[msgilligan]

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.

[msgilligan]

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

[kelnos]

> 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.

[msgilligan]

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)

[tomrod]

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.

[msgilligan]

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

[tomrod]

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.

[fakedang]

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).

[naniwaduni]

I'm not sure that is ironic.

[asdfasvea]

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