Fret Rockers: The most inaccurate tool in your shop

Digital Nut Slotting Gauge: https://amzn.to/4f8sstY

I had ChatGPT work out some of the statistical probability for me but I admit I probably didn't enter in all the relevant info to get a good answer, if someone is good with with statistical mathematics, feel free to double-check the A.I.s work.

Via chatGPT:
Key Takeaway:
Accuracy of the fret rocker for correctly identifying high frets is around 11.1 percent.
Total error rate (false positives and false negatives) is 22.2 percent, meaning that in nearly 1 out of 5 uses, the tool might give an incorrect indication of fret height.
These estimates reveal significant limitations, making a strong case for tools like a digital gauge for precise measurements over the fret rocker tool.

Via chatGPT:
Let's break down the problem to address each type of error and calculate the potential for false positives and the likelihood of accuracy. We'll approach this by examining the probability of each scenario and calculating the odds of correct identification by the fret rocker tool. I’ll base the analysis on some simplified assumptions about fret heights to make this manageable.

Key Scenarios:
False Positive (Rocking without a high fret): This happens if:
Frets 1 and 2 are equal in height, but fret 3 is lower.
The fret rocker rocks because fret 1 is higher relative to fret 3, but fret 2 is not actually high.
False Negative (No Rocking with a low middle fret): This happens if:
Frets 1 and 3 are equal in height, but fret 2 is lower.
The fret rocker does not rock, even though fret 2 is not at the same height as frets 1 and 3.
Correct Positive (Rocking with a high middle fret): This is the ideal scenario:
Fret 2 is indeed higher than both frets 1 and 3, and the fret rocker correctly rocks over this section, identifying fret 2 as high.
Correct Negative (No Rocking with level frets): This occurs when all three frets are actually level, and the fret rocker correctly does not rock.
Basic Statistical Setup
To calculate probabilities, we’ll need some assumptions:

Each fret has a random chance of being higher, lower, or equal to adjacent frets.
We’ll assume three possible height states for each fret (higher, lower, or level with adjacent frets) and use these to estimate outcomes.
For simplicity, let's assume:

Each fret has an equal one-third chance of being higher, lower, or level with an adjacent fret, based on random small variations in fret heights.
Calculating False Positives and False Negatives
1. False Positive (Rocking without a high fret)

Probability of Fret 1 equals Fret 2, but Fret 3 is lower than Frets 1 and 2.
Probability calculation:
Chance Fret 1 equals Fret 2: one-third
Chance Fret 3 is lower than Fret 1 and Fret 2: one-third
Combined probability for False Positive = one-third times one-third, which equals one-ninth, or approximately 11.1 percent.
2. False Negative (No Rocking with a low middle fret)

Probability of Fret 1 equals Fret 3, but Fret 2 is lower than Frets 1 and 3.
Probability calculation:
Chance Fret 1 equals Fret 3: one-third
Chance Fret 2 is lower than Fret 1 and Fret 3: one-third
Combined probability for False Negative = one-third times one-third, which equals one-ninth, or approximately 11.1 percent.
3. Correct Positive (Rocking with a high middle fret)

Probability of Fret 2 being higher than both Fret 1 and Fret 3.
Probability calculation:
Chance Fret 2 is higher than Fret 1: one-third
Chance Fret 2 is higher than Fret 3: one-third
Combined probability for Correct Positive = one-third times one-third, which equals one-ninth, or approximately 11.1 percent.
4. Correct Negative (No Rocking with level frets)

Probability of all three frets being level.
Probability calculation:
Chance Fret 1 equals Fret 2 equals Fret 3: one-third times one-third, which equals one-ninth, or approximately 11.1 percent.
Summary of Probabilities
Each outcome here has a roughly equal probability of about 11.1 percent, which means the tool will produce false positives or false negatives almost as frequently as it correctly identifies a high or level fret.

Key Takeaway:
Accuracy of the fret rocker for correctly identifying high frets is around 11.1 percent.
Total error rate (false positives and false negatives) is 22.2 percent, meaning that in nearly 1 out of 5 uses, the tool might give an incorrect indication of fret height.
These estimates reveal significant limitations, making a strong case for tools like a digital gauge for precise measurements over the fret rocker tool.

Merch
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