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Tennis Math - Probability and Statistics

Let's leave the tennis world for a minute and head to Vegas?  Have you been to Vegas?  There is a picture of the strip below.  That is pretty much all built by a small advantage.  All the games in the casinos in Vegas have a "house edge".  That means that even if the gambler plays the game perfectly, they are still going to lose more than they win.  Complex games like Craps, Blackjack and Baccarat have a house edge of about 1% when the player plays well, while easier games have an edge from 5% up to 30% (30% is Keno - don't ever play Keno!).

Image by Daniil Vnoutchkov

Let's say they average about 5% because people tend to play the easier games, or they don't play the harder games correctly.  What does that mean?  Essentially, any time someone bets $5, the house gets 5% of that, or a quarter.  All that stuff in the picture was built by a 5% edge.  If you walk into a casino and only place one bet, you have a 45% chance of walking away a winner.  But, the more times you bet, your odds of walking away a winner go down a lot:

  • One bet:  45% chance to be ahead.

  • Five bets:  41% chance to be ahead.

  • 25 bets:  31% chance to be ahead.

  • 100 bets:  15% chance to be ahead


Vegas doesn't break the rules or cheat to make money - they've just created games where they make that quarter, over and over and over again.

Why am I talking about gambling?  Sure, I play poker, but it also applies to tennis.  How?  Glad you asked.

In 2019, SHS Girls Tennis had:

  • Team record of 13-2 (87% win rate)

  • Individual match record of 95-25 (79%)

  • Record for individual sets played: 199-65 (75%)

  • Record for each game played: 1411-792 (64%).

  • I don't have it tracked to the point level (I'm only mostly crazy), but you can see the trend and it's probably about 55-58%.

So, the team went nearly undefeated as a team by winning only 55-58% of all the points we played during the season.  That seems crazy!  Don't believe it?  Rafael Nadal has a record of 92 wins and 2 losses at the French Open.  He has won just 56% of the points he's played.  (There is an important non-math lesson in this too - click here).

A typical high school tennis match is about 100 points.  5% is five points.  Pretend you are the casino - a 5% edge on 100 bets means you are only going to lose 15% of the time, and a 5% edge in tennis translates to winning 6 matches out of 7.

How can you be the casino in tennis?  Do the little things that give you a little advantage, and avoid the things that do the opposite.  For instance, don't hit a normal shot to the net player in doubles - you will lose that point 3 out of 4 times.  If you do it over and over again, you are giving them a 25% edge.


Here is a list, starting with the very simple stuff and getting more advanced, with the improvement against an opponent you are pretty even with.

Percent Edge Gains.JPG
Before all you top players start adding those up, note that you only get to count them if they are improvements.  If you hit 10 out of 14 put-away volleys to the right target (feet of the volleyer) already, and you improve to 12/14, that's only 2 new (for a 1% gain).
Notice that they are color-coded:
  • Green:  These have very little or nothing to do with hitting a ball.  As in, these are places you can improve your chances to win without having to actually hit better shots.  They add up to about 20%
  • Blue:  These deal with hitting better shots.  None of them are about hitting the ball harder though - just putting more shots in play, to improved targets, with the right shot attempted.  They add up to another 20%, at least.
That's 40% total.  That would mean you win 90% of the points!!!  Okay, that's not going to happen.  But if you could actually instantly do all of these things, and started doing them against someone who played just like you did yesterday, you would beat them very, very easily.  Think of how many points these "little things" add up to.  It's a lot!
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