HOFER TENNIS
TIP OF THE WEEK ARCHIVE
PROBABILITY OF WINNING

Over 10 years ago I was introduced to the theory of Markovian chains of  applied
mathmatics as they applied to the probability of winning a tennis match.
Very simply put, there is a mathematical table that shows the probability of winning matches
based on the method of scoring. Tennis players do not have to be math scholars to benefit
from this information.

Scoring       Percentages
    
POINT       .500 .510 .520 .530 .540 .550 .560 .570 .580 .590 .600 .650
GAME       .500 .525 .550 .575 .599 .623 .647 .670 .693 .714 .736 .830
SET          .500 .571 .640 .705 .763 .815 .859 .895 .924 .947 .963 .996
MATCH     .500 .606 .705 .790 .859 .910 .946 .969 .984 .992 .996 1.000

As you can see by the chart, a player that wins 50% of the points will also the game, set
and match 50% of the time.
Now the real difference is in the small number of points won to achieve a higher percentage
of matches won. For example, if you won only 55% of the points in a match the probability of
you winning the games is 62.3%, the probability of winning a set is 81.5% and lastly the
probability of winning the match is 91%.
What this means for you and me is that if a player is only a small amount better than their
opponent the odds of them winning the match is much greater. If you were to play Roger
Federer in a single point, your odds of winning that point are much greater than if you
player Federer in a whole set. So the Markovian chain shows me that Federer would beat
me 100% of the time we played a match, but if I played him only one point I would have a
35% chance of winning that point (.650 for Federer, .350 for me).
How does this help you? Well, it does show the importance of each and every point played.
Players need to work hard at developing focus and concentration for each point played.
The slightest lapse in concentration during a game can mean the difference of winning or
losing with closely matched players.

Doug Hofer, USPTA                      November 15, 2005
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