I apologize in advance to anyone who is really hoping that the title of today's blog implies that I'm going to talk about some of Zeno's paradoxes. I usually write the title first - in haste - to get it out of the way, then revise it accordingly later. There's just something about this one that I find myself unable to revise. Perhaps I could start by revising half of it?
See, there you go, we got that out of the way. The focus is actually on car insurance commercials, though to be fair what you find inside is really more about what you take with you.
Good to get those Empire quotes out of the way early on as well, right?
I'm sure that almost all of you have seen the kind of commercials that I'm going to talk about. I spent some time on Google pulling some of them up, and it seems that almost every company has one (or two). I could have spent plenty of more time, but here are a few:
People who switched to Allstate saved an average of $348 per year.
Drivers who switched to Allstate saved an average of $396 a year. $473 if they dumped GEICO.
21st Century's customers saved an average of $474 a
year by dumping their current carrier.
Drivers who switched to Progressive saved an average of $550.
15 minutes could save you 15% or more on car insurance (Geico)
I'm betting that you as a reader might have one of two predominant thoughts. The first would be the thought that for this to hold true some of the companies must be lying. The second would be the thought that these companies know how to pick their wording well.
The key wording here is that people who are saving (or can save) are those people who switched. Well, of course you'd only switch if you were going to save, you might say. Exactly. This is another pretty nice example of commercials that are really talking to a small segment of the audience while making it sound like they're talking to everyone.
Let's walk through it, shall we?
I wanted to put together some data to illustrate some of what's happening here, and figured that a good way to do it was to come up with some random variables that give a potential picture of what people might be paying (or could be paying) across a number of car insurance companies.
I created a random variable, then created some random variables that correlate a decent level with the first (~.70). By virtue of the nature of these correlations these other variables also correlate a bit with each other. The lowest correlation among any of these variables is around .45.
We could just use these random variables to illustrate our point, but we can also make things a bit more concrete by finding some actual numbers. Numbers seem to be a bit tricky to find on the average annual cost of car insurance, and finding something like standard deviations on that average is that much more unlikely.
The broad average I've been able to find for annual car insurance costs is somewhere right around $1000, which is a reasonable place to start. Standard deviations might be more important if we were looking to replicate the exact amounts that people are saving, but for these purposes I'm going to just use a SD of $100 to keep things pretty straightforward.
Using all this information it's easy enough to create a matrix of people and the insurance quotes they'd likely get at a number of different companies. These are simply transformations of the random numbers that were generated. I've used the base numbers as the 'middle of the road' company, which is closest to the actual mean of $1000. Two companies are a bit cheaper (around $950 average), and two are a bit more expensive (around $1050 average).
Again, we can argue all day about how accurate these numbers are, but you can also translate things to a different level but simply scaling all these numbers a little differently. The intent is to illustrate a general concept, not to replicate the actual situation. There are also more than five car insurance companies out there, so this by no means would cover the entire market.
I've created 100 cases to work with, and each of those cases represents a person who can select from one of five car insurance companies. If we look at the overall average of what things would be like if people were randomly assigned to a car insurance company the average cost of car insurance for this group (not surprisingly) is right around $1000. I've heard there's certainly some money to be made by switching companies, though?
It's easy enough to examine - what's the average difference in cost between the company you're currently assigned to and each of the others? Well, averaged across all companies it should be near zero, but if we look at each individual company we should see a pretty clear pattern.
Switching away from the two cheaper companies will - on average - cost you around $15. Switching away from the more expensive companies will actually save on average around $50, and switching away from the middle of the road company for a random sample of those people will also save a little money (around $20). Such is the nature of random noise and low sample size.
Looking at the reverse actually gives us a picture of how much customers can potentially save by switching to that company. In this case there is a small benefit to switching to one of the two cheaper companies, but that's it. On average the savings is right around $15. Let's see if we can't make that number a little larger.
As was pointed out earlier there's no reason to switch to a company that's going to charge you more money (assuming that coverage stays constant). If we look at this first cheap company there's some people who will save money by switching and some people who won't. If you go back to the lines from commercials above you might now - if you haven't already - be picking up the language that lets us start to work these numbers.
$13 is the average savings for anyone to switch to the first cheap company. But why switch if you're not going to save money? There are plenty of people for which this isn't the cheapest company. If we look at just the people who have a reason to switch (i.e. those who would save money by doing so), we come up with a much different number. Now we're talking about a savings of $119 dollars - over $100 more.
Now that's something you can put in a commercial.
The reason is that all the people who wouldn't save money (in this metric people who would save negative dollars) are being removed from the calculation. These sorts of numbers do little to give us an ordering or magnitude of how cheap or expensive a company is, but rather how much noise there is in the market.
I'm sure we can do better, though. There's plenty of small values - $2, $0.74, etc. If you wanted the numbers to look a little better you might even tell your sales staff to discourage individuals from switching if they weren't going to save much money at all - it might not be worth the hassle. If we cut out the people who would save less than $10 annually we can move that average savings up to $129. Not too shabby.
This should only hold up for the cheapest companies, though, right? Nope, the same should be true for the expensive ones (in a reasonable market). There will be fewer people who save money by switching, but taking the average of those who have a reason to switch will always produce a savings (unless you're really doing something wrong/right). The savings for those who switch to expensive company 1? Right around $66. We can make the same <$10 cut here and raise that number to an average savings of $75 for those who switched.
That's not the only trick, either. If that $75 doesn't seem impressive enough we could also look at the 'up to' sorts of numbers. It's rare, but a few people can actually save over $300 a year by switching to expensive company 1. From this data I could make the statement that 'customers who switched to expensive company 1 can save up to $348 a year on their car insurance'. Run the percent on that and you're looking at something even harder for the average person to wrap their head around.
Before we go, there's another way we can look at this. We have five companies, and without assigning customers to any of them we can simply compare the numbers and see what percent of the time each of these companies actually has the lowest rate of all five companies. Here's how that breaks down:
Cheap company 1 = 30%
Cheap company 2 = 33%
Middle of the road company = 37%
Expensive company 1 = 0%
Expensive company 2 = 0%
Certainly interesting. The easy question from this set of information is how the middle of the road company is able to provide 37% of people with the lowest rate while still having a higher average price overall. Well, as all of this was derived randomly it does turn out that the middle of the road company has a slightly higher standard deviation than the cheaper companies. Also, the difference in means is not very large, so it doesn't take too much to undercut the cheaper companies. They end up making more money by - I'm sure some of you already have this figured out - charging a different segment of the population more than their average.
It's actually quite interesting in and of itself. A market such as this - with fixed but correlated rates - would eventually settle out (over some period of time) such that everyone ended up with the insurance company that was the best for them. The market does not have fixed rates, however, and those expensive companies need to find some way to stop the slow flux of customers away from them to the cheaper companies. Left alone, they would eventually stabilize to zero market share.
We can do this by strategically cutting or raising rates on certain segments of the population.
While there's no customers in this group that find expensive company 1 or expensive company 2 to be the cheapest place to go for insurance, it is occasionally close.
If we look at the 10 people who expensive company 1 find the cheapest to insure already (sorting expensive company 1's rates over all people), we find that on average these people are about $85 more than the lowest option. Thus, to get these 10 people on board they'd have to lower those 10 rates by at least $85 each, at least to pull them from a company that actually has a lower average rate. Let's say they decide to toss $90 a person at this (and now tell their sales staff that $5 is a big deal). That's still $900 just to get 10 customers, which doesn't seem that great.
Or does it? We still have 90 other people, some of which might already be customers of expensive company 1. All you have to do is transfer this loss onto the bills of people you've already sold, and you're set. It gets more expensive as you try to get customers that would be more and more of a risk to you (exemplified by higher rates), but that problem actually solves itself. If you bring on people with lower rates, you're still eventually going to have to raise those same rates. You'd need to do this to cover the new people you're bringing on with lower rates, or to cover the original deal you gave them. Soaking each of those new customers with an extra $90 the second year would be a very easy way to make this all work, obviously. Things will eventually get to the point that people are either paying a lot more than they should. At this point one of two things will happen. They'll either stay with you, or leave.
If they stay, great! Keep raising their rates and hope they don't notice. You didn't get a reputation of expensive company 1 for nothing. If they leave, even better! You now have new potential customers to win back by leveraging current customers costs into a means of undercutting other companies. If you don't believe that this works for insurance, might I point you to how cable companies work? It's actually a lot more transparent (yet still somehow effective) there. Try calling your cable company and getting your rate lowered - you can usually make some pretty quick money and solidify that fact that you're being overcharged.
This concept works so well at destabilizing equilibrium that I find it very hard to believe that insurance companies *don't* use it. Flaunting it in commercials is merely tipping their hand.
Let's take a step back, though. There's a lot of points here, and the main one that I think has the potential to get lost as I continued to expand on it is the trap of allowing others to define their own reference groups, and thus hide useful information. Saying that customers who switched to your company saved money is a triviality. By simple definitions this will be the case for all companies in even semi-competitive markets.
To bring it back to the start I made the point that some of you would assume that every company having one of these commercials must mean that (at least) some of them are lying. You can see now that it's possible that none of them are lying, depending on how you define lying (it's clear they're all misleading). These are exactly the sort of situations where people like to cite the old 'lies, damned lies, and statistics'. Statistics don't lie to people, car insurance companies do.
Does this mean you shouldn't have car insurance, or that you should switch companies several times a week? No, and not necessarily, respectively. You should get rid of cable, though.
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