Have you ever played a tennis match and come off the court with the feeling that you could have been the victor with a point here or there? That gut feeling is founded in the mathematical theory, Markovian Chains, discussed below. (The discussion is basic so keep reading).
Tennis has a unique scoring system. The ultimate outcome, or the match, is based on the number of sets won. A set is the first to win 6 games and be ahead by two, while a game is the first to 4 points and win by two.
The probability of winning a point, game, set and match are substantially different. For example, a player has a better chance of winning one point against Roger Federer or Maria Sharapova than they have of winning a game, set, or match.
It is possible to use Markovain chains and basic probability theory to explain the amplifying effect in going from point probabilities to match probabilities. The size of the amplifying effect quantifies the difference in the probabilities for points, games, sets, tiebreaks, and matches.
To save you the hassle of learning the mathematical theory, the table below provides the probabilities for you. In that table you will see the following three scenarios:
• It should be intuitive that if a player wins 50 percent of the points, that player will win 50 percent of the games, 50 percent of the sets, and 50 percent of the matches (column I). There is no amplifying effect.
• The impact of the amplifying effect can be seen when a player increases the percentage of points won from 50% to 54% of the points (column V). A player winning 54% of the points will win 59.9% of the games, 76.3% chance of the sets, and 85.9% of the matches. In non-mathematical terms, this means that by finding a way to increase the percentage of points won from 50% to 54%, or 4 percentage points, a player theoretically has increased the chances of winning the match by 36 percentage points.
• The amplifying effect is even greater if a player can increase the percentage of points won from 50% to 60% of the points (column IX). This increase in points won translates into a 73.6% probability of winning the game, a 96.3% probability of winning a set, and a 99.6% probability of winning the match. By finding a way to increase the percentage of points won from 50% to 60%, or by 10 percentage points, a player theoretically has increased the chances of winning the match by almost 50 percentage points.
By developing a discipline in which a player focuses on each point, it will suddenly become very easy to pick up several points a set – and these points will be enough to make the difference in a match.
