Rate, probability and matching: comments on "The identities hidden in the matching laws, and their uses" by David Thorne.

Rachlin et al. (2010) wrote a short theory paper. They looked at the math tricks hidden inside the matching law.

The authors warn that these hidden formulas can confuse students. The tricks make simple rate data look harder than it is.

The paper says some textbook identities hide the real story. Kids learn the law faster when you show plain response rates.

Skip the algebra shortcuts. Plot responses per minute versus reinforcers per minute. The relation is clear.

Killeen (2015) extends the same worry. That paper says the matching law is just logistic regression wearing a mask. Together, the two pieces say: drop the fancy math, use tools we already know.

Nakamura et al. (1986) is the classic review the target critiques. That study showed the law works, but it used the same opaque identities Howard now questions. The new note does not cancel the old data; it just offers a cleaner way to teach it.

Caron (2024) gives a concrete fix for one messy by-product: undefined log ratios. Where Howard warns, Caron shows how to handle the mess with modern stats.

When you teach staff or supervisees, start with plain rate graphs. Avoid the algebraic identities that hide in textbooks. Your learners will see the matching relation without the fog.