The two numbers represent slightly different meanings. The MLS exchange way is the average $/sq ft of a house. Your method is the average $/sq ft of the area.

Using the first method you would be able to determine the standard deviation to see what percentage of houses fit into each range. For example, if the average is 100/sq ft and the std deviation is 10, then I could say that 66% of the houses are between $90-$110/sq ft.

Going to your analogy, if I put all the shells from all buckets into the same bucket, weighed it and divided it, I have calculated the average weight/shell of shells. If I the weight/shell of each bucket and average those, I am calculating the average weight/shell of a bucket (i.e. looking at the differences between buckets vs looking at the differences between shells).

I’ll have to do it the same way we always do – the non-MLX way. I’m still having conversations with MLSChange about this. It looks like their sticking with their way so once I know that’s a done decision, I’ll have to decide if I want to change how I do my own stats.

Normally I put the stats out after the 15th because it takes that long for most of the solds from the month before to be marked “sold” by the listing agents. We’re suppose to do it within 10 days after a sale.

By the 10th we’d probably have most of them, but even when I post them after the 20th I notice the numbers still change later.

Taking a quick sneak peak at the data as it stands now, the number of sales stayed about the same and the average sold price went up from $242K to $249K. That may change of course, and that’s the MLXChange averages.
Steve

Steve

Thanks

Correct. We don’t just limit to sqft when setting a price, but it is something that is always looked at and given high weight.

But you’re right that in older neighborhoods such as Travis Heights or in Hyde Park where a lot will cost $250K, and many smaller homes are tear downs, we evaluate value in a different way when deciding on list price or offer price.

Nevertheless, when we see that the average price per square foot in MLS area 1B is around $280 psf, the land price is necessarily embedded in and reflected by the high price per square foot. It is a very reliable measure when the flaws are understood and other factors are properly noted.

From a practical standpoint, right or wrong, price per sqft is the language agents, buyers and sellers use when we are negotiating and determining value. On over-priced listings we often call the listing agent to ask which comps they used and how they set the value. If price per square foot can’t be validated by comparable sales of similar homes, or explained in some other way, we can’t justify to a buyer that they should set the new high water mark on price per square foot in the neighborhood. If the last 5 comparable sale in a neighborhood have been at $100 per square foot, and the seller wants to price the home at $110, I don’t need to do further analysis to know that the home won’t sell for $100. It just won’t, and average price per square foot accurately informs me of that.

In other words, it would be stupid not to look at price per square foot and compare it with that of other sales.

Square footage is the best and fastest measure of a starting value in homogeneous areas when looking at similarly sized homes, built by the same builder, in similar condition, on the same size/value lots, etc. Many, many Austin neighborhoods fit that criteria.

We do in fact see narrow ranges in homogeneous areas. That’s why it’s a lot easier to price a home correctly in bland subdivisions. On most CMA reports I will through out the high and low sale if they depart too much from the others, but we also know that in a rising market, we need to allow for upward movement in pricing.

In the broader sense of looking at ppsf, we don’t do it simply to price one home, we do it to look at trends, to compare last year to this year, to see which areas have rising values year over year and which areas are staying flat.

And along with ppsf we look at average sold price and median sold price, inventory levels, Active/Pending ratios, number of recent sales compared to number of active/pending, etc.

So, though I’m focused on price per square foot in this particular discussion, I don’t want to give the impression that it’s the only thing that matters or the only thing we look at.

Don: Thanks for your explanation. If I might add my own analogy:

Let’s say I have a bucket of sea shells. I know there are 1,000 shells in the bucket . The full bucket of 1,000 shells weighs 101 lbs and the empty bucket weighs 1 lb. So 1,000 shells weight 100 pounds. 100/1000 = 0.1.

Assume that there isn’t time to weigh and log each individual shell. You just have the total count and the weight. Is it a false statement to say that the average weight of each shell is 0.10 pounds? If so, what is the mathematical term used to describe what 0.10 represents? I thought, maybe incorrectly, it was “Harmonic Mean”.

And if I had 4 additional buckets with different amounts of shells (houses), and I wanted to know which bucket had the heaviest shells (higher ppsf) and which had the lightest (lower ppsf), wouldn’t the non-Arithmetic Mean method provide useful and meaningful data so long as it’s being used consistently and applied equally?

The real question still remains, why is Arithmetic Mean the best and most proper method of measuring average price per square foot in real estate data given that it is more subject to being skewed by small variances in the data set?

I think about it like a car with extremely touchy steering. The touchy and responsive steering may technically be “better” or more “accurate”, even technically superior in every way, but does it really serve my driving needs as well as a less touchy steering wheel would?

In looking at price per square foot averages, the Arithmetic Mean may be technically more accurate, but does that level of accuracy, and “touchiness”, best serve the real estate needs of agents, buyers and sellers as we evaluate sales data, pricing and trends?

Steve

I’ve decided that you shouldn’t be alone in having your head hurt from this response and that I would post to your blog (despite the fact that it is long and tedious).

The problem that you raised has nothing to do with harmonic means and harmonic means do not help you or MLXChange (which I will show below after I’ve addressed what is truly the issue).

MLXChange gives you the arithmetic mean of the rates (the $/sq.ft.) for a set of houses. What you generated is, in effect, the weighted average of the prices per sq ft of housing. Hopefully this will become clear below.

Let’s say that a 4000 sq ft house is sold at $100/sq ft, a 2000 sq ft house is sold at $80/sq ft, and a 2000 sq ft house is sold at 60/sq ft. When you ask for the average price/sq ft, for what are you truly asking? If you are asking, “what is the price per sq ft of the average house”, then MLXChange, when it says $80/sq ft, is giving the correct figure (because you are asking for the average across houses treated equally as one unit each). But if you are asking, “what per sq ft does housing cost in Austin (or in some particular neighborhood)”, then, with my example above, you have to account for the fact that much more house was sold at $100/sq ft than at either of the lesser rates, which is accomplished by taking the weighted average. If you take the total price of these three houses and divide by the total sq footage you get a rate of $85/sq ft, which makes sense. Because much more house was sold at $100/sq ft than at either of the lower prices, the weighted average is pushed closer to $100/sq ft. (Although it is complicated, you can calculate weighted averages directly by working with the proportions of the total sq footage sold at different rates—and this better fits with the concept of a “weighted” average.) So what is it that you want to know, how the price/sq ft compares among houses (treated as discrete units regardless of their relative size), which is the figure that MLXChange gives you, or how much housing costs per sq ft, which must account for the relative size of units sold at different prices?

Harmonic mean is irrelevant. I don’t think that I need to do anything more to prove that than to note that the harmonic mean in the scenario above is $76.6, which can’t possibly be a useful figure. Nevertheless, I will say more: The harmonic mean will always be closer to the lower rate. This is because whatever exactly is the work being done at this rate (traveling along a road or paying a price) it will always take longer at the slower rate, so it is always the case that more time is spent at the lower rate, and thus that the harmonic mean will be closer to the lower rate. For example, if you go up hill at 10mph and down at 30mph your average speed is not 20mph. Since you spent much more time at 10mph than at 30mph, your average is closer to 10 than to 30 (the average rate is actually 15—since ¾ of the time is at the lower speed, the rate is ¾ closer to the lower speed). This issue, however, is intrinsic to rates and the fact that lower rates always take longer than higher rates. So harmonic mean is about how to relate rates (on the presumption, in effect, that they are applied over the same total work/distance/price).

Even more of a digression on harmonic mean: To get the figure of $76.6 you would need to do the following: Pick a fixed price, say, $100,000. How large would three houses have to be at that price to have their prices per sq ft equal $100, $80, and $60 respectively? The answer is 1000 for the first, 1250 for the second, and 1666.66 for the third. Now, if you add up those square footages (3916.66), and divide that into the total money spent ($300,000), you will get the figure of $76.6/sq ft. So the harmonic mean is only relevant when you hold constant the amount of work to be done, be it the distance traveled or, in this case, the price to be paid for each house. The figure came out closer to $60 than $100 because, in our example, more of the sq footage was purchased at $60/sq ft that at $100/sq ft. This form of mean is completely irrelevant within your industry because it tells you only something intrinsic to the relationship of the rates, not anything about houses in the community.

This is a fundamentally different thing than a weighted average. Note that in my mph example the distance was the same in both cases and all we were relating was the rates (exactly the sort of case in which harmonic mean is relevant as shown in the wikipedia link and in my paragraph immediately above). The issue would have been rather different if we had traveled different distances at those different rates (and this is exactly what is addressed by a weighted average). Square footage of houses is analogous to distance in the mph example. We need to account for the fact that the rate is applied over different distances (sq footages). Obviously, this isn’t addressed by harmonic means because there is no way to put different distances into the formula (which only addresses the rates themselves).

Well, I hope that this was more interesting than it was tedious.

Don

At some level, such selection of comparables and knowledge of local conditions will always be the core value add of a realtor.

Just to give some context, we’ve been trying for years in construction to improve estimating with computer methods — and while we can count bricks better than ever and even systematize some of the art, there will always be room for judgement in assessing total costs.

Overall, I’d say that the averages that you report for market areas are broadly illustrative, but otherwise I would very suspicious of any CMA where the fundamental characteristics — lot size, house size, bedrooms and baths, location, schools, finish quality, soils, landscaping, community amenities aren’t considered. I suspect a limited comparison with true similarities will give a straightforward price for square foot. And when the calculation methods show some divergence, that is where intangibles based on judgement come in — attractiveness, market momentum, etc.

I honestly don’t think most Realtors would notice the difference. Only the ones who really pay attention to stats and like to crunch the numbers in different ways.

Sam,
> So we’re looking at the average of averages?

if you click on Peter’s link to the Wikipedia article about Harmonic Mean, it explains it. I also liked the “Arithmetic Mean” link in that article which further explained how Arithmetic Mean (what MLXChange uses, can be skewed by outliers while Harmonic Means remains more constant (as my examples showed).

Here is a quote from the AR article:
“The arithmetic mean is greatly influenced by outliers…A classic example is average income. The arithmetic mean may be misinterpreted to imply that most people’s incomes are higher than is in fact the case…For instance, reporting the “average” net worth in Medina, Washington as the arithmetic mean of all annual net worths would yield a surprisingly high number because of Bill Gates.”

This may be why most of the MLXChange produced price psf are higher than the ones I come up with, though they are sometimes lower as well. I think it depends on how many “outliers”, or sales amounts that are way above or below the meat of the pack there are.

I’m learning more about math than I need to know. I do know I want our MLS software to report the stats by whatever method would be deemed appropriate for than type of computation, and it appears they are not.
Steve

Exactly. For getting the average of rates (blah per blah), the harmonic mean is the “mathematically correct” way to go. However, if they did that in mlxchange, I’m sure they’d have even more realtors calling and asking them where they pulled that voodoo number from

Love the blog!