Bird's Tennis Tips: The Geometry of Tennis

February 7, 2005


Mike Swanberg is a former collegiate player at Livingston University and each month he will give us a new tennis tip.

Okay, in this second installment of "Bird's Tennis Instruction," we will be discussing one of the most important facets of tennis tactics. It is a system by where you will know where to hit the ball and also where the ball will be hit.

Okay, okay, I know. No system can really give you all that. But this is important stuff! This is where it's at, people. So, without further ado, I give you:

The Geometry of Tennis

Back in the early 80s, when I was but a lad, playing tennis nearly every day, entering upwards of 30 tournaments a year, my mother decided to move me to a different club. The one I had been taking lessons at was pretty far away, and there was another facility much closer.

At the time, the teaching pro at this club was a man by the name of Bob McKenna. I took one lesson from Bob, and then he went to New York to open a fried chicken store. But before he left, he gave me the greatest hour of instruction I've ever had. This is part one of a three-part instructional series on the geometry of this game we call badminton… er, I mean, tennis.

Wherever you are, Bob, thank you.

The Court

Every tennis court has the same dimensions. It's a rectangle, 78 feet long, 27 feet wide (36 feet if you include the doubles alleys). Your singles court consists of three boxes, the deuce service box, the ad service box, and the backcourt, or "no-person's land." It used to be called “no-man’s land” but Congress changed its name in 1987.

These three boxes, in their entirety, comprise the sum of all possible shots your opponent can hit, while still remaining in the point. Therefore, these are the shots that you are responsible for getting to and returning.

The service boxes are 21 feet long, leaving 18 feet for the backcourt. The "T" is the spot where the dividing lines between the three boxes meet. The precise center of your singles court, therefore, is 18 inches from the T along the center service line toward the net.

But I’ll tell you what. This isn't school geometry. There won't be a test at the end of this. So, let's make things easy. Let's just say that the center of the court is the "T". I suppose a case could be made that the 2 feet along the net aren't realistically playable anyway, so the "T" is actually a very good representation of the center of your singles court, or "The Center of All Possible Shots Your Opponent Can Hit."

The "Average" Shot

Since the center of all the possible shots your opponent can hit is the "T", it stands to reason that we could call this the "average" shot. If your opponent simply hit random shots for the entire match, and then we looked at where all those shots landed, and then took the geometric center of all of them… bingo! The "T".

Going forward, since your opponents shots are traveling the distance from his racquet to your court, it seems logical that the ball will continue to travel in that same direction (by the way, for you smarties out there, we are dumbing this down a lot… we're not talking spins or wind or earth's rotation or gravimetric shear or burps in the space-time continuum… strictly Newtonian stuff here, you Relativists!). This gives us an arrow, or a ray, as my geometry teacher called it. The origin of the ray is your opponent's racquet and the direction of the ray is the ball's direction of travel.

“Where is all this leading?” you may be asking yourself. Well, it's all very simple. Imagine that your opponent is standing slightly behind the middle of his baseline. He is hitting balls your direction. The average ball will bounce on the "T" and continue onward past the center of your own baseline. So, where would you stand, knowing that this is the case?

Exactly! The center of your own baseline. Give yourself 10 points if you got that right.

Statistical Extremes

Okay, so not every shot lands on the "T". In fact, your opponent is probably going to avoid that shot as much as his abilities will allow. But where, then, will he hit the ball?

Well, let's go back to the bit about random shots and all the places they landed. Let's stop looking inwardly (toward the norm) and start looking outwardly (toward the extreme). What are the most outlandish shots your opponent can hit?

Well, he can hit those spots on your singles sidelines about 2 feet from the net (remember, we said that the 2 feet along the net is a near-impossible shot to hit). This takes the ball on a path 18.2 degrees off the line that leads straight toward you. But it can go to your forehand side or your backhand side.

Bisection of Angles

No, this section is not about alternative lifestyles in the heavenly realm. Angles, not angels.

So, given this 18.2 degrees to either side, where do you stand?

Exactly, right in the same spot: the middle of your baseline. What you've done here is bisected the angle. Essentially, you are telling yourself, "he can go here, or he can go there, or he can go anywhere in between, so I am going to stand in the middle of all those possibilities."

Back to Reality

Okay, now we have to interject a little reality into all this. Your average player -- heck, the top pros in the world -- cannot hit the point on your singles sideline 2 feet from the net. And even those that can hit there are going to be smart enough to know that they don't have to go for that much to win a tennis match.

So, for the sake of keeping things somewhat real, we are going to say that any shot that approaches your sidelines is most likely going to be farther from the net. See the illustration. The red areas are realistically possible shots. The yellow areas do not need to be bothered with.

"Why are we ignoring those shots, Bird?" I hear you asking. "Won't my opponent just go for those shots knowing I am not covering them?"

To put it bluntly, if you are playing against someone who can hit those shots with any consistency, then your best strategy is to put your racquets in your bag and leave the court, because Mr. Federer is going to crush you!

What Does This Mean?

Okay, I think you are getting the gist of all of this. The point is that the best place to be when looking to get to your opponent’s shot is to bisect the possible angles that he can hit. When your opponent is in the center of his backcourt, you need to be in the center of your backcourt.

But what if he is out wide? What then? How do you know how to bisect the angles?

Well, it goes back to our “center of the court” ideal. Remember the “T”? If you draw an imaginary line from your opponent’s point-of-contact through the “T”, that is a great approximation of the bisection. So, where should you be? Answer: on that imaginary line!

Let’s look at an example. Say, for argument’s sake, that your opponent has been pulled wide to his (right-handed) forehand. Where would you stand to maximize your chances of getting to his next shot?

Well, he is pulled wide to his right. Draw a line from his point-of-contact through the “T” on your side of the court and you find that you should stand a few feet to the right of the center mark (the small mark protruding toward the net from the center of the baseline).


Take a look at the illustration here. The angle shows your opponents likely possible shots. Note where the bisection is. And as you can see, your opponent’s best down-the-line shot (to your backhand) doesn’t take you off the court at all. However, his best crosscourt shot takes you far off the court on your forehand side (assuming you are right-handed like your opponent).

Net Play

I am sure many of you have heard your coach or instructor or perhaps a more-experienced player say, “when at net, you have to cover the down-the-line.” This is a direct result of that. If you are between your “T” and your opponent’s shot, then it stands to reason that you will be on the same side of the center service line as your opponent.

The intuitive reason for this is simple and pretty obvious. Your opponent’s best shots from his forehand corner cross the net, and your position, at points to the left of the center. If he tries to pass you down-the-line, his shot may well still be out over the doubles alley as it crosses the net. But if he tries to pass you cross-court, the ball will cross the net in the interior of the court, much closer to the center of your court than the down-the-line possibility. So, you need to cover that down-the-line when at the net, and this is the geometrical explanation as to why.

Next Steps

Okay, this has shown you where you need to be in response to your opponent’s possible shots and also his position on the court. But there is more… oh so much more.

Note that where your opponent is on the court is a direct result of where you chose to hit your shot. The next two installments of “The Geometry of Tennis” are going to explore this notion. First, we will look at what shots to choose, when, and why. We will discuss defensive tactics in the next lesson. And then we will take it to the next level and discuss offensive tactics.

As for what you should do from here… well, your level shouldn’t matter much. Beginners and advanced players alike should be aware of their own center of the court and use it to position themselves accordingly.

Stay tuned.


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