Mapping the Sweet Spot - part 1
11/4/25
Most players are vaguely familiar with the term PBCOR (Paddle Ball Coefficient of Restitution). It's a term used by USAP (USA Pickleball) relating to a test indicating the power of a paddle. Paddles that pass the test display a logo indicating the paddle is certified for tournament use.
The test consists of propelling a ball toward the paddle at various locations with a known speed (50 or 60 mph) and recording the rebound speed after impact. The inbound speed, the rebound speed, the location on the paddle face and several other factors are entered into a complicated equation. The equation spits out a number for each location. The maximum number becomes the paddle's PBCOR score and must be less than 0.43. If the PBCOR score is over 0.43 the paddle is disqualified for USAP tournament play.
Most manufacturers will not reveal their paddle's maximum score, nor will they reveal their paddle's score at all the locations nor will they reveal their paddle's rebound speeds.
Coefficient of Restitution (COR) for various paddles (Vinbound = 50 mph).
The graph shows the COR scores for 8 of the many paddles in my possession. There is quite a variety of shapes. COR (PBCOR, KEWCOR, etc.) is an excellent method to compare the power of different paddles with different swing weights, balance points, size, and face stiffness, but the one number (e.g. 0.43 or 0.385) is meaningless for most players.
Better yet, is a plot of rebound velocities Vre vs impact location. Rebound velocity Vre in miles per hour will be used as it's a metric familiar to all and is an integral part of determining COR. Notice the steep increase in Vre as the impact location moves from the tip of the paddle to the neck.
We always try to hit the ball at the paddle's sweet spot which is usually located about 4" from the tip of the paddle. But we're not always successful. Ball impacts away from the sweet spot can lead to unwanted vibration and rebound velocities that are different - both less and more as shown in the graph. There is quite a variety of shapes.
One might guess that a flat shape would be best. What is the best shape? Flat? Dome? and what's the size of the sweet spot and how should it be measured? The performance of a Ronbus Quanta R2 will be explored by quantifying the rebound velocities for a block, serve, punch and dink at different impact locations along the paddle face.
Rebound Velocities (Vre) for various paddles (Vinbound = 50 mph).
Blocks, Serves, Punches, Dinks
Blocks at the Net
A typical scenario requiring a block is a 3rd or 5th shot "rocket" headed toward the opposing player at 50 mph. The ball can be blocked short and toward the sideline or block back toward the opponent with no paddle movement. This is the exact scenario used in COR testing were the ball is shot at the paddle at 50 mph while the paddle is stationary. The rebound speed is represented in the graph. For example, a ball impacting the paddle 2" from the tip would rebound at about 7.8 mph.
Summary:
Impact location 2", Ball velocity 7.8 mph
Impact location 4", Ball velocity 11.2 mph
Impact location 6", Ball velocity 14.0 mph
An hit off the sweet spot (4") would rebound either faster or slower. This is not a problem if directing the ball back to the opponent's feet. It might cause problems if the ball is directed close to the sideline.
The Serve
The serve is more difficult to analyze as the paddle is rotating around the shoulder, elbow and wrist. A high speed video of a Tyson McGuffin serve indicates the effective pivot point is about 10" off the end of the handle. Paddle face locations further away from the pivot point are moving faster (higher linear velocity) than points closer as indicated in the picture. The linear paddle velocity at 22" from the pivot or 4" from the tip is standardized at 50 mph. The other two velocities are at 2" and 6" from the tip.
Note: The swing mechanics of different players might lead to different results
A two frame overlay of shoulder and wrist rotation during a serve revealing an approximate paddle pivot point.
The resultant linear velocities at different locations on the paddle face from a paddle pivoting around a point 10" off the end of the handle.
The Equation of Motion was discussed in a previous article and can be used to determine the ball speed during a serve, dink, block, flick, smash, etc. The outgoing ball velocity (Vrebound) is a function of the incoming ball velcity, the paddle velocity and the "bounciness" of the paddle face (eA).
Vrebound = eA * Vinbound + (1+eA) * Vpaddle
For a serve, the first term is discarded since Vinbound is zero for a serve.
For a location 22" from the pivot point (4" from the tip) let's standardize the paddle velocity at 50 mph . The elasticity of the collision eA is 0.22. The velocity of the rebounding ball Vrebound is then 61.0 mph. (=50*1.22)
For a location 20" from the pivot point (6" from the tip) the paddle velocity is slower at 45.5 mph . The elasticity of the collision eA is 0.31. The velocity of the rebounding ball Vrebound is 59.6 mph. (=45.5*1.31)
For a location 24" from the pivot point (2" from the tip) the paddle velocity is faster at 54.5 mph . The elasticity of the collision eA is 0.12. The velocity of the rebounding ball Vrebound is 61 mph. (=54.5*1.12)
In Summary:
Impact Location 2", Ball velocity 61.0 mph
Impact Location 4", Ball velocity 61.0 mph
Impact Location 6", Ball velocity 59.6 mph
The Quanta paddle's rebound velocity is close to the same and is relatively insensitive to impact location during a serve. Even though the paddle is moving faster at the 2" location (54.5 mph v 50 mph), the extra velocity is offset by the lower bounciness of the paddle face (eA=0.1 v eA=0.22).
What is eA?
eA is the bounciness of the paddle face measured as the ratio of rebound velocity to inbound velocity.
eA = Vre/Vin
Referring to the graph above, Vin is 50 mph and Vre is 11.2 mph at the 4" location. Therefore, eA = 0.22
eA will have a different value for a different impact location or inbound velocity.
The Punch
The punch involves the snap of the wrist and rotation at the elbow leading to an effective pivot point about 1" off the end of the handle. Paddle face locations further away from the pivot point are moving faster (higher linear velocity) than points closer.
Gabe Tardio executes a punch during a fire fight at the net. In the first frame Gabe positions the paddle at his chest as the ball approaches. In the second frame the paddle has been rotated around the elbow and wrist propelling the ball back to the opponent.
The resultant linear velocities at different locations on the paddle face.
From a previous analysis of a fire fight it was found that the ball approaching a player is moving at about 25 mph and the paddle is moving at about 25 mph
Using the Equation of Motion: Vrebound = eA * Vinbound + (1+eA) * Vpaddle
For a location 13" from the pivot point (4" from the tip - the sweet spot) let's standardize the paddle velocity at 25 mph and the incoming ball velocity at 25 mph . The elasticity of the collision eA is 0.22. The velocity of the rebounding ball Vrebound is 36.0 mph. (=0.22*25 + 1.22*25)
For a location 11" from the pivot point (6" from the tip) the paddle velocity is 21.2 mph . The elasticity of the collision eA is 0.30. The velocity of the rebounding ball Vrebound is 35 mph. (=0.3*25+1.30*21.1)
For a location 15" from the pivot point (2" from the tip) the paddle velocity is 28.8 mph . The elasticity of the collision eA is 0.14. The velocity of the rebounding ball Vrebound is 36.3 mph. (=0.14*25+1.14*28.8)
In Summary:
Impact Location 2", Ball velocity 36.3 mph
Impact Location 4", Ball velocity 36 mph
Impact Location 6", Ball velocity 35 mph
The Quanta paddle is insensitive to impact location during a punch or flick. The higher paddle velocity is offset by the lower bounciness (eA) of the paddle face.
The Dink
The dink involves rotation at the shoulder with a locked wrist and elbow leading to an effective pivot point about 20" off the end of the handle. Paddle face locations further away from the pivot point are moving faster (higher linear velocity) than points closer.
Federico Staksrud executes a dink using a locked wrist with rotation around the shoulder.
The resultant linear velocities at different locations on the paddle face.
From a previous analysis of a dink rally it was found that a small difference in ball velocity (17 mph v 14 mph) can turn an excellent dink into a popup. Many players find the dink the hardest shop to master. During a dink rally the ball is approaching at about 10 mph and the paddle is moving at about 7 mph. The resultant ball speed back toward the opponent at an upward angle is around 15 mph.
The efficiencies used in the previous analyses at a relative speed between ball and paddle of 50 mph cannot be used. During a dink rally the incoming ball speed is 10 mph and the paddle speed is 7 mph for a relative speed of 17 mph. A new set of paddle face efficiencies (eA) at 17 mph (paddle speed zero, incoming ball speed 17mph) must be collected using the air cannon and speed gate.
Rebound velocities at different impact locations on the paddle face with an inbound velocity of 17 mph.
Using the Equation of Motion: Vrebound = eA * Vinbound + (1+eA) * Vpaddle
For a location 32" from the pivot point (4" from the tip - the sweet spot) let's standardize the paddle velocity at 7 mph and the incoming ball velocity at 10 mph. The elasticity of the collision eA is 0.44 (7.3 mph/17 mph). The velocity of the rebounding ball Vrebound is 14.5 mph. (=0.44*10 + 1.44*7)
For a location 30" from the pivot point (6" from the tip) the paddle velocity is 6.6 mph . The elasticity of the collision eA is 0.48. The velocity of the rebounding ball Vrebound is 14.6 mph. (=0.48*10+1.48*6.6)
For a location 34" from the pivot point (2" from the tip) the paddle velocity is 7.4 mph . The elasticity of the collision eA is 0.32. The velocity of the rebounding ball Vrebound is 13 mph. (=0.32*10+1.32*7.4)
In Summary:
Impact Location 2", Ball velocity 13 mph
Impact Location 4", Ball velocity 14.5 mph
Impact Location 6", Ball velocity 14.6 mph
A player would have more consistent results hitting the ball 4" to 6" from the tip rather than at 2".
Future Articles
Part 2 will compare the Quanta to other popular paddles.
Part 3 will explore off center hits across the face and the importance of twist weight.
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