Friday, October 24, 2014
One of the best examples of using this kind of mathematical persuasion about draw-fixing is in this article. It is a very well written article in which the writer clearly has a very good understanding of statistics. However, the writer also has an agenda, which can result in drawing the wrong conclusions.
It was written by Katarina Pijetlovic and the trick she used was simple, but well disguised. I'll explain it with an example: Consider the match between John Isner and Nicholas Mahut. There were 137 holds to start the fifth set. Based on the stats, there was an 85% chance of Mahut holding in each game and an 87% chance of Isner holding in each game. That means there was a 0.000000106% chance of there being 137 holds to start the fifth set.
Based on this, you could conclude that Mahut and Isner decided that they wanted to hold the record for longest match ever so neither of them tried to break serve. Then maybe even add a narrative to make the argument even stronger. Say Isner and Mahut were trying to get players to receive more prize money for first round exits, so they made the match last three days to strengthen their argument that they deserve it.
However, this conclusion certainly false. Nobody who watched the match thought this was happening on purpose. Although the statistical probability makes this argument seem undeniable, an honest look at the events that took place shows that the match wasn't fixed.
Pijetlovic has made the same argument in her article. She took an event that has already occurred. Then she went back and measured the statistical odds of it. After finding the odds very low, she drew a wrong conclusion that she supported with a narrative about tournament directors wanting Rafael Nadal and Roger Federer in finals.
This can be done with almost anything.
There is one other stat that Pijetlovic uses that has nothing to do with odds that jumps out at readers. It's that Federer and Djokovic were on the same half of the draw in 12 consecutive grand slam events on hard and grass courts.
However, this stat is flawed too. Look at all the qualifiers that exist in this stat: Federer, Djokovic, slam event, hard, and grass court. That is five different qualifiers. If you have enough qualifiers, anything can be an impressive stat.
Consider Tobias Kamke - the No. 93 player in the world. He is a decent player but probably won't be remembered too long after he retires by most tennis fans. Yet, he is the best player that was born in Germany, plays a two-handed backhand, hasn't had a 29th birthday yet, and has a win over a top 10 opponent.
With just four qualifiers, I made Kamke the best player in the world. Pijetlovic uses five! With every qualifier added, her number loses statistical significance. After all five qualifiers, 12 seems almost expected - not a sign of fixing.
Pijetlovic did a great job using these tricks and I would do the same thing if I wanted to prove a theory like that. It's a very effective strategy, but it doesn't work this time because draw-fixing simply doesn't happen on the ATP or in the ITF.