Playing Tennis like "Deep Blue" Part 2: Computation and Tennis Tactics
After the release of the demo video of our 2023 prototype, the BallBOPPer returned to stealth mode. It will reemerge in 2026 when the Ultimate "True Game Play" preview and release are ready!
Here at RoBOPPics we are developing an autonomous robot that has the ability to play tennis. Not a humanoid robot like 3CPO in Star Wars, but a purpose-built robot that is more like R2D2.
This robot is called the BallBOPPer or "BB" for short.
Since BB is a computer driven device, it requires a scheme for describing tennis that can be computationally enabled. The BallBOPPer's scheme is built on three nested constructs: Skills, Tactics and Strategy. In order for these constructs to be programmable, we define them in a very specific way.
- Skills are sequences of biomechanical actions executed to generate shots
- Tactics are sequences of Skills executed to win points and games
- Strategies are sequences of Tactics executed to win sets and matches
These three constructs are logically related as shown in the following drawing. Skills are nested inside of Tactics, and Tactics are nested inside of Strategies.
Colloquially you can think of Skills as your repertoire of different shots, and Tactics as your repertoire of "Patterns of Play" or patterns of multiple shots.
In this post we will be discussing the BallBOPPer's Tactics and Strategy constructs and provide some detailed information on how Tactical and Strategic tennis decisions can be made through computation. In the process we hope to provide you with an understanding of the benefits that this computational approach can bring to your game.
Predictions and Decisions
The three constructs: Skills, Tactics and Strategy, are individual computational models that utilize contextual data gathered from hundreds and thousands of sets, and this combination of the models and data are what the BallBOPPer's uses to make tennis playing decisions.
Obviously, this is different from the way a human player makes tennis playing decisions. Human players play tennis using their gut or intuition, while BB does calculations. But in the bigger picture, both decision-making processes are based on the same thing - predictions.
Predictions are the basis of every decision we make, every day, in every moment throughout our lives.
Some of our predictions/decisions are data driven. We use weather predictions to decide what clothes to wear. We use health predictions to decide what to eat and how to exercise. We use economic predictions to decide whether to spend, save or invest.
Other decisions are purely intuitive such as when we predict what others are like from nothing more than a glance or a single photo.
The selection of each shot in the course of a tennis match is no different.
We do our best to predict the impact of the options we have and choose the ones that we predict will have a positive effect. Some of these are "data driven" - for instance, we may have executed a "One Plus" serve hundreds of times before and therefore have an intuitive sense of how often it works and under what circumstances. But many other shot choices have greater uncertainty and we are forced to make those decisions using vaguely remembered experiences along with a fleeting impression of the current situation in a combination we refer to as a "gut" feeling.
BB makes the same shot decisions as its human counterpart, but instead of gut feelings, it has the ability to gather, maintain and update a large amount of very specific data, and then use that data to calculate the probabilities for each Skill, Tactic and Strategy. In real time, in the midst of playing a point, BB mathematically evaluates each of the possible Skills, Tactics and Strategies to determine the most advantageous choice for that particular moment.
One of the consequences of using computation is that BB ends up not having any of the many foibles that trip up human players.
BB never tightens up. It never feels any pressure. It never chokes. It never needs more confidence. It never suffers a "brain fart" by making a completely illogical shot choice. It never daydreams about the trophy or gets angry at a coach or another player. It doesn't "care" one way or another if it wins any particular point, game or set. It doesn't have any inkling of this mysterious thing called "momentum" going back and forth between it and its opponent. And it is always "in the moment".
BB's computational engine simply determines and executes the Skill, Tactic and Strategy, selected from all the possibilities available at each particular moment, that has the highest probability of leading to the winning of the match.
But this doesn't mean that the BallBOPPer is designed to win every point, game, set or match.
BB is not designed to outclass its human opponents. It is designed to operate at the player’s playing level and to continuously adapt to ensure the challenge to the player is meaningful without being insurmountable. It does this by assuming the same skill level and accuracy level of either the player it is playing against, or that of the player that it is simulating.
This gives the BallBOPPer the ability to train players in how to think about, and make, the most effective playing decisions in a way that can help players apply the resulting inferences and insights to win more tennis matches.
Competition between Humans and Computers
The history of competitions between humans and computers is defined by many groundbreaking milestones, including:
- In 1997, IBM’s chess-playing Deep Blue shocked the world when it defeated grandmaster Garry Kasparov. Deep Blue relied on brute-force computational power to evaluate 200 million moves per second, analyze the probabilities, and find optimal strategies.
- In 2016, DeepMind’s AlphaGo used neural networks and reinforcement learning, to play the ancient game of Go, a game with nearly infinite possibilities, and defeated several notable international Go experts. AlphaGo didn’t just calculate - it adapted and learned, developing creative strategies that surpassed human understanding.
- In 2019, the Facebook and Carnegie Melon poker program called Pluribus made history by defeating five elite human poker players in multiplayer no-limit Texas Hold’em. Pluribus learned poker from scratch without any human data by playing trillions of poker hands against copies of itself and in the process optimized its own decision making to win.
These systems followed a theme: using computational power to thrive in tactical and strategic environments defined by rules, probabilities and psychology. Yet, these events didn’t just showcase superior calculation. They highlighted an interplay between human intuition and machine precision to change the way competitive players play their respective games.
Rather than replacing humans, computational players have pushed human players towards deeper analytical thinking, creative play, and a willingness to challenge established norms.
Chess Masters now favor more dynamic sacrifices. Go Masters explore space with new perspectives. And Poker Pros now embrace probabilistic strategies with a much greater degree of precision than in the past.
Computational game players have become tutors employed by human players to expand the boundaries of their tactical and strategic thinking.
GTO Play and Expected Value
Poker playing programs like Pluribus have developed over time into a class of programs called poker solvers. A poker solver is a computational engine designed to calculate optimal strategies for specific poker scenarios using principles from Game Theory Optimal (GTO) play.
GTO play is essentially a way to optimize "Expected Value" (EV) from each poker hand across all possible opponent strategies, ensuring that the player makes money over the long run.
EV is a way of calculating the average outcome of a particular decision if you repeat that decision a large number of times under the same conditions.
GTO play gives a poker player the ability to make decisions that are the best possible and therefore cannot be exploited by an opponent.
A side effect of this is that if a GTO player is playing against a number of other GTO players, then none of the players will end up winning or losing a significant amount. This is what is called a Nash Equilibrium - no player can play a better strategy than any other player.
Professional poker players therefore seek out tables and tournaments that have as many players as possible who are not practicing GTO play. Under those circumstances their chances of making a killing is significantly higher.
So how does GTO play work?
For a deeper understanding, you should take a look at books by professional poker players the likes of Nate Silver or Annie Duke. We provide only a brief overview here since our real subject and expertise is in computational tennis.
Poker examples of GTO Play
It is generally understood that in Poker, Expected Value or EV for a particular poker hand and pot, is calculated for each betting decision as follows:
EV = (Probability of Winning x Winning Amount) + (Probability of Losing x Losing Amount)
The expected value is a combination of the payoff if you win and the loss if you lose. If this sum is positive, then according to GTO play, you should place the bet. If it is negative, then you should not place the bet.
Imagine you are in a poker game and debating whether to call a $100 bet. The pot is $200 and based on your analysis you estimate that your hand has a 25% chance of winning. If you win, you get the entire pot of $250. If you lose, you lose your $100 bet.
Using the EV formula:
EV = (.25 x $250) + (.75 x -$100) = -$12.50
The .25 is your 25% chance of winning the hand, and the .75 is your 75% chance of losing your bet.
The fact that the EV produced by this calculation is a negative number, namely -$12.50, means that calling the bet will not be a profitable decision in the long run. You may in fact get lucky and win this particular hand, but in the long run if you keep playing this way, you will lose more than you win.
Alternatively, if you are playing the same pot with a hand that you calculate has a 35% chance of winning, the EV calculation results in a positive EV.
EV = (0.35 x $250) + (0.65 x -$100) = 87.5 - 65 = $22.5
You may not win this particular hand either, but the whole point of GTO play is that by consistently playing hands with a positive EV you will end up making a profit.
You may wonder how it is that you can make a profit from a bet that you only have a 35% chance of winning.
A 35% chance of winning would normally, according to a player's gut or intuition, seems like a bad decision. In fact, GTO play is naturally aggressive - more aggressive than the way non-GTO players normally play.
Anatomy of a "Big Point" in tennis
Tennis is quite different from poker, and we cannot apply the EV concept in the same way. Poker is based on poker hands, each of which a player can simply fold out of. In tennis, the "point" is the fundamental scoring unit and there isn't any benefit to dropping out of any of them.
If you watch televised tennis tournaments, you will have heard commentators saying something like: "...that player lost the match because they didn't play the big points as well as their opponent."
This prompts the following questions.
- What makes one point "bigger" than another?
- How can you use computation to recognize Big Points?
- How does this information subsequently effect the tennis playing decisions that you make?
We will answer these questions using a computer model called the Point Value Model that simulates the playing of tennis sets.
The main properties of the Point Value Model is that the scoring is the same idiosyncratic scoring used in tennis including deuce points and tiebreaks, and it simulates the winning of the points in these sets between two players who are equal in Skill level.
- they both have a service winning percentage of 65%
- they both have a returning winning percentage of 35%
These two values are around the average values for WTA/ATP players.
Running this model through a million simulated sets results in data on over 1500 possible scorelines in a tennis set.
During this process the model calculates the winning percentage for each particular scoreline. In other words, it calculates the frequency with which the simulated player will win the set based on the current scoreline.
For example, here is a single scoreline from the generated data.
| Games (You-Opp) |
Points (You-Opp) |
Server | Win % Current |
Win % Win Point |
Win % Lose Point |
Point Value |
Wins |
Total |
|---|---|---|---|---|---|---|---|---|
| 4-3 | 30-30 | You | 83.5% | 89.7% | 71.7% | 18% | 34,599 | 41,421 |
The score is 4-3, 30-30 and you are serving.
On the far right, the "Wins" are the number of times that this scoreline occurred in a simulated set that You won. The Total is the number of times this scoreline occurred in any set during the playing of the one million sets that were simulated.
The winning percentage for this scoreline is calculated as: 34,599 / 41,421 = .835 or 83.5% of the times that you played this scoreline in a set, you ended up winning the set. We therefore call this value Win % Current or the Winning Percentage of the Current scoreline.
The other three columns in this scoreline are best illustrated using a single sample set played between you and your opponent as shown below.
Note: all of the predictions that the Point Value Model makes are based on the frequencies of particular events, such as winning and losing, that are then expressed in the tables as "percentages". Colloquially you can think of these percentages as probabilities although technically they are frequencies.
If you understand scoring in tennis, you can walk through the sample set from top to bottom and follow your progress through each point. The match is between "You" and your Opponent (Opp) and all of the values in each scoreline are recorded from your perspective. For the sake of simplicity, this set represents a one set match.
Sample Set Table
| Games (You-Opp) |
Points (You-Opp) |
Server | Win % Current |
Win % Win Point |
Win % Lose Point |
Point Value |
|---|---|---|---|---|---|---|
| 0-0 | 0-0 | You | 50.1% | 52.4% | 45.7% | 6.8% |
| 0-0 | 15-0 | You | 52.4% | 54.1% | 49.3% | 4.9% |
| 0-0 | 30-0 | You | 54.1% | 55.1% | 52.3% | 2.8% |
| 0-0 | 40-0 | You | 55.1% | 55.4% | 54.5% | 0.9% |
| 1-0 | 0-0 | Opp | 55.4% | 59.8% | 53.0% | 6.7% |
| 1-0 | 0-15 | Opp | 53.0% | 56.2% | 51.3% | 4.9% |
| 1-0 | 0-30 | Opp | 51.3% | 53.1% | 50.3% | 2.9% |
| 1-0 | 0-40 | Opp | 50.3% | 50.9% | 50.0% | 0.9% |
| 1-1 | 0-0 | You | 50.0% | 52.7% | 45.2% | 7.5% |
| 1-1 | 15-0 | You | 52.7% | 54.5% | 49.2% | 5.3% |
| 1-1 | 30-0 | You | 54.5% | 55.6% | 52.6% | 3.1% |
| 1-1 | 40-0 | You | 55.6% | 55.9% | 54.9% | 1.0% |
| 2-1 | 0-0 | Opp | 55.9% | 60.7% | 53.2% | 7.5% |
| 2-1 | 15-0 | Opp | 60.7% | 67.8% | 56.9% | 10.9% |
| 2-1 | 15-15 | Opp | 56.9% | 63.1% | 53.5% | 9.6% |
| 2-1 | 15-30 | Opp | 53.5% | 57.8% | 51.0% | 6.8% |
| 2-1 | 15-40 | Opp | 51.0% | 52.8% | 50.1% | 2.7% |
| 2-2 | 0-0 | You | 50.1% | 52.8% | 45.0% | 7.8% |
| 2-2 | 0-15 | You | 45.0% | 49.3% | 36.6% | 12.7% |
| 2-2 | 15-15 | You | 49.3% | 52.9% | 42.2% | 10.7% |
| 2-2 | 30-15 | You | 52.9% | 55.5% | 48.2% | 7.3% |
| 2-2 | 40-15 | You | 55.5% | 56.5% | 53.7% | 2.8% |
| 3-2 | 0-0 | Opp | 56.5% | 62.0% | 53.6% | 8.4% |
| 3-2 | 15-0 | Opp | 62.0% | 70.2% | 57.7% | 12.5% |
| 3-2 | 30-0 | Opp | 70.2% | 80.7% | 64.6% | 16.1% |
| 3-2 | 30-15 | Opp | 64.6% | 75.6% | 58.7% | 17.0% |
| 3-2 | 30-30 | Opp | 58.7% | 68.9% | 53.2% | 15.7% |
| 3-2 | 40-30 | Opp | 68.9% | 88.0% | 58.6% | 29.4% |
| 3-2 | 40-40 | Opp | 58.6% | 68.6% | 53.2% | 15.5% |
| 3-2 | 40-A | Opp | 53.2% | 58.6% | 50.1% | 8.5% |
| 3-2 | 40-40 | Opp | 58.6% | 68.6% | 53.2% | 15.5% |
| 3-2 | A-40 | Opp | 68.6% | 88.0% | 58.6% | 29.4% |
| 3-2 | 40-40 | Opp | 58.6% | 68.6% | 53.2% | 15.5% |
| 3-2 | 40-A | Opp | 53.2% | 58.6% | 50.1% | 8.5% |
| 3-3 | 0-0 | You | 50.1% | 53.4% | 43.9% | 9.4% |
| 3-3 | 15-0 | You | 53.4% | 55.7% | 48.9% | 6.8% |
| 3-3 | 15-15 | You | 48.9% | 53.2% | 41.0% | 12.2% |
| 3-3 | 30-15 | You | 53.2% | 56.3% | 47.7% | 8.5% |
| 3-3 | 40-15 | You | 56.3% | 57.5% | 54.1% | 3.4% |
| 4-3 | 0-0 | Opp | 57.5% | 63.6% | 54.2% | 9.5% |
| 4-3 | 0-15 | Opp | 54.2% | 58.5% | 51.9% | 6.6% |
| 4-3 | 0-30 | Opp | 51.9% | 54.2% | 50.7% | 3.5% |
| 4-3 | 15-30 | Opp | 54.2% | 59.9% | 51.2% | 8.6% |
| 4-3 | 15-40 | Opp | 51.2% | 53.6% | 50.2% | 3.4% |
| 4-4 | 0-0 | You | 50.2% | 54.1% | 43.0% | 11.0% |
| 4-4 | 15-0 | You | 54.1% | 56.8% | 48.9% | 7.9% |
| 4-4 | 15-15 | You | 48.9% | 53.9% | 39.5% | 14.3% |
| 4-4 | 30-15 | You | 53.9% | 57.2% | 47.6% | 9.6% |
| 4-4 | 40-15 | You | 57.2% | 58.6% | 54.8% | 3.9% |
| 4-4 | 40-30 | You | 54.8% | 58.6% | 47.2% | 11.5% |
| 5-4 | 0-0 | Opp | 58.6% | 65.6% | 54.9% | 10.7% |
| 5-4 | 0-15 | Opp | 54.9% | 59.9% | 52.1% | 7.9% |
| 5-4 | 15-15 | Opp | 59.9% | 69.2% | 54.8% | 14.4% |
| 5-4 | 15-30 | Opp | 54.8% | 61.3% | 51.6% | 9.6% |
| 5-4 | 30-30 | Opp | 61.3% | 74.8% | 53.9% | 20.9% |
| 5-4 | 30-40 | Opp | 53.9% | 61.4% | 50.1% | 11.3% |
| 5-4 | 40-40 | Opp | 61.4% | 74.9% | 54.1% | 20.7% |
| 5-4 | A-40 | Opp | 74.9% | 100.0% | 61.4% | 38.6% |
| 5-4 | 40-40 | Opp | 61.4% | 74.9% | 54.1% | 20.7% |
| 5-4 | 40-A | Opp | 54.1% | 61.4% | 50.1% | 11.3% |
| 5-5 | 0-0 | You | 50.1% | 53.8% | 43.2% | 10.7% |
| 5-5 | 15-0 | You | 53.8% | 56.5% | 48.9% | 7.6% |
| 5-5 | 30-0 | You | 56.5% | 58.0% | 53.8% | 4.2% |
| 30-15 | You | 53.8% | 57.1% | 47.4% | 9.8% | |
| 5-5 | 30-30 | You | 47.4% | 54.4% | 34.3% | 20.2% |
| 5-5 | 30-40 | You | 34.3% | 47.2% | 8.4% | 38.7% |
| 5-6 | 0-0 | Opp | 8.4% | 15.4% | 4.7% | 10.7% |
| 5-6 | 0-15 | Opp | 4.7% | 9.9% | 1.9% | 8.0% |
| 5-6 | 0-30 | Opp | 1.9% | 4.7% | 0.5% | 4.2% |
| 5-6 | 0-40 | Opp | 0.5% | 1.4% | 0.0% | 1.4% |
Remember that the BallBOPPer simply decides on and executes the Skills, Tactics and Strategies, that have the highest probability of leading to the winning of the match.
In alignment with the "winning of the match" objective, the ultimate arbiter for the value of each point is the frequency that that point participates in sets that are won.
That may seem like a stretch, but tennis players do not care all that much about winning any particular point or game. What they really care about is winning the match.
- Win % Current is your winning percentage for the set/match at that scoreline
- Win % Win Point is your winning percentage for the set/match if you win the current point
-
Win % Lose Point is your winning percentage for the set/match if you lose the current point
The value of each point, it's Point Value, is then the amount that that point will affect your winning percentage for the set/match.
The formula for Point Value (PV) is:
PV = (Win % Win Point) - (Win % Lose Point)
Point Value measures how much winning or losing a point shifts your winning percentage for the set (this is typically called "Leverage" in sports analytics).
For instance, if you look at the 3-3, 40-15 scoreline.
| Games (You-Opp) |
Points (You-Opp) |
Server | Win % Current |
Win % Win Point |
Win % Lose Point |
Point Value |
|---|---|---|---|---|---|---|
| 3-3 | 40-15 | Opp | 56.3% | 57.5% | 54.1% | 3.4% |
You currently have a winning percentage for the set of 56.3%. If you win the point the score changes to 3-4, 0-0, and your winning percentage for the set will go up to 57.5%. Looking at the next row, this is exactly what happens.
| Games (You-Opp) |
Points (You-Opp) |
Server | Win % Current |
Win % Win Point |
Win % Lose Point |
Point Value |
|---|---|---|---|---|---|---|
| 3-4 | 0-0 | You | 57.5% | 63.6% | 54.2% | 9.5% |
If you lose the point, your winning percentage for the set will go down to 54.1%. That scoreline doesn't exist in the set, but it does in the larger dataset from the Point Value Model since the Point Value Model contains the data on every possible scoreline in any tennis set.
The Point Value of the 3-3, 40-15 point is 3.4%. This is a relatively small value due to the fact that you will suffer very little if you lose the point. In contrast, two rows above when the score is 3-3, 15-15, the Point Value is 12.2%. If you win that point, you are improving your potential for staying on serve, whereas if you lose it, you increase your risk of being broken.
But it is not intuitive that 3-3, 15-40 is so much less valuable if won, then the point at 3-3, 15-15. That is the kind of precise information the Point Value Model can provide to players. It can differentiate the true value of a point from what you might intuitively feel.
The difference in value between these two points may be surprising and counter intuitive, but neither of these points are anywhere near the most important points in this set.
In the following chart of the Point Values for this set, the most important points show up as the highest peaks.
You can see that there are four peaks going left to right. These points are the points that are highlighted in the Sample Set Table.
At the first peak the score is 3-2, 40-30 with your opponent serving. At the second one, the score is 3-2, A-40 with your opponent serving. Both of these are break points and the Point Values are 29.4%. They represent a very large swing, depending on whether you win or lose this point, in your probability of winning the set.
At the third peak, the score is 5-4, A-40 with your Opponent serving. This is a break point and match point in your favor, with a Point Value of 38.6%. You end up losing that point and instead of winning the match, your winning percentage drops from 74.9% to 61.4%.
And the last peak is at 5-5, 30-40 and now your Opponent has a break point whitch has a Value of 38.7%. After winning this point, your Opponent subsequently serves for and wins the match.
The following chart shows a second example set that ends in a tiebreak.
There is a lot of back and forth in this match. You go up a break. Then your Opponent breaks back. At the third peak you actually serve for the match, but end up getting broken, and ultimately the set ends in a tiebreak.
In a tiebreak every single point has a high Point Value, and this one went all the way to 6-6 where every single point has a Point Value hovering around 50% for both players since the entire match is on the line with every point.
What should be clear from these examples is that PV quantifies how pivotal a point is. A point with PV equal to low single digits will barely nudge the set outcome. A point with PV greater than 10% or 20% can most certainly swing a match.
Using PV to make Strategic Decisions
Looking again at the PV equation:
PV = (Win Prob Win Point) - (Win Prob Lose Point)
Point Value is the difference between your winning percentage for the set if you win the point, and your winning percentage for the set if you lose the point.
High PV points such as break points, game points and set points are important points and our intuition and gut do not have any problem recognizing them as Big Points. The contribution that computation brings to the table is the PV calculation for every possible scoreline including many Big Points that you are unlikely to perceive intuitively.
But what are we to do with this information?
If we try to handle PV points the same way as EV in poker, then a higher PV would mean you need to get more aggressive and take more risk.
In tennis, taking more risk means losing more often. This doesn't mean that being more aggressive is a bad thing in tennis. Pushing the other player around the court instead of letting them push you around is very important. But not to the extent that your winning percentage goes down. It never makes sense to lose more Big Points when what you actually want to do is win more Big Points.
Tennis commentators make it sound like the player should simply play the Big Points "better". And this makes sense in a match where you are clearly the better player and therefore can play most points using only a 90% effort level. Then you have 10 more percent more that you can engage on the Big Points. But in a competitive match with a player that is equal to you or better, you have to play every point as well as you possibly can, which means you have to give 100% on every point, and there then isn't any headroom available for Big Points.
What tennis players actually need to do instead to increase their Winning Percentage on Big Points is to make better Tactical and Strategic decisions.
Strategy by our definition is the sequencing of Tactics - in other words, the decision on which Tactics to play, and in what order to play them in, is Strategy.
Every tennis player has a repertoire of different Tactics that they can play and each of these Tactics are not created equal. In particular, each has a different point winning percentage. We call this the Tactical Win Percentage (TWP) and we calculate it using the equation:
TWP = (Tactic Execution Percentage) x (Tactic Winning Percentage)
The Tactic Execution Percentage is the percentage of time you are able to successfully execute the Tactic. The Tactic Winning Percentage is the percentage of time, when executed successfully, that the Tactic leads to the winning of the point.
Applying this formula to an actual set of Tactics is beyond the scope of what we can do here, but what we have done instead, is modify the Point Value Model to show how effective this approach can be.
The modified Point Value Model uses a set of Tactics that have a range of TWP values. The original Point Value Model was setup with two exactly equal players both with a Service Winning Percentage of 65% and a Returning Winning Percentage of 35%.
The modified Point Value Model expands the Service Winning Percentage and Returning Winning Percentage into ranges from 3% above and below their previous values. The Service Winning Percentage of 65% now ranges from 62% to 68%. The Returning Winning Percentage of 35%, now ranges from 32% to 38%.
Of course, this isn't going to make any difference unless we strategically apply this expanded range of values. To accomplish this, the simulated player gets the Point Value for the current point in the match and then selects a higher Winning Percentage Tactic when PV is higher and selects a lower Winning Percentage Tactic when PV is lower.
Even though we apply the higher and lower values to an equal number of points, so that on average the SWP is still 65% and the average RWP is still 35%, the resulting increase in your Winning Percentage is dramatic.
In a simulation of 100,000 sets, each player in the original Point Value Model will win approximately 50,000 sets. 50% each. With the modified model that adapts your Tactics to the Point Value of each point, you are now winning 57,778 sets.
With the modified model that adapts your Tactics to the Point Value of each point, your Set Winning Percentage goes up from 50% to 58%.
To be clear, there isn't any great mystery as to why this works. We can easily intuit why it is true, but to back up that intuition, here is an illustration:
The Point Value Distribution is not a straight line. The median for PV for all of the scorelines in the Point Value Model (exclusive of tiebreak points) is 6%. In other words, there are the same number of points with PVs between 0 and 6% as there are between 6% and 50%.
This distribution is the result of the structure of the tennis scoring system. The game structure of first to four points ahead by two naturally leads to a large number of low value points, and a smaller number of dramatically high value points or Big Points. The result is that winning a small number of Big Points easily out-weighs losing a larger number of Low PV points, giving your Winning Percentage a substantial boost.
Of course, PV is not the only criteria that the Strategic model uses to determine which Tactic to play at each particular moment in a match.
Predictability is an equally important Strategic criterion.
If you were to select and use the same Tactics for all Big Points, then your opponent, if they are paying attention, will quickly learn to predict which Tactics you will use and your Winning Percentage for those Tactics will decline.
Predictability is an extremely important strategic element in all of sports. One of the reasons for this is that humans have a very hard time being unpredictable. So much so that professional athletes will often use some external cue to help randomize their playing decisions.
Some baseball pitchers are well aware that if they decide on each pitch intuitively, even if they are trying to be unpredictable, they will end up following a subtle but predictable pattern. So, they do not leave it up to intuition, and instead they use something else such as the position of the second hand on the stadium clock to determine which pitch to throw.
Computers on the other hand, have built-in random functions that make them the masters of unpredictability.
The Bigger Picture: Enhancing the Game
The issue of predictability and the role it can play in your tennis strategy is beyond the scope of this post.
Our intention here has been to give you an inkling of the potential importance of Tactics and Strategy to your tennis game, and show you that strategic insights from computational players, such as the BallBOPPer, can provide you with a significant advantage that can help you win.
The nuanced strategic approach to the playing of "Big Points" that we have advocated is only the tip of the iceberg. There is much more to come.
In future posts we will disclose more information on the BallBOPPer's Tactical and Strategic decision-making models. But we believe that the only way these insights can become second nature so that tennis players can utilize them "intuitively" in the moment to moment of their matches, is by actively training on a tennis court, in competitions against a computational opponent, in the context of real points, games, sets and matches.
If you are interested in looking at the examples cited in this post, drop us a request at support@roboppics.com and we will send you the examples along with the complete 1500-point spreadsheet with the winning percentage for every possible score in tennis.