The Bateman Impossibility Theorem

Anyone who's put together tennis clinics has heard the following:

"My child needs to play with better players to get better."

The implication of this statement is far-reaching. It means simultaneous improvement of two or more players is impossible. Don't believe me? I'll prove it.

1. Let A and B be any two elements of the set of all tennis players.
2. Both A and B want to improve.
3. To improve, A and B must play with better players:

For A to improve playing with B, A > B,
For B to improve playing with A, B > A.

4. Since both A > B and B > A cannot simultaneously be true, A and B cannot improve playing together.
5. What holds for A and B holds for all tennis players.
6. Therefore, simultaneous improvement of two (or more) players is impossible.

I call statement 6 The Bateman Impossibility Theorem -- simultaneous improvement of two (or more) players is impossible.

Since we know that tennis players do improve, we know that something in the proof is wrong. Perhaps condition 2 is wrong and not all players want to improve. But why would such a player want to be in a clinic, and especially pay for a clinic? Perhaps if the parent of inferior player A pays for superior and indifferent players C, D, and E, then they'll join the clinic even though they don't want to get better. I suggest parents make this offer to the coach setting up groups. "Since my child needs to play with better players, I will pay the better players to be in the group with my child." Seems the right thing to do.

Perhaps condition 3 is not true. Do we have any evidence that condition 3 is not true? To that end I offer up the improvement of Rafael Nadal over the past few years. Nadal did not practice with Roger Federer, the only player arguably better than he over the last few years, and only rarely played against him. If we accept that Nadal has improved, then we must be very suspicious of condition 3. In fact, it seems to me that the continued improvement of most of the top players in the history of tennis falsifies condition 3.

In addition to the world's top players, I think we observe that the top player on a college team can and does improve, despite not having anyone on the team better than he or she to practice with.

In fact, I think we observe players getting better all the time practicing with equal or lesser players.

Therefore, I think we can safely say that condition 3 above, the assertion that playing with better players is a necessary condition for improvement is false.

Much as I hate to admit it, The Bateman Impossibility Theorem does not hold. Good thing. I'd hate to be stuck paying better players to play with me all the time.

I encourage coaches to share this proof with any parents who request that their child play with better players. It won't make any difference, I'm afraid. But you can try it.

Soft Courts

I've been looking into affordable soft tennis courts lately. Clay in Colorado, and other dry climates, is an expensive pain. Grass is a pain everywhere. The soft Rebound Ace type courts are not what I'm looking for, too high a coefficient of friction. I want soft courts that allow sliding, like clay.

Omni and Classic Clay are two that I've tried recently. The Omni has sand, almost dirt, on top of an artificial grass surface. Pretty good. It gets my socks and legs dirty, but the playability is good, good traction with sliding to stop at high speeds. The ball bounces are pretty true and of decent height. Classic Clay is good, too. That's a less dirty product. The surface seems softer than the Omni and has a lower bounce, I thought.

On the USTA's tournaments web site I saw that a high school in Minnesota, Brooklyn Center High School, has artificial grass courts. They look to be Omni. I'm curious if there are any other high schools in the US that have soft tennis courts -- grass, clay, carpet, artificial grass or clay.

The Trouble with Slice

I told a kid the other day, "If you master that slice forehand you can be a very good bad player. But if you keep working on that topspin forehand maybe you can become a good player."

It's not that good players can't hit slice forehands, of course. Good players can hit all the shots. Turn on your TV, though, or head to a local Division I college match and you'll see mostly topspin shots.

We tennis players cannot escape from physical reality and physical reality dictates that for a ball to be hit hard, over the net, and within the boundaries of the court, topspin is necessary. Unfortunately it's much more difficult to master topspin. Why? Because almost every ball that bounces comes off the court toward you with the top of the ball spinning in the direction of travel. That means if you want to hit a shot the other direction with topspin you must reverse the ball's spin direction. It's much easier to simply redirect the ball back the other direction without changing the ball's spin.

Also, for little kids, underspin, or slice, gives the ball lift which maximizes the carry of the ball. That's great if you're small and weak and have trouble getting the ball over the net and deep into your opponent's court. Slice is also great for kids because it bounces funny. Funny is fun and funny is difficult for beginning players to handle. They don't have much experience with extreme spin and they are surprised by the bounce of the ball.

All those advantages of slice disappear fairly quickly as players grow in size, strength and experience. But habits once learned can be hard to break. Kids who spend a few years hitting a lot of slice struggle mightily to master topspin.

This allure of slice makes life tough for coaches. Coaches have to intervene and get kids to forego the immediate reward of slice in favor of the short-term pain of learning to hit topspin. Smaller courts, lower nets, smaller racquets, and bigger, lighter balls can help get kids to hit with topspin. But even in the scaled down environment of Quick Start tennis, slice has many advantages. It's up to coaches to do the difficult job of selling kids on topspin. Kids who like to watch professional tennis on TV are much easier to sell on topspin since that's what they see on TV. The kids who come out for tennis but who are not fans of the professional or college games prove much tougher. If I come up with a way to solve this problem of slice, I'll post it here.

Practice Tired

While watching the Kansas at Colorado basketball game last night I remembered how important it is to practice tired. Execution and decision-making both suffer when players become fatigued. In tennis this generally happens late in long points and late in long matches. Therefore it's important to engage in drills that extend beyond the length of most points to train fatigued shot-making and decision-making.

Since most points are not very long (six hits total or less) most of a player's practice will be, and should be, focused on the early stages of points. After all, even long points start at the beginning! But it's important not to totally neglect the longer points. I think one general strategy to point play may be to play more conservatively the longer the point goes. Since at most levels the vast majority of points are lost and not won, playing conservatively all the time is probably a winning strategy. But supposing you don't play that way all the time, at least consider refraining from going big late in points for two reasons. You don't have as much control and as precise timing late in points so you're more likely to miss. Your opponent is more likely to miss as s/he tires. I guess if you both adopt my strategy here the point will never end as you both turtle and just get the ball back. Maybe pull the trigger on your 50th shot!

Hideous

As bad as my driver impact is my iron impact is more pathetic. No wonder I tear up short courses and get torn up by long courses.

Cheating and Tennis

I have a project idea for an enterprising psychology graduate student. Here's the hypothesis: competitive tennis players are more likely than average to cheat in school. This can be tested at the high school or college level. Players can be identified by their membership on their high school or college teams. Cheating can be measured by students subject to academic discipline. Unfortunately privacy rules probably prevent such a study.

My theory, unfortunately, is that tennis encourages cheating. Players make their own line calls in tournaments. We see cheating all the time and we see immense gains from cheating. It is very difficult to catch or stop a player from cheating. Opponents can request line judges, but the judges seldom stay on court for long. Even where umpires are on court, in college matches for instance, cheating still takes place.

So we have a situation where cheating is easy, rewarding, and has few negative consequences. My thesis is that this creates a habit of cheating that carries over into other aspects of tennis players lives.

I hope my theory is wrong.

My Sorry Swing

Based upon what we see below, it's amazing I can hit the ball at all.