# Chebyshev’s inequality, Jack Welch and Performance Appraisal.

Are you unhappy with your appraisal system? Do you find ratings system confusing? Do your managers blame your poor rating (in spite of putting lot of hard work) on HR managers who have come with strange animal called bell curve/forced distribution?

To understand this better let me tell you about two people- Pafnuty Chebyshev and Jack Welch.

Pafnuty Chebyshev was Russian mathematician who came up with concept called as Chebyshev ‘s Inequality. What it states is for any distribution if we know mean and standard deviation then at least 1-1/K2 of data from a sample must fall within K standard deviations from the mean. For example if we want to know how much data will lie within 2 standard deviation then for K = 2 we have 1 – 1/K2 = 1 – 1/4 = 3/4 = 75% i.e. 75% of data will fall within 2 standard deviations.

This was then tested on different features of population like intelligence, height, scores in exam etc. If population is normally distributed then almost 95% of data lies within two standard deviations. Anything that lies beyond this (depending on range which is of interest to you) is called outliers.

Normal distribution curve looks like bell, hence is also called bell curve.

It needed a genius like Jack Welch, ex. CEO of GE, to connect this concept of bell curve to performance appraisal- outliers on right side of bell curve were your stars, those within standard deviation were solid citizens and outliers on left side of bell curve were dead wood. Some numbers were given to this distribution ex. top 20% stars, next 70% solid citizens and bottom 10% dead wood i.e 20-70-10 system.

Things did not stop here, pay hikes, succession plans, career planning etc. also got linked to this classification.

Managers from other companies started copying this system and came up with their own variations ex.10-20-40-20-10, 10-15-60-10-5 and so on.

This new distribution had little to do with Chebyshev (or for that matter normal distribution), some companies started applying this distribution to small teams of 10-15 employees (for normal distribution sample size should be more than 35 items).

Today the whole idea of forced distribution is redundant; if your performance appraisal system and MIS are robust then forced distribution is not even needed.