Compare prediction rates between K means clustering and Multinomial Regression

Stat/Math wizs, if you could kindly shine your beacon on this problem.

I'm running some statistics using a k means clustering algorithm and it had classified objects in category A, 33 in Cat B, 41 into Cat C and 24 into Cat D.

Out of a total of 144 objects, Cat A then has a proportion of 32% (0.319), 22.9%, 28.4%, and 16.6% respectively.

I was given a formula by a professor which involves the follow calculation

1. Squaring each proportion and then adding them to get the sum (0.319^2 + 0.229^2 ....)

2. This yielded a value of 0.263

3. Multiply 0.263 by 1.25 to get 0.329

The professor then said, within the context of a multinomial regression which yielded a prediction rate of 53%, that this particular set of classification results reflects a prediction rate of 32.9%. I didnt get a chance to clarify what he meant and, more importantly **what formula he was applying**. Could anyone shed light on what statistical formula was used to derive the value of 0.329 or 33%?

Thanks guys