Frequency of Simpson's Paradox related to level?

[BMC9670]

For the past year, I've been tracking the junior matches of my kids and some of their peers. These are intermediate to advanced 12U and 14U players. One thing that I noticed yesterday was in nearly 80 matches of data collected, the player that won more points lost the match 15% of the time (Simpson's Paradox). This seemed high to me so I did some searching but could not find much info on how often this stat occurs in tennis. I found a 2012 college research paper that studied 55,000 matches and found it happened 5% of the time and a few references in articles citing between 6% and 8%.

So, it got me thinking, is my small data sample simply an anomaly or does it happen more often in juniors because there are wider score swings within a match than, say a college or pro match? Thoughts?

 

[Chas Tennis]

This shows the probability of winning a 2 of 3 sets match vs the probability of winning a single point. It does not take much change in the probability of winning a point to have a large effect on the win or loss probability.
http://gene.bio.jhu.edu/tennis/tennis.html

If the probability of winning a point remained the same for the entire match that simple graph would describe things.

Some bigger hitters like Serena don't do as well in the first set as they work on their timing. Their single point probability probably is lower in the first set and higher in the second set. I'd like to see Serena's percentage of winning set 1, set 2, and set 3 and compare those percentages.

Another factor is to 'always change a loosing game'. Then the probability of winning a single point would hopefully change by at least a percent or two for each positive change.

Somehow, I don't know how, 'always change a losing game' might have more effect for juniors.

 

[BMC9670]

Somehow, I don't know how, 'always change a losing game' might have more effect for juniors.

Make sense. If one junior is able to "change a losing game", which is a great skill to have, perhaps the other hasn't yet developed the skill to adapt to the change. Also, I've seen huge swings of emotion at the younger age groups that evens out a bit as kids mature. Probably plays in as well.

 

[Tennisanity]

There was a story on this for the ATP about a year ago. Apparently Federer has played a lot of matches like these where he wins more points but loses the match. Most other pro players including the top ones do not have this occurring to them. Mainly Federer.

 

[Chas Tennis]

There was a story on this for the ATP about a year ago. Apparently Federer has played a lot of matches like these where he wins more points but loses the match. Most other pro players including the top ones do not have this occurring to them. Mainly Federer.

This looks like the story

http://www.theatlantic.com/entertai...player-does-better-than-roger-federer/283007/

 

[sureshs]

Admit it you made the thread just to show off your knowledge of Simpson's paradox

 

[heninfan99]

Admit it you made the thread just to show off your knowledge of Simpson's paradox

 

[BMC9670]

Admit it you made the thread just to show off your knowledge of Simpson's paradox

I'll admit that when I saw the stat in my data, I didn't know it had a name. Came across that one in my research.