Are we decentralized yet?

TIL about the Herfindahl–Hirschman Index and I wanted to test it with a weird corner-case that I remember.

At one point in the late 1980's Microsoft had a GREATER than 100% market share of the Macintosh spreadsheet market.

How is this possible?

Market share (for a given period) is the participant's sales in the market divided by total sales. It just so happened that Lotus had more returns than sales of their failed spreadsheet, Lotus Jazz. So Lotus, had a negative market share and Microsoft had more sales of Excel than total sales in the market, resulting in a greater than 100% market share.

I don't remember the exact numbers and I believe there was at least one other competitor in the study. But let's just say the numbers were:

Microsoft: 102% Lotus: -2%

In that case the Herfindahl–Hirschman Index would be 102^2 + (-2)^2 = 10404 + 4 = 10408.

So, in this pathological case it is possible for the HHI to exceed 10,000.

Edited: Added (for a given period) above, for clarity.

That's the beauty of software: It doesn't have a physical form, so you can buy it once but return it infinity times!

> The only way that makes any sense is if you subtract returns for sales made in a different period to the sales period you are considering

Exactly. That's the way accounting works. They did not know in the previous quarter that the product would be returned in the following quarter, so they end up having negative sales in the current quarter.

Yes it produces "garbage output", which I find amusing.

But that isn’t how you calculate market share, so what you’re saying is nonsense.

The story sounds fishy, but one way to have returns exceed sales is to ship 1,000 to stores on consignment, the store sells 500 of those for cash, the buyers return their 500 for refunds, and the store returns the remaining unsold 500. So 500 actual sales but 1,000 returns.

That is how it was calculated in a published trade magazine (either Infoworld or MacWeek, I think) I'm not sure if the the analysis was done by a market research firm or the magazine.

Presumably by a journalist who doesn’t understand what market share is

There are multiple ways of calculating market share (e.g. units vs dollars or for different time periods) but assuming it is measured in dollars for a quarterly time period, how would you calculate the market share based upon my sample data above?

I've heard of companies doing things like this to "cook the books" for a quarterly report.

I have diligently searched for this article online and have been unable to find it. (It might be on microfiche somewhere...)

I did however, find this humorous anecdote:

> A Lotus executive later joked, "The first month we shipped 62,000 copies, and the following month we got 64,000 copies back. It was such a failure they sent us the bootlegged copies back."

https://www.forbes.com/2003/12/16/cx_el_macslide.html

HHI is a super useful metric -- glad you like it!

The squared sum of normalized shares proves to be very useful in a lot of contexts -- not just market share. Voting is one great example.

>So 500 actual sales but 1,000 returns.

Sure. As long as we keep in mind that "return" doesn't mean "reverted sale", but "reverted shipment to retail".

Sounds depressing (i.e. ~5000 in a typical US election)

Everybody else is telling you you're wrong and you're doubling down and insisting that respectable journals are morons who don't understand anything.

You should stop, reflect on this fact for a moment, then go pick up a goddamn book

It gets really interesting when you look at the precinct and county level in the US, and similar types of views in European countries where they do real representative government.

(company sales in period - company returns for sales made in said period) / (industry sales in period)

With this formula market share for past periods can keep changing arbitrarily far into the future (depending on the companies' return policies).

It's ironic that national level politics mirrors the kind that the founding fathers did not ever want happening, while local politics has the kind of representation that they actually had in mind (in most places).

I'm not sure that is ironic.

Yes.

> Market share (for a given period)

That's not a thing. Market share has no time period. It's an instantaneous measure of the state of things right now. How many of your company's units are out in the wild right now being used, vs. how many total units (sold by any company) are out there in the wild right now being used.

That number can and will be different at different points of time, as people buy and return your products, and buy and return your competitors' products[0]. You can certainly say that your market share increased by 300% or by -40% over a given period of time, but your actual market share is always a number between 0% and 100%.

> Market share (for a given period) is the participant's sales in the market divided by total sales.

No, that's a company's share of sales as compared to the industry/product category as a whole. Not market share.

[0] You also should take into account people who throw your product in the trash (or for software, delete it) without returning it. Depending on context, you might even want to take into account people who put your product in a box in their basement and never use it again. Assuming you could actually divine those numbers, which of course you likely can't.

The 500 sent back by the consignment store aren't "returns" though, as they were never sold. That's just the equivalent of moving inventory from one warehouse to another.

No it's definitely ironic, in the rain on your wedding day kind of way.

The wikipedia definition is here:

https://en.wikipedia.org/wiki/Market_share

There are multiple methods of measuring multiple (related) things. What you are describing sounds more like the share of the installed base, which only works for certain types of products. (i.e. it doesn't work for consumables like apples or electricity)

Which is to say, the ultimate irony of Ms. Morisette's song is that there is no irony named.