Tennis's Siren Song

To hit a tennis ball hard is pretty easy.  To hit it pretty hard and get it in is also pretty easy.  To hit it pretty hard and get it in often enough to play good tennis is very hard.  Let's go to the numbers.

If you're a basketball player and you make 85% of your free throws, you're considered among the best of the best.

If you're a baseball pitcher who throws strikes 85% of the time, you're better than good.  You're great.

If you're a young hockey goaltender and you save 85% of the shots you face, you're darn good.

How about if you play tennis and can hit the ball in the court 85% of the time at a given speed and spin?  How good are you?

Well, if the ball doesn't come back much, then you're awesome.  But nobody can hit a ball in the court 85% of the time and have it not come back, unless we're talking about overheads and volleys struck just above the net!  Nope, any shot that you can put in the court 85% of the time is likely to come back most of the time, too.

So, what does that mean for your rallying?  If you and a partner decide to rally back and forth, hitting shots that each of you can get in 85% of the time, what is the probability that you'll succeed on any given attempt?  In order to execute a ten shot rally, you and your partner need to hit ten consecutive shots in the court.  That means you need to multiply 85% times itself ten times.  We write that 0.85^10 (the "^" being the way of denoting an exponent).  Whipping out my trusty calculator and entering 0.85^10, I get roughly 0.197.  That means you have less than a 20% chance of hitting ten balls in a row with your partner.  You'll need to try, on average, five rallies before you'll get to ten consecutive hits.

That's not very good.  What if you want to make it to twenty hits? You're down under a 4% chance of doing that.  You'll need to try 25 times for every successful 20-ball rally.


It's pretty alluring to hit a ball at a velocity that you succeed at 85% of the time.  Frankly, I think it's pretty alluring to hit the ball at a velocity that I succeed at 75% of the time.  The bad news is that I'm likely to make 10 consecutive hits (forget my opponent) only about 5% of the time at my 75% success rate pace.  That's horrible.  By choosing to hit at a pace where I can get the ball in three out of four shots, I'm going to lose to anyone who can make me hit more than three shots a point.  Why?  Because 0.75^3 = 0.42.  I'll succeed in making three consecutive shots less than half the time.  That's a losing proposition in tennis.

No wonder pushers win.  They just put the ball in play and let the Siren Song of high-paced tennis draw their opponents into failure.