Randomness, Probability, and House Selling

Yesterday for my birthday my darling wife got me a copy of The Drunkard’s Walk: How Randomness Rules Our Lives.  I’m only about a third into it, but it’s really a great read and I highly recommend it.  I’m kind of hoping by the end it will reveal to me whether my way of coping with the last bout of house selling blues was actually based in any kind of realistic mathematical models, or just silly superstition.  Though if anyone cares to take a whack at this particular problem I’d love to hear your feedback.

OK, here’s the deal: back in March we made our second attempt to sell our house.  It had been on the market from early September to late November last year with no success, but that’s a slow time of year for house selling so we weren’t completely discouraged yet.  The spring market is pretty active and a lot of people came, saw, and rejected the house.  Finally in late April we got an offer – two offers in fact.  The first was a real low ball, but our agent was able to use it as leverage to get the second – “We’ve got another offer, so if you want to make one now’s the time!”

Everything seemed great, and though it was taking longer than usual for the buyers to arrange for an inspection, we were happy to wait as we thought we could use the extra time to find a house to buy ourselves.  Then, on May 13th (my wife’s birthday) we were ready to put in an offer on a house we liked when we got the news – the buyer of our house had received a job offer in New Hampshire and was pulling out.  We had to put the breaks on our own offer and were basically back to square one.  Ugh.

We debated going back on the market.  Could we really handle round three?  Would we ever get an offer?  I logged into MA Pass, the system used by realty agents to schedule viewings of our house and to leave feedback, and collected a little data.  Between March and May we had 20 showings, of which two resulted in offers.  Thus, I reasoned, 1 in 10 people who see the house liked it well enough to make an offer.  It felt a little bogus given the fact that both offers came at the end of the 20 showings.   After showing 19 the number of offers was still 0.  Of course, that line of thinking though will lead down to hundreds of other unknowns — how many of those showings were second showings?  What about open houses, from which we have no stats?  There are so many factors I knew I had to pull back and ignore them all and just look at the raw numbers from a wide view — 20 showings, 2 offers, thus 1 in 10 showings results in an offer.

So we started showing the house again, and I started counting.  When a request came in I’d email Jenn – “it’s #5!”, “here we go, #8, almost there!”, etc.  Many showings ended with the same feedback that we had seen so many times before: “The second floor layout doesn’t work for my family.”  Yeah, the layout on the 2nd floor is a little unusual, it’s a very old house and that’s part of it’s charm.  We talked about adding a floor plan to the listing, but our agent advised against it.  “That might scare some people off,” he reasoned, “better to get as many showings as possible and hope someone loves it despite the odd layout.”

Showing number ten occurred on June 23rd, and the feedback was not surprising: “they decided the layout would not work.”  Then, we had a dry spell of no showings for over a week.  I admit, I was pretty discouraged at this point.  My theory had failed, and to be honest I wasn’t totally surprised.  We had had a few promising bits of feedback along the way.  Some buyers had narrowed their search down to ours and one or two others, but seemed to always choose one of the others. We had a couple relocating from Colorado say they liked it, but were waiting on their own house to sell.  Another couple apparently really liked it and saw it twice, but that was back on June 15th and we hadn’t heard anything from them since.

Then on July 3rd, three days before my own birthday and on the eve of a four day weekend we had another showing scheduled.  To be honest I didn’t expect it, I figured the holiday would mean people would be off traveling and not looking at houses.  I expected nothing from this showing, but was at least slightly buoyed by the fact that at the dry spell had ended.  The next morning, the 4th of July, I got an email from our agent — they liked it so much they put in an offer after just one showing.

And that’s where we are right now, trying not to get our hopes up too high as we’ve been here before.  Once the inspection is over and we have a signed contract, then I’ll celebrate.  Still, it’s encouraging, and I noticed very close to my original estimate.  It took 11 showings instead of 10, reducing our rate of offers from 10% to 9.677%.

Or maybe that math is pure baloney, and we just got lucky.  Ultimately it probably doesn’t matter, the math did what I needed to, it kept me sane from showing number one to showing number 9, from mid May all the way to the end of June.  Still, I can’t help but feel a little pride in how close I got with my prediction.  Perhaps I should take up a career in meteorology.  What do you think?

4 thoughts on “Randomness, Probability, and House Selling

  1. Glad you’ve got an offer on the table, definitely hope it works out for you.

    For what it’s worth, your math question is of course a statistical one (inferential): can we estimate the population proportion from a presumed random sample? In your case, the sample size is really too small to confidently make a prediction. The rule of thumb in the book that I teach out of is that successes and failures in the sample both have to be at least 5 (whereas you only have 3 offers at this point). If you broke that rule and applied the formula blindly in your case, then you’d come up with a 95% confidence interval that the real proportion was anywhere from 0% to 20%. (Link)

  2. Thanks Delta, I was pretty sure you’d swing by eventually with a nice mathematical proof that I’m full of shit. In fact, almost immediately after writing this I reached the part of my book covering Bernoulli and the law of large numbers, and read this little gem:

    The misconception — or the mistaken intuition — that a small sample accurately reflects underlying probabilities is so widespread that Kahneman and Tversky gave it a name: the law of small numbers. The law of small numbers is not really a law. It is a sarcastic name describing the misguided attempt to apply the law of large numbers when the numbers aren’t large.

    There’s nothing quite like being the target of a mathematician’s sarcasm. 🙂

    PS – It is my sincerest hope that I’m never able to determine the likability of my house with any level statistical certainty.

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