Please check the following dummy example to explain the paradox.

Both areas in the company keep the same market share during the years, but at the end company lost share in the market!

Math is 100% correct, both Areas worked well and reached their goal, but need to clarify why this happens (in simple words without using math).

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    $\begingroup$ This is not a paradox. [30% * (100/110)] < [25% * (110/100)], meaning overall sales and market share declined because the company positioned itself in a way that did not account for the shift in market size. I.e., the company had a larger share of the declining market (a relative loss) that outpaced the smaller share of the growing market (a relative gain). $\endgroup$ – amdopt Feb 5 at 12:41

This is known as the Simpson's Paradox in Statistics, which occurs when groups of data show one particular trend, but this trend is reversed when the groups are combined together.

Check the wikipedia page for some examples.

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  • $\begingroup$ Thanks, I didn't know and this is confortable to exist. But how I can explain my case in simple words? $\endgroup$ – Gianluca G Feb 5 at 12:17
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    $\begingroup$ In this case, in simple words, I would say both areas maintained their market share (25% and 30% respectively) but the area with 25% increased in relative terms (1100 vs 1000) whereas the area with 30% decreased in relative terms (1000 vs 1100). So the final market share in the current year has a bit more of the 25% and a bit less of the 30% than last year. $\endgroup$ – David Duarte Feb 5 at 12:28
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    $\begingroup$ Simpson's paradox, as already said. The market was flat over both areas, but the company was down, because it was more exposed than the market to the declining area. Therefore it lost total share, even if it's share of both areas rose. Everyone else lost share bottom-up, but gained it top-down, because they were more exposed to the better area. $\endgroup$ – demully Feb 6 at 9:27
  • $\begingroup$ This ( "the company was down, because it was more exposed than the market to the declining area") explains very clear. Thanks! $\endgroup$ – Gianluca G Feb 6 at 11:36

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