How to Interpret Market Share Changes: Reading a Ratio

When a market share moves, two numbers moved: the business's own sales and a total for the whole field. If they moved in opposite directions the share's direction is settled. If they moved the same way it is not, and no amount of thinking will settle it without both sizes. Half the readings an analyst meets cannot be read at all.

A share moved. What actually moved to make that happen?

Market Share: Where the Figure Actually Comes From sets out where a market share figure comes from, who assembled the document carrying it, and what the four routes to a field total actually are. The reading of a movement starts a step after all of that, and the step is small enough to say in a line: the figure exists, it moved between two years, and somebody is standing up in a meeting about to say what the movement means.

Two numbers went into that movement. One is the business's own sales, and a business can count its own sales. The other is a total for the whole field, and that cannot be counted. The work ahead is telling which of the two did the moving, and being honest when the answer is that nobody can tell. A market share is a ratio of two moving numbers, and that sentence is the whole of it.

A share is a fraction. The numeratorThe top number of a fraction, the one being divided. In a market share it is the business's own sales for the period. belongs to the business and the denominatorThe bottom number of a fraction, the one being divided by. In a market share it is a total for the entire field, and somebody had to estimate it. belongs to everybody, including every rival nobody has heard of. When that fraction changes, at least one of those two changed, and possibly both. Nothing about the changed fraction tells which.

The finance version is exactly the same shape as the household one, so the household version is worth holding on to. A salary went up nine per cent this year. Is that person further up the office pay list or further down it? Nothing is known about what happened to everybody else's pay, so there is no saying. The answer feels obviously unknowable when it is about salaries. The arithmetic has not changed at all when it is about registers, so it is precisely as unknowable there. A share is not a measurement of one business; it is a comparison, and a comparison has two participants, one of whom never agreed to be in the figure.

How many readings do two directions on two terms produce?

Most accounts of a moving share carry two stories. The share went up and that was good, or it went down and that was bad. Two things that can each go two ways produce four combinations rather than two, and a classification has to have as many cells as its tests produce. So draw all four and see what survives.

Own sales up while the field went down. The top of the fraction grew and the bottom shrank, so the fraction had to get larger. The share rose, and it is determined by direction alone, with no sizes needed anywhere. Own sales down while the field went up is the same reasoning in reverse: the top shrank, the bottom grew, so the fraction had to get smaller. The share fell, determined, again with no sizes.

Now the other two, and this is where the reasoning earns its keep. Both up: the top grew and the bottom grew. The fraction may be larger, smaller or exactly what it was. Both down: the top shrank and the bottom shrank, and the fraction may again be larger, smaller or exactly what it was. The word undetermined belongs in both cells, written in full. A hedge is a guess with better manners, so neither cell should be left blank and neither should be hedged with a probably.

Half the table cannot be read without both sizes, and the emptiness is the finding itself. It matters more than it looks, because the two open cells are the two that happen most often. Businesses and their fields tend to move together: a good year for one register maker is usually a good year for register makers, and a bad one is usually bad for everybody. The two cells a reader can settle by instinct are the two that turn up least.

What is the one rule that settles the two open cells?

There is a rule, and it is short. The share rises exactly when the business's own factorThe number being multiplied by. A factor of 1.125 means a rise of 12.50 per cent, a factor of 0.90 means a fall of a tenth, and a factor of 1.00 means no change at all. is larger than the field's factor. The share falls when the business's factor is smaller. The share does not move when the two are equal. The rule has no cases outside it.

The rule swallows the first two cells. If the business's factor is above 1.00 and the field's is below 1.00, then the business's is larger, and nobody needed to compare anything to know that: any number above one beats any number below one. If the business's factor is below 1.00 and the field's is above it, the business's is smaller by the same reasoning. The two determined cells are simply the cases where the rule answers itself without being asked for a size.

So the four cell table is not four separate rules but one rule, and two of the four cells are the cases where the rule needs no arithmetic to run. In the other two, both factors sit on the same side of 1.00, and knowing that they are on the same side says nothing about which is further along it.

The distinction is worth more than it looks, and it changes what a reader should do on hitting an open cell. The open cells do not need more thought, they need two more numbers, and the difference between those two things is the difference between a reader who waits and a reader who guesses. Thinking harder about a question with missing inputs produces a confident answer rather than a correct one. Somebody who knows the rule knows exactly what is missing and can go and ask for it.

What does it look like when sales rise and the share falls?

Take a business with a genuinely good year on the record. Anjani Stationers Private Limited, an invented stationer, took Rs 2,40,00,000/- of revenue in the first year and Rs 2,70,00,000/- in the second. The rise is Rs 30,00,000/-, and 30,00,000 divided by 2,40,00,000 is 12.50 per cent. Its factor is 1.125. Both of those revenue figures come off its own accounts and both are published in these notes; nothing about the 1.125 was made up here.

Now set a field factor of 1.25 beside it. The 1.25 is arithmetic that demonstrates a property of a ratio, and it is not a field. It carries no trade, no country and no year, and nobody publishes a movement for any field of Anjani Stationers Private Limited in either direction. The 1.25 is only a divisor with a value, set beside the 1.125 to give a division something to divide by.

Divide. 1.125 over 1.25 is 0.90 exactly. The share is 0.90 of what it was, a fall of 10.00 per cent, in a year when sales rose 12.50 per cent. One sentence carries the case: the business sold a great deal more, by any measure, and its share of the field fell by a tenth.

Notice how little the arithmetic needed. The starting share never came into it, and no field total for either year came into it either. Two factors went in and one factor came out, and the answer is a statement about the share compared with itself rather than about any level of anything.

Can one unchanged business produce a rise, a fall and no movement at all?

One unchanged business can do all three, and the claim is worth touching rather than reading. Below is one control and one fixed number. The business's own factor is published and does not move, so it stays at 1.125 at every setting. The only thing the control changes is the divisor.

Can the share rise without selling one more register?

Hold the business completely still now. The same registers, the same accounts, the same revenue as last year, to the rupee. Its factor is exactly 1.00, the arithmetic way of saying nothing happened. Set a constructed field factor of 0.90 beside it, on the same terms as before: no trade, no country, no year, a divisor put here to make a division visible.

1.00 divided by 0.90 is 1.1111. The share rose 11.11 per cent with not one extra register sold. Nobody worked harder, no account was won, no price was changed, and the figure a meeting would have looked at went up by more than a tenth.

The pair is far stronger than either half alone, so put this case beside the one before it. In the first, everything the business controls went right and the figure went down. In the second, nothing the business does changed and the figure went up. Between them they take away any reading of a share movement as a report card, in both directions at once.

The everyday version is a shop on a lane. The shop sold exactly what it sold last year. Two other shops on the lane shut. The shop is now a larger fraction of the lane and it is not a larger shop, and if somebody hands the shopkeeper a medal for it, the medal is being awarded for arithmetic. Notice too that a fall of a tenth in the divisor does not give a rise of a tenth in the answer. Falling by a tenth and rising by a tenth are not opposite operations, and that is why the number is 11.11 and not 10.00.

Why does subtracting one growth rate from the other give the wrong answer?

Almost every reader subtracts one growth rate from the other. The move is reasonable and it very nearly works, so start there. Sales up 12.50 per cent, the constructed field up 25.00 per cent, so take one from the other and call the share down 12.50 per cent. But the answer worked out by division was a fall of 10.00 per cent. The gap is 2.50 percentage pointsThe plain arithmetic difference between two percentages. A move from 10 per cent to 12 per cent is two percentage points, and it is also a rise of twenty per cent. The two units are never interchangeable. and it is not a rounding error.

The mistake fits in one line. Subtraction would be exact only if the field had not moved at all, and the field is the very thing being divided by. So the difference between the two growth rates has to be divided by the field's factor as well. Minus 12.50 divided by 1.25 is minus 10.00, exactly, and the gap closes to nothing.

One worked correction reads as a trick and two read as a rule, so run it on the second case too. Sales flat is 0.00 per cent and the constructed field fell 10.00 per cent, so subtraction gives 0.00 less minus 10.00, or plus 10.00 per cent. The true answer was a rise of 11.11 per cent, so the gap is 1.11 points, and 10.00 divided by 0.90 is 11.11 exactly.

The direction of the two errors is the easiest thing here to get backwards. In the first case subtraction overstated the fall, giving 12.50 where 10.00 was right. In the second it understated the rise, giving 10.00 where 11.11 was right. Subtraction is not consistently generous or consistently harsh. It is wrong in whichever direction the division happens to push. Subtracting the two percentages is right only when one of them is zero, and it is wrong by more the faster the field moved.

Where does the leftover go, and who decided?

The gap of 2.50 points is an old problem, and it has an old name. Splitting a change up into named effects leaves something over that belongs to neither of them, and the work of showing why, and of setting out the honest ways to deal with it, is done at length where a change in revenue is split into activity and yield.

One idea and one sentence carry over from that work. The idea is the choice. Measuring what one term did means holding the other term somewhere while the measuring happens, and there are two obvious places to hold it. Held at the opening levelThe value a term held at the start of the period, before anything moved. The alternative is the closing level, being the value it held at the end., where the period began, it is the convention Etienne Laspeyres put forward in 1871. Held at where the period finished instead, it is Hermann Paasche's, from 1874. Laspeyres and Paasche are named because the choice is theirs, and the choice is older than any slide it now sits behind.

The sentence worth carrying is inherited rather than invented here: a split that shows two numbers and no residualWhat is left over once the named effects have been taken out. A residual is a normal product of splitting a change up, not a sign that somebody worked carelessly. has not escaped the residual. Somebody put it somewhere, and the table does not say where.

So a share change presented as the business's growth minus the field's growth is a claim about a convention as well as a claim about a business, and only one of those two claims is usually on the slide. Which convention was used is a fair question, and the answer is often that nobody chose one at all, which is a different and more interesting problem.

What did this arithmetic compute, and what did it never need?

What has actually happened is unusual and worth pointing at, so turn round and look at it. Every figure produced here is a share compared with itself. Zero point nine of what it was. One point one one one one of what it was. Down 10.00 per cent. Up 11.11 per cent. Every one of them is a ratio of a share to a share, and a ratio of a share to itself needs no level at all.

The consequence follows. Not one of those figures required a starting share. So not one of them required a total for the field. So the whole argument ran without the one number nobody has. A ratio of a share to itself needs no level, and that is the only reason the argument can be made at all.

The freedom comes at a cost, and a trick shown without its price stays a trick. Knowing that a share fell by a tenth says nothing whatever about whether it fell from something large or something small. A business at a commanding position losing a tenth of it and a business at the edge losing a tenth of that are the same figure and completely different situations, and anybody deciding anything needs to know which. The arithmetic can read the movement and it cannot read the position, and a reader who assumes it managed both will act on a distance that was never measured.

How does a room get this wrong, and what does the mistake cost?

What should be asked before saying anything about a share that moved?

Which part of this is settled by location?

What may be said about the year after the one measured?

Every figure worked out above describes years that are finished. The 12.50 per cent happened. The 10.00 per cent fall follows from it and from a divisor made up here. Neither is a statement about a year nobody has observed yet, and turning either into one takes only a sentence and destroys the whole thing.

One observation is a level and not a direction, a point settled where the shape of a field over time gets worked out. A single movement between two years is exactly that: a movement, with two ends and no slope beyond them. Carried into a third year it becomes a projection, and a projection cannot be checked until the year it names arrives. Being uncheckable is precisely why projections get written and precisely why they should not be.

So the honest close is short. The size of the movement may be said. Which of the two terms moved further may be said, when both sizes are known. A reader may also be told that the direction is unknown, when it is unknown, and it will be unknown about half the time. One thing may not be done: taking a movement that describes a finished pair of years and handing it to somebody as a description of the next one.