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Path Dependence: What is It?

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Path Dependence: What is It?

 

                Path dependence is a fancy term used to describe what happens when you choose one road over another. Just think of Robert Frost’s famous lines: “Two roads diverged in a wood, and I – I took the one less traveled by, and that has made all of the difference.” Often, there is no ability to revert once this choice is made. One clear way that path dependence is often used (misused!) with respect to tennis is the idea of momentum. Here’s what Deconstructing Tennis has to say on the subject:

Does momentum exist in tennis?  This is an extremely important question for us to answer within the framework of the 4-D System. If it exists, then we would hope that the 4-D System would allow us to manage it better. If it doesn’t exist, then it can be ignored and you can play comfortably within the System.

The use of the word momentum suggests that what has just happened will continue to have an effect on the immediate future. Similar to the “hot hand” framework in basketball which holds that Player A is more likely to hit the game-winning shot if he is “hot,” i.e., has made a high percentage of his recent shots, momentum in tennis might mean: if I’ve just won a point, does it increase the likelihood that I will win the next point? It could also ask: if I’ve just won a game, does that increase the likelihood of winning the next game?  The same question could also be asked at the level of the set because of the unique scoring system of tennis.

If the answer is yes, then the 4-D System is built to limit the momentum of your opponent, while at the same time propelling your own. This is because 4-D allows a player to “recover” between each point. This recovery will mute the effects of an opponent’s strong play (because you will make adjustments) and propel your own strong play forward by maintaining touch with your game plan and your focus.

Momentum can be real or it can be psychological. Either way, 4-D takes care of it. One formal test is a point-by-point analysis using sophisticated statistical tools to answer the question: does winning (losing) a point on serve make it more (less) likely that I will win the next point on serve? The results from professional tennis suggest that there is momentum, but that it is not of a very large magnitude when compared to point importance. These results strongly suggest that “the recent past” has no meaningful effect on the present. This contrasts with anecdotal reporting of momentum by sports broadcasters in tennis and many other sports.

                So, if momentum is close to zero, is there some other way in which path dependence matters in tennis? YES! And, here it is:

             Each and every point played begins with a serve or return of serve. The better (worse) the quality of the start, the more likely it is that the shots to follow will be easier (more difficult) ones. These two shots, more than any others determine the path or trajectory of what is to follow. For example, a solid serve to your opponent’s weaker side elicits a mid-court ball which can be attacked by an approach shot with sufficient pace and depth which will, in turn, lead (usually) to a volley or overhead of only moderate difficulty. In contrast, a weak second serve to your opponent’s strength will usually receive the drubbing that it deserves.

             These two shots are the most under-practiced in tennis below the professional level. When practicing, please remember that placement beats power. For example, one of my students asked how an opponent played in a match against my team. I replied: “She has an excellent forehand return of serve. But I have no idea about her backhand because not even one serve was directed there in the entire two sets.”

                Don’t let this be you – take the road less traveled – practice your serve and return!

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