Lego sets come in all different sizes with different numbers of Lego pieces. Of course bigger sets cost more, but is there a linear relationship between set size and cost? Let's take a look. Oh, and yes - I did look at this before, but that was a long time ago. It's time to revisit the data.

Lego Price Data —————

It's not too difficult to find data for Lego prices and number of pieces. If you just look on the Lego online store. There you can find both the price and the number of pieces for each set. You can even sort them by "themes" - like "Star Wars" or "friends"

Even though it's easy to get, I only collected price data for a subset of the themes (mostly because I am lazy). If I put all of this data together, I can get a plot of the set price vs. number of pieces in set. Here is what that looks like.

Let's look at the linear function that fits this data. The slope of this line is 0.104 US Dollars per Lego piece. Boom. There is your answer. On average, one Lego piece costs 10.4 cents. Also, I think it's nice to notice that this data is fairly linear.

But wait. What about the y-intercept for this fitting function? The value from the fit is 7.34 USD. That means that for this function, if you had a Lego set with zero pieces in it, it would still cost $7.34 - you know, for the box and instructions and stuff. Yes, I know that there are Lego sets cheaper than $7.34 - this is just the y-intercept for the fitting function.

Now let me point out the three outliers in this plot. Notice that all of these (one from Duplo and two from the City theme) are train sets. Of course train sets are going to be more expensive than a set with the same number of pieces (but not a train) because of the electric motors and stuff.

If you are looking for a "good deal", might I suggest the Trevi Fountain (21020). This set has 731 pieces for just $49.99. According to the fitting function, a set with this many pieces should cost about 83 dollars.

Which Theme Is the Most Expensive? ———————————-

Suppose I break all the data into the different themes. If I fit a linear function to each of the different themes, I can get both the price per piece of Lego and the price of a zero piece set.

Here are the brick prices for some of the Lego themes. The error bars are the uncertainties in the fit parameters.

If you know what a Duplo block is, you probably aren't surprised that they are the most expensive (63 cents per brick). These are bricks created for smaller kids. They are all large so that you can't swallow them. It just makes since that they would cost more. The other expensive bricks are the City sets. But this is deceiving due to the high set prices of the train kits. I suspect if you removed these train sets from the plot, it would be a more normal price.

What about the base cost? This is the y-intercept of the linear fit.

Here you will notice that the City theme has a negative base cost. This means that if there were no pieces (on average) in a City set, Lego would pay YOU money. But why is this negative? It's because of the high price of the train sets. They increase the slope of the linear fit but also push the y-intercept into negative values.

The real bargains are the Architecture themed sets. These have a base cost of only 70.7 cents where as the Marvel themed sets have a base cost of 3.61 USD.

Homework ——–

I've probably already answered some of these questions in the past, but it would still be fun as a homework assignment. Some of these aren't too difficult. You could think of them as Duplo Homework.

In my linear fits, I did not set the y-intercept to zero. What if you used the data and made fits with a zero y-intercept? What would that do to your price per Lego piece?

What about the other themes? Do they have similar prices per piece? Are there any unusually priced themes?

If you remove the train sets from the City data, what is the price per piece?

If you built a mini-fig scale model of the Death Star, how much would it cost?

I heard someone say that there are enough Lego bricks for everyone on the Earth to have 75 bricks. If these bricks were then sold (at a reasonable value) to some alien (off world) traders, how much would they have to pay for all the Earth's Lego bricks?

Notice that not even once did I use a plural version of the term "Lego".

Homepage image: fdecomite/Flickr