NBOP National Board of Operations Professionals

Part two. The MixLesson 7 of 15

Every segment improved. The total got worse.

Simpson's paradox is not a curiosity. It is a routine feature of any business with a changing mix.

The instrument Simpson's paradox

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A rate can improve in every single segment and get worse overall. This is not a trick and not a rounding artifact. It happens whenever the mix shifts towards segments with lower rates. Enterprise margin rises. Small business margin rises. Both improved. If the share of revenue coming from small business rose far enough, the blended margin fell, and every segment owner can accurately report an improvement while the business declined. So any organization reporting blended rates has a permanent source of undetected error, and it is worst exactly when the mix is moving, which is when it matters most. Two habits fix it. Never report a blended rate without the mix beside it. And when a blended number moves, decompose before explaining.

It is possible for a rate to improve in every single segment and get worse overall. This is not a trick and not a rounding artifact. It happens whenever the mix shifts toward segments with lower rates.

A concrete version. Enterprise margin rises from thirty to thirty two percent. Small business margin rises from ten to twelve. Both improved. If the share of revenue coming from small business rose from twenty percent to sixty, the blended margin fell, and every segment owner can accurately report an improvement while the business declined.

The consequence is that any organization reporting blended rates has a permanent source of undetected error, and the error is worst during exactly the periods when it matters most, because those are the periods when the mix is moving.

Two habits fix it. Never report a blended rate without the mix beside it. And when a blended number moves, decompose before explaining: how much came from the rate changing, how much from the mix changing. Those two have completely different causes and completely different responses.

The failure mode to watch for is a team that has learned to move the blended number by changing mix rather than by improving anything. It is not usually deliberate. Incentives do it on their own.

Two things worth doing, neither of which costs anything

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