What Is The Relationship Between A 100m Sprinter´s Height And His Sprint Time?

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Introduction

In 2009, The retired Jamaican sprinter, Usain Bolt broke the world record for the fastest 100 meters sprint at the World Athletic Championships in Berlin. He is the only person to ever sprint a recorded 100 meters under 9.6 seconds. The reason this is fascinating to me is because, I have been running track and field, on a team for 2 years and during Physical education for over 5 years, and am always very amazed to see someone running the 100-meter sprint in less than 11 seconds. I have seen many people beat their personal records and have also personally done so but never saw anyone close to Usain Bolt. This raised my interest a while back and I have also researched the science behind a human being able to run so fast. I have also come across videos, articles, and forums with the theory that it is not possible for a human to run much faster than Usain Bolts World record time. There have been reasonings behind this theory, of which one is that his height is one of the crucial reasons he was able to set the World record and if he were to be a few centimeters shorter he would not be the world record holder. Thus, I believe that this is the perfect topic for me to look into for my Internal Assessment as, it interests me a lot as well as others.

There are many factors that can affect a sprinters time such as: Starting block (A device used by sprinters to position their feet in order to avoid slipping) strategy, Stride length, weight, height, muscle composition, flexibility, etc. For my Internal assessment I am going to be investigating how the height factor relates to a Sprinters time.

Investigation

I will be using the data from the Top 10 fastest male sprinters and their respective heights and analyze how they are related. The times of each sprinter were recorded with professional devices, thus making them as accurate as possible for the current technological capabilities.

Using the entry chart above with the data found from the website alltime-athletics.com, I was able to create a scatter plot chart.

It can be seen that the points of data are decreasing in height but increasing in time. This means that the line of best fit would be negative or at a decline. This can mean that a correlation between the height and time of a sprinter can be seen.

Afterwards, I calculated the exact correlation for the data above. I did so by using “Pearson´s correlation coefficient”. Pearson´s correlation coefficient is a method used to measure the strength of a relationship between 2 variables (in this case the relationship between the height and sprint time of 10 sprinters). This correlation can range from -1 to +1, and is denoted by “r”. A correlation of -1 shows that there is a total negative linear correlation while, a correlation of +1 shows that there is a total positive linear correlation. Correlations of 0 indicate that there is no linear correlation between 2 variables. I then created a table with all the needed values in order to calculate the correlation.

The steps I took to calculate the correlation between the Sprinters Height and their 100-meters sprint were as following:

First, I calculated the mean time and heights of the 10 sprinters. I did so by using the following formula:
Secondly, I subtracted the means of the Heights and Times from all individual data´s to get “a” and “b”
Thirdly, I multiplied “a” and “b” together to get “a*b”
Next, I squared both “a” and “b” to get “a2” and “b2”
Finally, I divided the sum of “a*b” by the square root of [(sum of “a2”) *(sum of “b2”)]. As a formula it looks like this: = = -0.72149

With a correlation coefficient of -0.72149, it can be said that a correlation between a sprinter’s height and 100m Sprint time is present. In this case as the height of the sprinter increases the time decreases, or as the time decreases the height of the sprinter increases.

Next, I will be finding the optimum height for a sprinter assuming all other factors involved are the same between all. Other factors involved in a sprinters 100m time will be assumed to be the average of each factor in all sprinters. For example, one factor involved in a sprint is “stride length”. I will be assuming that the stride length of each male sprinter is 30 inches, as that is the average stride length of a man.

In order to find the optimum height for a male sprinter, I will be using calculus and derivatives. I began by removing Usain Bolts data from Graph 1 as his data was an outlier. I then proceeded to create a new graph excluding Usain Bolt´s data and added a trendline on the graph with the highest suitable value and, also added the graphs equation. I also switched the axes on the graph in order to be able to find the minimum time and for convenience. The result was following:

Conclusion

In conclusion, I was able to find the relation between the height and sprint time of a sprinter successfully. Firstly, I used the correlation coefficient method to first of all find out if there even is a correlation between the two. The results showed that there is and the shorter you are the less likely you are to get a faster sprint time. Furthermore, I was also able to find the optimum height for a sprinter assuming they are the average male. The result showed that a height of 181cm is optimal for the best sprint time.

These results were however not very surprising to me as, I had speculated for this correlation to be present from personal experience. Knowing this however, it could be beneficial to predict the winner for a race. But, it would not always work because, the data was from professionals and not the general public.

Evaluation

There were some limitations involved in my Internal assessment one of which being that I only used the data from Professional athletes and this might not be perfectly generalizable to the public. However, it does still show proof for the fact that shorter people might have higher times in a sprint but, this is not always the case. Another limitation involved is that the optimum height was found assuming all involved factors in the sprinters are the same except height. This makes it less generalizable as not everyone is the same exact average in all factors, however due to the fact that I assumed for them to be the perfectly average human being it is still generalizable to the vast majority.

Bibliography

Larsson, Peter. “All-Time Men’s Best 100m.” Men’s 100m, 28 Sept. 2019, https://www.alltime-athletics.com/m_100ok.htm.

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What Is The Relationship Between A 100m Sprinter´s Height And His Sprint Time?

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