Math Software Helps Predict How Many Medals the US to Win in 2020

Written By: Luke Westbrook

After all of the hype leading up to the Opening Ceremonies, I am always so amazed at how quickly the Olympics run their course.  I frequently feel a sense of longing after the Closing Ceremonies, a feeling similar to that experienced when I finish a very good book. Now how will I spend my free time?

Men running an olympic marathon. Math software can help predict how many of these men will win gold, silver, and bronze

Men running in the 2016 Olympic marathon.

A Historic Look at US Wins

As I was contemplating the excitement of the Summer Olympics, I started to get curious about trends over the years. So, using my math software, I compiled medal counts for the US throughout the history of the Olympics, both Summer and Winter. I removed the 1980 Moscow Summer Olympics from the record, since the US boycotted that year as the Cold War was still going strong.

Worksheet showing raw data in math software

Raw data for US medal counts in Mathcad math software

Initially, I plotted the count for Gold, Silver, Bronze, and the Total against the year. I was hoping to see any sort of trends or indications of how US might fair in future Olympic events. It quickly became apparent that showing the raw medal counts wouldn’t give a very clear indication of how a country performed in a given year, since the number of total events has gone from 43 to over 300 in the past 120 years.

It is more informative to see the medal count as a percentage of available medals, so I plotted the totals divided by the number of events multiplied by three (three medals per event). I multiplied this value by 100 in order to see the plot in terms of percentage. This is a far cry from any sort of real data analysis, but it was certainly interesting to look at history in this way.

Here is the data from the Summer Olympics, going all the way back to the inaugural modern Olympic event in Athens in 1896.

Graph of Olympic medal wins since 1896

Olympic medal data graphed in math software

Note that the Gold, Silver, and Bronze data lines are the medal count, and the blue line is the percentage of medals that USA won out of the total medals available. The average “market share” of medals for the USA is right around 20%.


You can see that that percentage has been going down in the past 20 years or so, hovering in the 10-15% range. I place plot markers on all the years that the Summer Olympics were held in the US Perhaps not surprisingly, there is usually a noticeable bump in medal count during those years.

A 1904 Spike Emerges

But the most noticeable part of the data is seen in 1904, when there was not only a significantly higher raw medal count, but also an almost 85% market share in medals won by the US.

The 1904 Olympics were held in St. Louis, MO (which is actually where I’m from). If you don’t know much about the 1904 Olympics (why would you?), I strongly encourage you to investigate. The stories of those Olympic games, which lasted nearly five months (!), are utterly bizarre.

Tom Hicks winning 1904 marathon

Marathon runner Bill Hicks won the 1904 marathon with a little help from strychnine and brandy Img. Wikimedia Commons

Only 12 countries participated, and 523 of the 630 total athletes competed for US, explaining why the US won so many medals that year.

The marathon of the 1904 St. Louis Olympics is perhaps the most unbelievable story. If anyone has any connections with Hollywood producers, please tell them to make a movie about the 1904 Olympic marathon:

Seriously, the 1904 Olympics were messed up.

What about the Winter Olympics?

The data for the Winter Olympics is less exciting, but perhaps a bit more informative, as the results have less variability.

Data from winter Olympics graphed in math software

Here we can see that the average percentage of medal market share is around 10%.


We can also see the various spikes on the years that the Winter Olympics were held in the United States. There is another spike in 2010 that closely resembles that of the 2002 Winter Olympics in Salt Lake City. That is the 2010 Vancouver Winter Olympics. Given that it was still in North America, it’s perhaps not altogether surprising that the US would have a good performance that year.

How Will the US Fare in the 2020 Olympics?

Now even though the data doesn’t really tell us a whole lot, other than highlight some very interesting bits of Olympic history, I’m going to make some predictions for future Olympics.

The next Summer Olympics will be held in Tokyo in 2020. The last time Tokyo hosted was 1964. US won around 18.5% of the medals that year. But the US has been losing ground percentagewise, so I’m predicting around 13% of those medals. Assuming the event count stays at around 300, my official prediction is 116 medals for US at Tokyo 2020.

The next Winter Olympics will be hosted by PyeongChang, South Korea, in 2018. The last 5 Winter Olympics have delivered an interesting up-and-down pattern, where the “ups” have taken place at North America-hosted Olympics. So I am predicting another “down” year for US However, I think we will do slightly better than in Sochi 2014 (28 total medals). Thus, my official prediction for PyeongChang 2018 is 30 medals for US. But the only thing I’ll be watching is curling.

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Banner image, Olympic medals by Tomaz Silva/Agência Brasil

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About the Author

Luke Westbrook

Luke joined PTC in 2014 as a PTC Mathcad Application Engineer and spends his time supporting the sales process in a technical manner, conducting product demonstrations, answering technical questions for customers, and assisting with Product Management and Product Definition, among other things. He graduated summa cum laude from Southeast Missouri State University, having majored in both Physics and Engineering Physics, with a focus on Mechanical Engineering and a minor in Mathematics. He has also conducted research at both Southeast Missouri State University and Boston University, with additional experience in Project Management at a mechanical contracting company.