The stats look really damning. Notice the p-scores : 4e-19 for worlds 2013 and 5e-8 for olympics 2016. And you can see it so clearly in the graphs too. No question, there was a big difference between one side of the pool and the other!
Most sports aren't really 'fair' per se. Making them fair wouldn't be cost effective, and wouldn't make for good TV. E.g. everyone knows that some lanes are faster than others in rowing due to the lack of wind screens around the venues. And that's not even to mention the people who spend ten years training only to get violently ill and unable to compete due to the water quality. The reality is that even at the highest levels of competition there is still a lot of luck.
It really depends on the sport. For instance, football (soccer) is very random, and this is amplified by the tournament format. But in many other sports, there is no suspens at all. Actually, it would be interesting to somehow evaluate the random factor for each sport.
For example people in Poland are still discussing over the beer whether we would have been world champions if only it hasn't been raining so heaviliy during Poland - West Germany semi-final in 1974.
P.S English is not my language and I'm pretty sure I messed up with conditionals, hope you still get what I meant in the last sentence.
http://www.todayifoundout.com/index.php/2010/06/the-origin-o...
http://deadspin.com/map-what-every-country-calls-the-thing-w...
Change "hasn't" to "hadn't" and your conditional is perfect.
(If you're curious, you've made what I would consider a definiteness error three times -- I would say 'the ridiculous name "soccer"', 'discussing over beer', and 'the Poland - West Germany semi-final in 1974'. Those won't affect understanding and you give the impression of being very fluent; there are no other errors.)
Merely empirically determine the appropriate exponent to input for the pythagorean win percentage[1]. Baseball uses an exponent slightly under 2, while basketball uses an exponent slightly under 14. The higher the exponent, the less likely a poor team is to defeat a good team.
In fact this can be generalized to sports without points if you have some other way of estimating a team/player's "quality" normalized to 1 being "average" which is all the points-scored/points-allowed ratio does.
[edit]
Note that the Jamesian (points-scored/points-allowed) quality metric doesn't work as well in games where draws are common (e.g. soccer/football), and different quality metrics will yield different exponents, so do not allow apples-to-apples comparisons. For what it's worth, applying James's quality metric to league football yields an exponent of about 1.3[2], which is in line with the intuition of ranking these 3 sports from most to least luck per win:
Soccer, Baseball, Basketball
1: https://en.wikipedia.org/wiki/Pythagorean_expectation
2: http://www.soccermetrics.net/soccer-pythagorean-theory/why-t...
That said, I still think fairness or at least perception of reasonable fairness is very important in high-level sports. No one is going to watch the games (or the ads as the GP pointed out) if they think the game's rigged.
Edit: Also you are right.