To understand what’s going on with MNsure, we can appeal to dogs for enlightenment.

Consider a world in which there are only four dog breeds: Border Collies, Huskies, Malamutes, and Utonagans (yes, there is such a thing). All Border Collies live for 17.2 years, all Huskies for 8.1 years, all Malamutes for 1.8 years (poor things), and Utonagans for negative 9.1 years (dying 9 years before they are born; best to overlook the metaphysical implications).

If we then compute the average lifespan, we’d find that the “average” dog lives to be 4.5 years. But does that 4.5-year average lifespan give you any meaningful information about how long your dog will live?

Not really. And what if there were altogether 22,000 dogs, but only 770 of them were Utonagans? Would that change things? Shouldn’t the life expectancy be adjusted according to the number of dogs in each breed?

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Welcome to statistics.

If we switch from dogs to MNsure providers, the above scenario is part of what’s at issue in the debate over the recently announced increase in MNsure rates. Last week, MNsure providers — Blue Cross Blue Shield, HealthPartners, Medica, and UCare — and the Minnesota Department of Commerce reported the percentage changes in rates for 2015 as, respectively, increases of 17.2 percent, 8.1 percent, 1.8 percent; and a decrease of 9.1 percent.

The strict mathematical average of these four numbers is indeed 4.5 percent. But does that 4.5 percent number give any meaningful information about individual rate increase? It doesn’t, for the same reason the average lifespan didn’t tell us about how long your dog would live. Unless you are bundling coverage in equal amounts from these four providers, the increase in a person’s premium will not come close to a 4.5 percent increase.

The 4.5 percent number gets even more confusing when we consider that the provider with the lowest rates and the most private health plans in MNsure (with 60 percent of them), Preferred One, is leaving the program. The exclusion of Preferred One further skews the statistics, because any Preferred One consumer who either switches to one of the other providers or stays with Preferred One will have a much, er, healthier increase. (We won’t even mention that a HealthPartners spokesman said that he wasn’t sure how the Commerce Department arrived at the 8.1 percent figure.)

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A better measure of the increase is a weighted calculation. That is, the providers with more subscribers would have their increases given proportionally greater significance in computing the overall change. Of the four providers, Blue Cross Blue Shield has 55 percent of the remaining MNsure subscribers (or about 12,300 people); HealthPartners has 30 percent (6,800 people); Medica, an 11 percent share (2,500); and UCare a 3 percent share (770).

Using a weighted measure, the aggregate increase in revenue for these four providers — assuming no changes in the subscriber base — would be approximately 11.8 percent, which more accurately reflects the increase in premiums. But that 11.8 percent still doesn’t take into account the wild card of the 60 percent of MNsure subscribers orphaned after Preferred One jumped ship.

The Commerce Department’s officially reported 4.5 percent increase, then, is a number that has little to do with the change in what any given MNsure subscriber will have to pay.

So the kerfuffle over the “true” measure of the MNsure rate increase is a wonderfully flexible plaything, a Crazy 8 ball that gives a different – and likely irrelevant – answer as many times as you spin it. (And let’s not forget the likelihood that increases for some MNsure subscribers will be offset by tax credits.) Perhaps the safest thing to say is: MNsure subscriber will almost certainly be paying more, in some cases not too much, in some cases more than not too much.

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David Brokken teaches math at the University of Minnesota.