Olympic Medal Analysis: 3 Myths About China vs. USA – Myth 3

Welcome to the final installment of my Olympic Medal Count Analysis series of posts.  With the Olympics now a good 2 weeks behind us, and the NFL season underway, this post feels as if it has lost its timeliness.  Nonetheless, I saved what I thought was the most interesting question for last.

If you’re not up to speed on the previous posts in this series, I suggest you review them.  In the first post I laid-out a scoring system for comparing each country’s performance (3 points for a Gold, 2 points for Silver, 1 point for a Bronze) and I addressed the question of whether China or the USA “won” the medal race.  In the second post I discussed the first of 3 myths (or at least pre-conceptions that I brought into the games) that were contradicted by the actual medal count data.  The third post addressed which country fared better in in Team events, versus Individual and Pairs events.

Today we will be focusing on…

Myth #3: “Despite China’s strong showing, it was the USA that brought the more well-rounded team to the Olympics.”

Reality: At first blush, this myth seems to be particularly likely to be true.  China made no secret of their “Project 119,” an effort to focus on winning the 119 Gold Medals available in Track & Field and Swimming events.  Moreover, we already know that the USA accumulated more medals than the Chinese did AND that the USA’s medals spread much more evenly across Gold/Silver/Bronze, a form of well-roundedness in-and-of itself.  Neither of these metrics, however, precludes the possibility that the USA won all or most of its medals in a narrow set of events.

Unfortunately, the IOC doesn’t seem to be particularly concerned with helping me answer this sort of question.  Instead of sorting the Olympic events into convenient categories, they have created a large number of events (somewhere between 28 and 39, depending on how you count).  Some events (such as baseball, soccer, softball, BMX Cycling) offer only 1-2 medals.  Others (such as swimming and track & field offer dozens).  The sheer number of events, combined with the disparity in possible medals, makes statistically significant comparisons very difficult.

So, the first thing that I did was sort the events into 7 Categories, as follows:

• Accuracy (Archery & Shooting)
• Acrobatics (Artistic & Rhythmic Gymnastics, Diving, Trampoline, & Synchronized Swimming)
• Athletics (Field Events including Decathlon/Pentathlon/Triathlon, & Weightlifting)
• Fighting (Boxing, Fencing, Wrestling, Judo, and Taekwondo)
• Net Sports (Beach & Indoor Volleyball, Tennis, Table Tennis, Hand Ball, & Badminton)
• Racing (Track Events, Cycling Events, Canoeing/Kayaking, Rowing, and Sailing Events)
• Team Spots (aka “Contact Sports” such as Soccer, Basketball, Water Polo, Hockey, Baseball & Softball)
• NOTE: The only sport that proved difficult to categorize was Equestrian.  Coincidentally, it is the only sport that involves another creature than the athletes.  Fortunately, between China and the USA there was only one Equestrian medal (a Silver, for the USA).  I counted it as a Racing medal.

Once the events have been grouped in this way we can easily apply our now-familiar scoring system and calculate what percentage of each country’s total score was derived from each event Category:

Interesting!  Not only does it become clear that the USA literally accumulated not just a plurality, but a true majority of its points in a single Category (Racing), but that China out-performed the United States in 5 out of 7 Categories!  This is certainly a strong argument against our assertion that the USA was the more well-balanced team.

Before we call this case closed, however, let’s take a closer look at the data.  After all, as we mentioned above, the total number of Olympic medals available in any given event varies rather wildly and, apparently, arbitrarily.  Thus, one could argue that if there are more medals available in a given event Category, then a well-rounded country should win more medals in that Category, and fewer medals in Categories where fewer medals are available. If we add a third set of columns, representing the % of the total medals/points available in each category, our chart looks like this:

From this new perspective the USA’s significant bias towards Racing events seems much less surprising.  After all, with fully 42% of the available points being awarded in these events, it makes sense that this is where the USA would earn the largest portion of its medals/points.  In fact, the percentage of points derived from any individual Category by the USA is closer to the overall distribution than China’s is, in 4 of the 7 Categories.

By this standard, it is fair to say that a country has “over-achieved” in an event Category if the % of its total score is greater than the % of the overall available points in that Category.  In other words, the USA “over-achieved” in Racing because Racing accounts for only 42% of the available Olympic points, yet represented 57% of USA’s total points.  Conversely, the USA “under-achieved” in Athletics and Fighting events.

Using these definitions, we can re-plot the same data to more clearly show in which Category each country over/under-achieved, and by how much:

Now, the argument in favor of the USA as the more well-rounded team becomes even stronger.  By definition, each country’s over/under achievements will balance each other out in a zero-sum game. Interestingly, the USA’s apparently single-minded focus on Racing events represents only a relatively modest over-achievement in this Category.  China, on the other hand, clearly compensates for a dramatic under-achievement in this largest of event Categories with very-strong performances in both Acrobatics and Net Spots.

It is the Absolute Value of these deviations, however, that is most telling.  Whereas USA’s performance in the various event Categories varies from the overall Olympic medal distribution by a total of 39 percentage points, China’s variance is fully twice as much, at 77 percentage points.  By this definition of well-roundedness, USA is the clear winner, with China proving to be extremely strong in some areas and equally weak in others.

Does China’s overwhelming dependence on some event Categories and it’s “no show” in others mean that our third and final Myth is not such a myth after all?  Or does the fact that China out-performed the USA in more Categories while also medaling in more events (25 to 22), make it the more well-rounded competitor?  Ultimately, it is the uncertainty of the answer to these questions that is most telling.

There are certainly countless more interesting questions that can be asked and analyzed based on the data that I have accumulated, but I suspect that my audience’s interest is waning even more than my own.  So, I shall bring my discussion of these most recent and most captivating Olympic games to an end.  If you are so inclined, however, please feel free to download my Excel workbook and use it as you see fit.  If you find errors (as I have no doubt that they exist) please let me know so that I can update my version and see if any of my conclusions are affected by them.