Distinguished mathematician and Associate Dean for Faculty Affairs at the Virginia Tech College of Science Trish Hammer is set to participate in the USA Pickleball National Championship in Dallas this November.
What sets her apart from most of her competitors is a secret strategy involving the application of mathematical principles and analytical thinking to gain a strategic advantage.
A Unique Perspective
Having earned her bachelor’s, master’s, and doctorate degrees in mathematics from Virginia Tech, Hammer‘s background as an applied mathematician brings a unique perspective to the conventional understanding of this widely enjoyed sport.
As Hammer says, “You use [math] all the time – you don’t even know that you’re using it.”
Hammer told Virginia Tech News how she has the ability to conceptualize how maths is interwoven into the principles of pickleball and is using that vision to improve her game.
She continues, “One big application of math in the calculus courses I teach is optimization, and for me, pickleball presents itself as one big optimization problem. I am trying to maximize output based on the variables I can control.
“Maximizing means winning, and I’m always thinking about adjusting the variables to beat an opponent.”
The Best Shot Angle
She goes on to quantify these variables, which consist of various techniques, game tactics, and physical characteristics: “You are constantly adjusting the different skills, strategies, and conditioning, and I approach it all, surprisingly, very analytically.”
Hammer also explained that she was constantly on the lookout for the best angle of shots and how to reduce the chances of making a mistake when executing:
“I’m trying to place a shot that optimizes my chances for success,” she said. “With each of those shots, you have to think about the angle, like 45 degrees, 80 degrees, and 10 degrees, while also thinking about the margin of error.”
A Higher Margin Of Error
When your opponent is positioned towards the back of the court, opting for a tighter angle shot is typically more effective. However, it also entails a higher potential to make a mistake. The objective is to pinpoint the exact point between the angle and the margin of error.
“If I wanted to minimize my margin of error, I would just hit it straight back to the opponent. Safe, but not very effective, so you’re always trying to weigh that balance.”
Hammer pointed out that while a pickleball player might be tempted to opt for a hit farthest from an opponent, it may not necessarily be the most challenging shot to return. This adds yet another variable to consider when looking to raise your game.
“Take into account how quickly your opponent moves in different directions,” Hammer says. “An opponent may move more slowly side to side, and if so, it may be more effective for me to hit it a little closer to them by their side, which has a smaller margin of error.”
She is similarly analytical about her positioning when it comes to returning shots: “Should I move up and then over? Should I just take the shortest path? What movement puts me in the best position to react? I think about it all the time that the direct distance may not necessarily be the quickest distance.”
The Value Of The Dink Shot
She recognizes the value of the dink shot, used when you and your opponent are positioned near the kitchen line (non-volley zone) and you engage in a strategic, low-risk exchange, all the time subtly shifting your adversary around before applying the coup-de-grace.
“The dink is a key to the game because you’re trying to move the opponent, and you’re trying to get them to hit it high enough that you can smash it and win a point,” Hammer says.
Lindsey Byars from Virginia Tech News again provides the following analysis of dink shots:
“Though it’s a very nuanced and delicate shot, there are lots of dink possibilities. At a very basic level, there are three places for a player to hit the dink: straight across the court, toward the center of the court, or diagonally across the court.
“A rally might involve three shots, which means with three choices for each shot, there would be 27 ways to sequence three shots. However, an advanced player is also considering placement, speed, and spin.”
Hammer goes one step further with her even more intricate mathematical take on the shot:
“All of a sudden, for every dink you hit, you have three placement choices, two speed choices, and three choices for spin. Every time I hit the ball, I have 18 different ways to hit this one shot, which translates to 5,832 ways to sequence three shots. Imagine the possibilities if the sequence is 10 or more shots.
“So this whole idea of permutations is a big deal. The idea is you want to consider these permutations in a way that optimizes your chances for success.”
The Repetitive Nature Of The Game
She is also aware of the repetitive nature of the game and turning that to her advantage:
“When you’re playing an opponent, you’re always looking for patterns.”
A fellow pickleball player shared an analytical approach to assessing opponents’ shots with Hammer. According to this method, there is a 75 percent likelihood that the shot will land in one specific place, a 20 percent chance it will land in a second location, and a 5 percent chance it will head in yet another direction.
With this calculation in mind, they ready themselves for the locations where the shot is most probable to land.
Hammer was surprised at the coincidence: “And I said, ‘Oh my gosh, I do the same thing, but I had never heard it explained quite that way.’ That’s exactly how you’re thinking when you play.”
Math All Around Us
Hammer finished by pointing out that we inadvertently use math all the time in our everyday lives. However, because of her intellect and experience, she is always aware of it and uses it to gain an advantage over her opponents:
“People don’t think that there’s math around them, that they never use it, but we all do without realizing it,” said Hammer. “I’m aware of it, and the more aware of it I can be, this becomes a strength of my game.”
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