Playing Tennis like "Deep Blue" Part 2: Computation and Tennis Tactics
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.
After the release of the demo video of our 2023 prototype, the BallBOPPer returned to stealth mode. It will reemerge Summer 2026 when the Ultimate "True Game Play" preview and release are ready!
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 information on how Tactical and Strategic tennis decisions can be optimized 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 data gathered from the playing of hundreds of live sets, and thousands of simulated sets, and this combination of the models and their 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 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 $250 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, seem 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 has a pot of chips or money as the payoff, and a player can cut their losses on any particular hand by folding.
The "point" is the fundamental scoring unit in tennis, but the value of each point is unclear, and there isn't any upside to dropping out of any of them.
In order to be able to run optimization simulations for tennis a method is needed for assigning a value to each tennis point.
If you have watched any televised tennis tournaments, you will have heard commentators saying things 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 we use simulation modeling to recognize and value Big Points?
- How does this information subsequently effect the tennis playing decisions that we make?
We will answer these questions using a computer model we have developed called the Point Value Model that simulates the playing of tennis sets.
The Point Value Model uses the same idiosyncratic scoring used in tennis including deuce points and tiebreaks to simulate the winning of points and games in the context of a one set match between two players of equal Skill level.
You and your Opponent (Opp) both have:These two values are around the average values for WTA/ATP players.
- a serving winning percentage of 65%
- a returning winning percentage of 35%
Also note that human psychology is not being simulated and therefore neither of these players exhibit any of the foibles listed earlier that human players are prone to.
Running this model through a million simulated sets results in data on over 1500 possible scorelines in a tennis set. You can look at a table of all of the possible scorelines by clicking here, although this information will probably make more sense after reading further on.
During the process of playing simulated sets, the model generates 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 complete scoreline from the original generated data.
| Games (You-Opp) |
Points (You-Opp) |
Server | Your Win Probability |
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 Your Win Probability or your probability of winning given that 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, and these are then expressed as "percentages". Colloquially we refer to these percentages as probabilities although technically they are frequencies.
If you understand scoring in tennis, you can walk through the sample set/match from top to bottom and follow your progress through each point.
Sample Set Table: highlighted rows are "Big Points" and will be discussed in detail.
| Games (You-Opp) |
Points (You-Opp) |
Server | Your Win Probability |
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 generally do not care all that much about winning any particular point or game. What they really care about is winning the match.
- Your Win Probability is your probability for winning the set/match given 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.
For instance, if you look at the 3-3, 40-15 scoreline.
| Games (You-Opp) |
Points (You-Opp) |
Server | Your Win Probability |
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 | Your Win Probability |
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 sample 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 in your probability of winning the set depending on whether you win or lose this point.
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 which 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 Optimize your Strategic Decision-Making
Looking again at the PV equation:
PV = (Win % Win Point) - (Win % 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 simulation-based modeling brings to the table is the PV calculation for every possible scoreline - revealing 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 means you need to take on more risk.
But risk does not work the same way in the Point Value Model.
In poker, GTO play sometimes means taking on more risk by placing bets on low probability hands that have highly valuable pots. By playing these high-risk hands, a player can end the night with the most chips even if they lose or fold the last twenty hands.
But in tennis, the winner is always the player who wins the final point.
The Point Value Model values each point by its probabilistically contribution to getting to and winning the last point. According to this model, a high-risk high-reward approach to playing points may give you a win every once in a while, but in the long run you will win fewer matches. Instead of taking on higher risk, tennis players need to consistently make decisions that have the highest probability of leading to that final point.
Then is there anything players can do to win more Big Points?
Tennis commentators make it sound like players should simply play the Big Points "better". But what they really mean is that players need to not play the Big Points so badly.
The easy to recognize Big Points such as game points, break points, set points and match points, are also the ones where the psychological foibles come to the fore. Players often tense up and suddenly become unable to hit the ball inside the lines.
The reasons for this have to do with the biology of fight or flight, and a good resource on this is a book called "The Hour between Wolf and Dog" by John Coates, a successful Wall Street trader turned neuroscientist.
At any rate, the players in our simulation-based model do not have any psychological foibles. They give 100% on each and every point. And by simulating the playing of millions of sets, the model ultimately reveals a way to win more Big Points and thereby win more matches.
The best way for tennis players to increase their Winning Percentage on Big Points is to Optimize their Tactical and Strategic decision-making.
Strategy by our definition is the sequencing of Tactics - in other words, Strategies are your decisions on which Tactics to play, and in what order to play them.
Every tennis player has a repertoire of different Tactics, and these Tactics are not created equal. In particular, each has a different point winning percentage. We call this the Tactic Win Percentage (TWP) and we calculate it using the equation:
TWP = (Tactic Execution %) x (Tactic Winning %)
The Tactic Execution % is the percentage of time you are able to successfully execute the Tactic. The Tactic Winning % is the percentage of time, when executed successfully, that the Tactic leads to the winning of the point.
We can now use this formula to define what we mean by "Aggressive play" in tennis.
An aggressive Tactic is one where the Tactic Execution % is low, but the Tactic Winning % is high. For instance, a Tactic that leads to a winner such as an One Plus serve has a high Winning % of say 98%, meaning your opponent will only return it 2% of the time, but have a low Execution %, say 66%, meaning you complete it successfully only 2 out of every 3 attempts. The resulting TWP is 65%.
A Tactic where the Tactic Execution % is high, but the Tactic Winning % is lower, implies you are depending on your defensive skills to win the point. For instance, a serve followed by a rally to the opponent's weaker side may have a Winning % of only 66% but an Execution % of 98%. Also resulting in the same TWP of 65%.
The TWP of the Tactics that you play needs to be optimized to be the highest that you are capable of playing, and it cannot vary greatly from your nominal Winning Percentage. In other words, playing either overly aggressive or overly defensive will result in you winning fewer matches. You must keep your TWP within a narrow "sweet" range.
Applying the TWP formula to an actual set of Tactics and then applying those Tactics based on the Point Value of each point, is what we call Optimized play, and we created a modified version of the Point Value Model that demonstrates how effective Optimized play can be.
The modified Point Value Model uses a set of Tactics that have a narrow 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 on average the RWP is still 35%, the resulting increase in your Winning Percentage is quite 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 repertoire of Tactics to the Point Value of each point, you are now winning 57,778 sets.
By Optimally playing each Tactic according 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. Your intuition is probably telling you it is true, but to back up that intuition, here is an illustration:
The Point Value Distribution is not a straight line. Points have much higher values on the right half of this graph than they do on the left half. 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 similar number of dramatically high value points or Big Points. Winning a small number of Big Points easily out-weighs losing a similar number of Low PV points.
The intuitive way of thinking about optimizing points might be to play the high PV points more aggressively, and the low PV points less aggressively. But simply hitting the ball harder and closer to the lines without considering the TWP of those Tactics will raise your risk level and lower your winning percentage. The opposite of what you are trying to do.
It is better to think of Optimization as relentlessly making the best possible Strategic and Tactical decisions. This may actually involve seesawing between aggressive play and defensive play, both can win points, but in the end, what players really need to strive for is solid decisive play.
Predictability is the enemy of the Good
The obvious question at this point is that if you have Tactics that are 3% better than the others in your repertoire, then why not play those Tactics all the time?
And the equally obvious answer is - predictability.
Predictability is an extremely important strategic element in all of sports. One of the reasons 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.
Likewise in tennis, you need to be able to predict what your opponent is going to do, and you need your opponent to be unable to predict what you are going to do.
If you were to select and use the same optimal Tactics for all Big Points, then your opponent will quickly figure this out and your Winning Percentage for those Tactics will subsequently decline.
Unpredictability is therefore one of the keys to playing Optimized tennis.
Optimal tennis play requires:
- a range or repertoire of Tactics that you are highly skilled at playing
- an intuitive understanding of the Tactic Winning % of each Tactic
- an intuitive understanding of the Point Value of the points in a match as you play them
- the strategic decisiveness required to match your Tactics with the corresponding points they Optimize
- and the ability to randomize these strategic decisions to keep your opponent guessing what Tactic you will play next
The Bigger Picture: Enhancing the Game
In this post we hope to have given you an inkling of the importance of Tactics and Strategy to your tennis game, and to have shown you that strategic insights from computational players, such as the BallBOPPer, can provide you with many significant advantages, including:
- Strategic Clarity: the ability to think in terms of Skills, Tactics, and Strategy, layered abstractions that mirror elite decision-making
- Point Value Awareness: the ability to evaluate tactical decisions based on their impact on match outcomes
- Tactical Discovery: the ability to see hidden opportunities and trade-offs, especially in high-pressure scenarios
- Optimized Play: the ability to optimize responses, enabling you to develop resilient tactics and avoid exploitable patterns
Tennis is ultimately a battle of adaptation. Each player is constantly adapting to the other's Skills, Tactics and Strategy in an effort to gain the upper hand.
In the next part of this series, we will dig into the mechanics of this battle of adaptation by exploring the decision-making players should employ for the selection of each Skill; how these Skills are then structured into the patterns we call Tactics; and finally how the decisions on which to play and when are ultimately brokered by the probabilities and frequencies of player and ball trajectories.
In the end however, though these discussions may be helpful to the way player's think, 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 and experimenting on a tennis court, in competitions against a simulation driven opponent, in the context of true points, games, sets and matches.
Click here to view the full Point Value Table for all Tennis Scorelines.
If you have any questions or wish to learn more, drop us an email at deepblue@roboppics.com.