak their performance on race day, assessing athlete’s traits and environmental factors may not be the most effective approach.

The undisputed fastest man of all time, Usain Bolt, received constant criticism throughout his career for having an underwhelming start off the blocks. Runners are disqualified for leaving the blocks prior to the gun sounding, and also if their reaction times comes before 0.1 seconds. The Olympic Committee implemented the false start rule after determining that reacting faster than 0.1 seconds is physiologically impossible. According to a study from the University of Athens, Greece, assessing the Beijing Olympic male hundred meter starting reaction times, competitors shared an average reaction time of 0.162. Bolt was typically average off the blocks in reaction time and Bolt’s top three world record reaction times averaged 0.146 (Pilanis, Kasabalis, Mantzouranis, & Mavvidis 2012). Knowing that the greatest sprinter of all time left an additional 0.046 seconds at the blocks is encouraging to world record hopefuls. The perfect start off the blocks at 0.11 seconds will certainly be a contributing factor in approaching Richmond’s 9.27 second predicted threshold.

In comparison with other sports on the surface, sprinting seems like one of the most simplistic competitions with no equipment required beyond running spikes and blocks. Those who are closer to the sport know that “simplistic” is the farthest thing from an accurate description for the oldest sport in the world. There are a variety of complexities that athletes, coaches, trainers, and the Olympic committee continue to navigate as the sport evolves. As long as competition exists, humans will seek to engineer advantages in every possible avenue. Last year, when runner Eliud Kipchoge broke the world record time for the marathon, controversy surrounding his shoes dominated the headlines. Kipchoge’s Nike shoes included a rigid embedded plate, along with special foam resulting in higher energy return and lower running times. The World Athletics Committee has introduced new regulations surrounding the amount of time a shoe must be available to the public before an athlete can wear in a race as well as standards around new shoe technology (Roan, 2020).

Sprinters are concerned about the mechanical advantage regarding the engineering of new running technology as brands compete to cut time under the radar. Usain Bolt stated, “I couldn’t believe that this is what we have gone to…that we are really adjusting the spikes to a level where it’s now giving athletes an advantage to run even faster (Raynor, 2021).” This presents the Olympic Committee with another dimension of regulation to assure uniform levels of competition. Especially when only a handful of athletes are sponsored by a certain brand that happens to be testing new technology, this poses additional risks of an uneven playing field. Beyond mechanical advantages, another unpredictable competitive advantage that has a strong presence in the sport is performance enhancing drugs. With winning stakes at an all-time high, Olympic regulations are in a constant ongoing battle to mitigate unfair advantages and their strategies implemented in the future have the potential to affect the speed at which we reach the human sprinting threshold. Seeing an athlete on the podium seems much purer when there is no question that they are there for their own abilities, versus running on springs and energy returning foam.

The history of modern track and field is barely over a century old, and the data collected regarding athlete’s and competition is sparse until recent decades. Supplementing our data with logical inferences regarding the assumed advancement in athlete’s ability to peak perform is the best way to approach new world record predictions. It took Usain Bolt ten years to improve the hundred-meter record three times in his career, lowering the previous record of 9.74 to 9.58. This incremental improvement of 0.16 over a dominant ten-year campaign shows a microcosm of how slow the progression through 9.5 and 9.4 will take. As the sport continues to evolve with modern technology, more data will be recorded to reveal regarding mechanics and individual physical characteristics that lend to faster running.

Mathematical models based on historical results can provide insightful and thought-provoking data, but can’t precisely pinpoint the variety of unpredictable variables involved in a sprint race. Variables such as improved training techniques and nutritional strategies that enable an athlete to peak perform on race day are just part of the equation. The ideal physical prototype sprint athlete must prepare flawlessly in addition to performing on race day. The preparation leading to race day is a critical component but nothing guarantees a perfect start reaction time followed by perfect race execution. Additional variables that a mathematical model can not predict are the limits to which the Olympic Committee will allow for mechanical advantage in terms of the surface of the track and the shoes worn by competitors. All of this to say, a strong headwind can thwart the most talented sprinter’s plan to etch their name in the history books.

While we can’t predict the timeline for innovation of peak performance sprint training or rule changes by the Olympic Committee, we can apply logic to mathematical models to make inferences about the future of the sport. The one-hundred-meter race will remain under a magnifying class as the benchmark for all out speed while the public waits for a new world record for the foreseeable future. With so many contributing elements to a perfect race, it could be hundreds of years before the perfect athlete, with the perfect lead up of training, executes a perfect race. The margin of error may be a millisecond to win the coveted title for fastest human on Earth, but achieving that feat requires not only the inherent physical capabilities and a lifetime of dedicated training, but also the perfect start reaction time and conditions on race day.

References

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Owen, J. (2007, November 17). Humans Were Born to Run, Fossil Study Suggests. National

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Raynor, K. (2021, July 19). Advances in Spike technology are laughable and unfair, Says bolt.

Reuters. https://www.reuters.com/lifestyle/sports/exclusive-olympics-athletics-advancesspike-technology-are-laughable-unfair-says-2021-07-19/.

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