# Math-Up! Diving into the Heating Bills!

It’s time for a Math-Up! Let’s combine some boring, routine subject with some FUN AND EXCITING NUMBERS and maybe a sprinkle of personal finance.

#### Today’s topic

Today’s inaugural Math-Up! will focus on some concepts around utility pricing, specifically heating (this could easily apply to cooling as well). The idea for his little post here came about over the last few weeks. As I wrote about in the  October Monthly Expense Report, our house just got insulated, for the first time ever!

Well, the first gas bill just arrived since that work was completed. And to our surprise, the price is higher than expected, and the actual amount of energy used is up 23% compared to the same period last year!

#### What’s the problem?

So let’s try and focus this post a little bit by putting a problem statement together. Obviously, after spending nearly \$2,000 on upgrading our home we were expecting a noticeable improvement in our energy bill. The question can be simply: Why didn’t we see any improvement in our gas bill after majorly increasing the insulation in our house?

Bonus question: Was the insulation work a good investment?

#### The approach

First let’s lay out some facts and a simple idea.

1. I know I used more energy in 2016 than I did 2015 for the same time period
2. Our house just got major insulation upgrades
3. It was abnormally cold during the last billing cycle
4. We are going to look at energy used, not the balances on the bills
1. Gas prices vary too much to effectively use them to evaluate… anything

Looking at fact 1, and the blurb above from the recent bill, it is clear we used a substantial amount more energy than last year. (If we were talking at 23% increase year over on net worth, I’d be happy 🙂 ). Not shown above is the actual quantity of energy used, something the gas company measures in therms. This is just a unit of measurement, like gallons or kilograms, to measure how much heat the natural gas could create in an ideal combustion. Let’s think of therms like gallons of gas.

Fact 2, is straightforward. We just spent a decent sum of money insulating our once empty walls and certain ceilings. Before the work, there was only sheet rock and a few layers of various siding preventing heat from escaping our little home. When it gets to be below 0 Fahrenheit, that is some serious heat loss. Adding insulation only slows the heat loss (it is impossible to stop unless we are dealing with some crazy vacuum sealed walls, which would still have thermal bridges). But slowing it down means your heating unit does not need to run as frequently. Our usage SHOULD go down! If I am going to make a car analogy, let’s think of our added insulation as upgrading from a Corolla to a Prius. We expect better efficiency and fewer gallons used per month.

And finally the fun part! I think that it was abnormally cold during the most recent billing cycle. How can I use that idea to help answer our question?

#### Heating Degree Days

If you have ever researched air conditioning units, furnaces, heat pumps or any type of HVAC system, you may have come across Cooling Degree Days (CDD) or Heating Degree Days (HDD). More or less, it is an alternative way to look at outside air temperatures. Instead of looking solely at a month, or even daily, average temperature, HDD is a quantification of how much and how long the outside air temperature was lower than an inside base temperature.

If you took calculus, HDD/CDD is the “area under the curve” where the curve is the outside air temperature and the baseline is your indoor temperature.

You can read much more about Degree Days on Wikipedia or the like. But if you end up wanting to evaluate your house, and any energy improvements, you can find historical data in downloadable format from: http://www.degreedays.net/

Back to our problem.

#### The approach, cont.

To answer our question about why the insulation didn’t decrease our energy usage, we need to gather some data.

1. Historical heating data in therms
1. I transcribed these from old bills available online (date and therms used)
2. Historical HDD for the same time period
1. I used the above site and downloaded in CSV format daily HDD values for the past three years near my house

What I want to do now is normalize the energy usage (therms) by involving the HDD values I downloaded. I didn’t state this above, but essentially we are going to measuring the efficiency of heating our house. By combining the therms data with the HDD we are going to create a unit similar to MPG found in a car. This is at best an educated estimate, there are too many variables to consider. More on that below.

So I pasted both sets of data into my spreadsheet and created a new type of unit, therms per HDD. This is our MPG rating for heating the house! Let’s see if it helps answer our problem statement.

#### Pretty charts

You can see clearly in this first plot that therms being used follows tightly with HDD. During the summer/warm months the HDD are very low, practically zero. But there the therms being used reliably outpaces the HDD, compared to the rest of the chart where the opposite relationship is true.

This is our first issue. The therms value being provided from the energy company is not just heating, but also gas consumed for cooking and the hot water tank.

Here is the plot I was hoping to get a clear answer from, our house MPG equivalent. First takeaway, the efficiency of the house on that Dec-2016 bar seems inline with everything else. We did use more energy per our bill, but it was most likely because the outside air temperature was much colder. This is good news! It means the insulation work didn’t create another problem.

What I do not see is a sharp decrease in the therms/HDD number, which in our case would mean higher efficiency. My first thought is that the billing cycle for that period had only about two weeks of insulated house, out of four. This might not be enough time to see a decrease in energy usage. This is our second issue. We do not have enough data since the house has been insulated to draw a conclusion if the investment was worth it.

But there is an underlying third issue. To go back to the car analogy. If you take the same car around the same track two times you can get wildly different MPG values. Driver A floors the accelerator, brakes hard for every corner, and floors it again. Driver B maintains one slow, but ideal speed the whole time (boring… ). Surely Driver A will have a MPG rating MUCH lower than Driver B.

All of the historical therms data does not capture how the heating unit was being used. We could have had a month where the heat was turned up because some was sick. Or we could have been on vacation and left the house turned down. Unless the temperature inside was a perfect constant, there is going to be some noise in the data.

#### Wrapping up

Our house got insulated, we received our first bill and surprisingly our energy usage was more than the same period last year. Creating a new value to gauge heating efficiency we saw that the insulated house is behaving mostly the same. Good that there is no new problem and provides an answer as to why the energy bill moved higher.

The question remains whether the insulation was worth the investment. However, the data at present is unable to conclude one way or the other.

The data points post-insulation are too few. Even with enough data, the signal will need to be strong enough to overcome the noise created by hidden gas usage from cooking and the hot water tank. Interior temperature will need to remain consistent between billing cycles to minimize effects from varying heat loads. Once this winter is over this post will be revisited.

But, stepping away from the numbers for a bit, the insulation was well worth the cost. This conclusion is based on physical comfort, something much harder to quantify. The room-to-room temperature variation seems to have stabilized.

Not all investments should be solely measured in dollars or cents. Instead, some investments are for peace of mind, which at the end of the day out values a few hundred in the bank. Take this as a reminder, that life is not about pinching pennies. Too often I read about those working towards FIRE making “odd” choices based on return on investment. I suggest everyone take a step back during all financial decisions to see beyond the bottom line.