Do You Remember Algebra?

If a > b and b > c, then a > c.

Remember that nugget? That’s the transitive property of inequalities. (I’ll confess I had to look up the name of that one.)

It’s common sense, right? 10 is greater than 9, and 9 is greater than 8, so 10 must also be greater than 8.

It’s always and forever true in math. In tennis, not so much.

You know I love the intersection of tennis and math. (Okay, maybe not geometry lectures during round robins.) But math only goes so far when humans are the variables.

Has anyone ever said to you something like, “Really? You lost to Janice? You’re better than I am, and I always beat Janice!”

In other words, you beat me, and I beat Janice, so you should beat Janice.

Except it doesn’t work that way. In tennis it’s about match-ups, how your weapons match up with my weaknesses and vice versa. Instead of the transitive property of inequalities, we might find ourselves in rock-paper-scissors territory. Rock crushes scissors, scissors cut paper, paper covers rock. (No, I don’t know why covering a rock with a sheet of paper vanquishes it. That’s the subject for another blog post.)

With obviously too much time on my hands this afternoon, I found myself imagining rock-paper-scissors scenarios in tennis. Let’s say we hold the world’s tiniest round robin. In the round robin draw are Players A, B and C with the following characteristics:

Player A — Lefty with big topspin.
Player B–Short. Great mover and slicer.
Player C–Tall. Excellent return of serve. Hits a hard, flat ball.

Here’s how the three matches could play out.

A beats B. A’s topspin shots kick up too high for diminutive B to hit effectively, especially with B’s one-handed backhand.

B beats C. Compared to A’s topspin, C’s flatter balls stay lower (more in B’s strike zone) and B can run down C’s shots. Tall C also has a tough time with B’s low slices.

C beat A. C is tall enough to be untroubled by A’s topspin, neutralizing A’s main weapon. A also doesn’t get as many free points with his lefty serve because C is a great returner.

We’re left with a three-way tie. (I guess you’d count games to determine the winner.)

Rock-paper-scissors helps explain how Federer, the greatest player of all time, can have a losing head-to-head against Nadal. It also explains why you lost to Janice, of all people. (How embarrassing for you.)

So the next time someone expresses surprise that you lost to a Janice, just tell them the transitive property of inequalities doesn’t apply to tennis.

That’ll shut them up.


I know someone’s now going to tell me that the transitive property of inequalities applies only to real numbers, or some similarly geeky caveat. So go ahead. Have at it. 😅🎾

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