*The Trap of the Big Point Theory*, by Happy Bhalla. Mr. Bhalla's thesis boils down to two points, 1) that all points are equal, and 2) even if this weren't true, it is unwise to council players to play points in any manner but the best manner.

This is a topic that I have been considering for a few years. A comment by a fellow pro during a women's NTRP 3.5 team practice sparked my interest. We were talking about tie-breaks and the pro said, "You should pick up your play during a tie-break." I've heard some variation of this advice fairly frequently and given it myself in the past. The obvious question is, if you have a better level, why have you waited until a set is tied at 6-6 to bring it out? Since I can't come up with a reasonable answer to that question, I've given up telling people to pick up their level of play in tie-breaks.

To discuss big points in tennis, I think we must have a definition of big points. Mr. Bhalla seems to divide points into two categories, big and not big. I don't think this is sufficient. I think there are degrees of bigness to points, just as there are degrees of bigness for players – some are over six feet and some are under six feet, but some of those over six feet are bigger than others over six feet. In stating his case that all points must be equal, Mr. Bhalla offers up a contrasting opinion from Brad Gilbert. According to Bhalla, Gilbert defines big points as points that win games or points that lead to points that win games. Mr. Bhalla then shows that logically the point preceding the point that leads to a point that wins a game must be just as important. By this logical chain, if any point is big, all points must be big. And that's indeed what Mr. Bhalla says, "At the very least, we would have to call each point big. Actually, they are equally important or equally insignificant, with the emphasis on equal."

So for Mr. Bhualla, all points are equal. If tennis were a game played with a clock where the player accumulating the most points at the end of the playing time wins, then Mr. Bhulla's logic would be valid. Basketball, football, soccer, hockey and many other games fall into this category. Tennis, however, does not.

We can show that all points are not equal by focusing on how tennis matches end. In order to win a match, one player must win two out of three sets (in some cases three out of five). In order to win a set, one player must win six games with a margin of two games (or win a tie-break at 6-6). In order to win a game, one player must win four points with a margin of two points. This scoring system places unequal emphasis on points. This system allows us to rank particular points in relative importance. A match point (defined as a point that, if won by the leading player, will end the match) is the biggest of the big points. If player A holds a match point on player B, a loss of the match point will lose the match for player B. No other point is as big (though there can be multiple match points in a match, each big). How would a set point in a non-decisive set rank in relation to a match point? It must be of lesser rank since a set point in a non-decisive set cannot end the match. Therefore we know that a match point is higher ranked than a set point in a non-decisive set. We have proven that all points in a tennis match are not equal.

We can continue this exercise to rank a game point in a game that does not determine the winner of a set. Such a point must necessarily be of lesser rank than a set-point since it does not end a set. Therefore a non-decisive game point is lesser ranked than a non-decisive set point which is lesser ranked than a match point.

Finally, we can rank a point which does not decide a game. Such a point must be of lesser rank than a point which does determine the winner of a game. So our ordinal ranking of points in a match, from lesser to greater rank, or from small to big if you want to call them that, goes as follows. A match point is bigger than a set point. A set point is bigger than a game point. A game point is bigger than a non-game point.

All that is of course trivial. What we're really interested in is not whether a match point is a big point or not. Of course it is. Nor are we intersted in whether set points or game points are big points. Again, of course they are. Mr. Bhulla would almost certainly not dispute this. But what about supposed big points within games, which is the emphasis of Mr. Bhulla's assertion that all points are equal? Can we put a relative value on them? Yes. That isn't as easy. Thankfully, Dr. Howard Brody has already done the heavy lifting for us.

In his book,

*Tennis Science for Tennis Players*, Dr. Brody uses conditional probabilities to show which points within a game are the most important. Dr. Brody defines the "importance factor" as "the probability of winning the game if you win the point, minus the probability of winning the point if you lose the point." Instead of classifying points into big and not-big, Dr. Brody offers us a way to rank points on their importance, clearly defined.

Dr. Brody does this and presents the results in tabular and graphic form in Chapter 8 of his book. The results clearly indicate that all points within a game are not equal, since the importance factor varies from over 0.69 to under 0.05. That is a wide spread. Therefore, from match points and set points on down to various game points and points within games, we can conclude that some points are more important than others.

Having disproved Mr. Bhulla's assertion that all points are equal, we still must deal with his second point, that even if some points are bigger than others it is unwise to council players to play some points differently from others. I'm sympathetic to Mr. Bhulla's position on this issue. As my anecdote about tie-breaks conveyed, I am hesitant to tell people to "pick up their games" when they get to a tie-break. But does it follow that players should not play certain points differently earlier in sets, or even use different strategies for different points in tie-breaks? I'm not sure that it does.

As Dr. Brody pointed out in his introduction to Chapter 8 in

*Tennis Science for Tennis Players*, tennis players have finite energy reserves. If a player exerts himself or herself maximally throughout a match, isn't it possible that he or she will have less energy at the end of a match than someone who has expended energy more judiciously?

Jack Kramer explicitly advocated this strategy. I remember reading a tennis instruction book by Mr. Kramer where he said that players should not expend energy to break serve unless they had a 0-30 lead or more. I even think I remember reading that Kramer said the worst mistake a player could make was to hold to go up 5-3 in a set and then expend energy trying to break serve to win the set with a break. Instead, Kramer said, a player should take it easy in the 5-3 return game, rest and get some water at the 5-4 changeover, and then serve out the match. Clearly Mr. Kramer didn't think all points were created equal. Mr. Kramer realized that the odds heavily favored him, and most male players in the era of grass-court tennis, when serving. He also realized that a tired server is less likely to hold than a rested server. Though I never adopted this strategy myself (lacking Mr. Kramer's serve and volley prowess), I find it hard to argue with his logic.

In addition to the differing probabilities dictated by the serve and the finite energy reserves of all players, I think it's also wise to use the different importance of points within a match to try alternate shots, tactics, or strategies. Mr. Bhulla, in his TennisOne piece, claims that a player can only be surprised once. I think is too narrow a definition of surprise.

Just as we did above regarding "bigness" of points, I think it's wise to allow for levels of surpise. I think that a player's ability to predict the next shot can be used as a proxy for his likely level of surprise. If he is likely to accurately predict the speed, location, or spin of the next shot, I would say he is not likely to be surprised. However, if he cannot accurately predict which shot is coming next, he is more likely to be surprised. This does not mean that a player, in order to be surprised, must have never seen a particular shot or tactic before. It only means that he shouldn't be able to anticipate the next shot or tactic with certainty.

Using this, rather than novelty, as the definition of surprise, I think it is wise for a player to set up future confusion by introducing multiple shots and tactics at less important points in a match. If a player uses a variety of shots and tactics in the lead up to a bigger point, it is less likely that an opponent will be able to predict which shot or tactic to defend against on a big point. Of course, any alert player will expect a shot or tactic that has been successful earlier. If player A is able to establish multiple successful shots and tactics against player B in the early games of a match, then player B will be less likely to anticipate the shot or tactic employed by player A on big points. I think there is value in this approach to match play.

I said that I am sympathetic to Mr. Bhulla's viewpoint regarding big points. From my discussion so far, that may seem confusing. I disagree with Mr. Bhulla that all points are equal. Since all points are not equal, I think that fact offers some opportunity for exploitation and experimentation. However, I think Mr. Bhulla is likely right when he says that the best players probably gain a reputation for playing the big points well because they play all points well. I also think that it's quite likely that poor players play even more poorly on big points, while better players are better able to maintain their higher level of play on the bigger points. [Two economists from Europe looked at all matches played at Wimbledon over a four year period in the 1990s and found that for the men, the better players did appear to play better on the bigger points, while that did not appear to be true for the women (link to research paper, which is a wonderful examination of several commonly held beliefs).] Nor have I come to any conclusion about how to council players to play what I consider to be big points other than to play their best. I am a big advocate of trying to figure out what the highest percentage plays are and sticking to them.

I do not share Mr. Bhulla's implied belief that playing within oneself means giving up opportunities to attack. Here is how Mr. Bhulla phrased that in his article,

"Another theory suggests that one should play within oneself on [big] points and avoid giving away easy points; however, giving up opportunities to attack allows the opponent to gain the initiative."I agree that "giving up opportunities to attack allows the opponent to gain the initiative" and that such a tactic on big points would be foolish. However, I don't think it follows that "playing within oneself" implies "giving up opportunities to attack." Since the rest of the piece is quite well thought out, I don't think that Mr. Bhulla really thinks that it does either. I think what he meant to convey in this passage was that to play passively on big points in order to avoid giving points away is foolish. I agree with that. But I think that players can seize opportunities to attack, while still playing within themselves and not giving away easy points. As I said, I'm pretty confident that Mr. Bhulla would agree with this, too.

I'm glad that Mr. Bhulla took the time to write his article. To challenge tennis orthodoxy, and to challenge those who challenge orthodoxy, helps move the game and the coaching profession forward. By jumping into the ring and throwing a well-reasoned punch in the tennis theories boxing match, Mr. Bhulla has done the game a service.

## No comments:

Post a Comment