Is This Paddle Legal? PBCOR=0.44
There is high consumer demand for power paddles. Manufacturers have responded with paddles designed to approach and sometimes exceed the power limit established by USA Pickleball (PBCOR=0.43). PBCOR testing is mandatory to obtain USAP certification. Tens of thousands of dollars are invested in the new paddle design process. Pass the test and certified paddles can be sold to the public. Fail the test and the design process has to be restarted. Plus, the inventory has to be scrapped.
The PBCOR measurement is based on the average speed of six balls rebounding off the paddle under test. There is statistical variability built into any test. It's probable that a valid paddle with an actual PBCOR of 0.43 or lower shows up erroneously with a PBCOR value of 0.44 or 0.45. Paddle manufacturers should be aware of the reason why.
Conversely, it's highly probable that an invalid paddle with an actual PBCOR value in excess of 0.44 or more shows up erroneously with a PBCOR value of 0.43 or less. In this situation the paddle is certified and manufacturers are probably not concerned at all.
USAP PBCOR Test Facility
USAP (USA Pickleball) subcontracts PBCOR testing to Element U.S. Space & Defense.
For a video of the facility click here
Background
The PBCOR Specification
"PBCoR Test -- Not To Exceed Limits:
0.43 effective Nov. 1, 2025.
Procedure
The longitudinal axis of the paddle is scanned at half-inch increments to find the maximum PBCOR location.
The PBCOR at each location is the average of six (6) impacts. The average PBCOR value is rounded to the nearest one-hundredth (2-decimal places).
Sample Report
The manufacturer receives a summary report similar to the one shown below. The paddle has slightly exceeded the limit (0.44) and will not be certified.
The Problem
There is a high likelihood that the PBCOR for the above paddle is 0.43 or lower and should be certified. The average PBCOR reported by USAP (0.44) has been determined from six impacts which is only an estimate of the true PBCOR average. The true PBCOR may be higher or lower than the reported PBCOR. It depends not only on the average, but also on the spread of the six impacts (standard deviation) which is not normally sent to the manufacturer. However, the data is available upon request. In the case above the six values were:
0.4193
0.4453
0.4331
0.4613
0.4394
0.4152
Average=0.4356
Standard Deviation=0.0171
The Question
"I have six samples with an average of 0.4356 and a standard deviation of 0.0171. What is the probability that the true average is lower than 0.435?"
Note: The PBCOR value of 0.435 is rounded to 0.43 which is the PBCOR limit. The question restated is "What's the probability that another PBCOR test with a different set of 6 samples will result in a certifiable paddle."
The Answer from Google
The probability that the true population average is lower than 0.435 is 46.74%.
Because your sample size is small (n = 6) and the population standard deviation is unknown, we use a Student's t-distribution to calculate this probability.
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Find the Standard Error of the Mean (SEM):
The SEM measures how much the sample mean is expected to vary from the true population mean.
SEM = s/sqrt(n) = 0.0171/sqrt(6) = 0.006981
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Calculate the Degrees of Freedom (df):
df = n-1 = 6-1=5 -
Calculate the t-statistic:
The t-statistic tells us how many standard errors our target value (0.435) is from the sample mean (0.4356).
t = (u-x)/SEM = (0.435-0.4356)/0.006981 = -0.0859 -
Find the Cumulative Probability:
Using a t-distribution table or a statistical calculator for t = -0.0859 with 5 degrees of freedom gives a left-tail probability of 0.4674 or 45.75%.
Discussion
The sample average (0.4356) is very near to the PBCOR limit of 0.435. It's understandable why this paddle was declared illegal and why this paddle might be declared legal upon retest. If this paddle was tested 100 times, it would be declared legal 47 times and illegal 53 times. This begs the question, "What is the actual PBCOR and the actual standard deviation?" We can never find an exact answer and can only get closer by taking more and more samples. For instance, if the above paddle was sampled 100 times, and had the same average (0.4356) and standard deviation (0.171) the probability of being tested as legal drops from 47% to 36% - not much of an improvement.
What happens to the probability when the sample average is further away from the PBCOR limit or when the standard deviation is different? The table below lists a combination of reported PBCOR values and standard deviations for a supposedly illegal paddle plus the probability that the true PBCOR value is below the PBCOR limit and is legal. The table helps answer the question, "What is the probability that another PBCOR test with a different set of 6 samples will result in a certifiable paddle."
Paddle manufacturers can use the table or the methodology or Google to determine whether to spend money and time on a retest.