title: A Fair Price for Darth Vader's Medidation Chamber? A Lego Price Analysis

tags: Lego, Python

Earlier this week I was taking a break from work and browsing lego.com (as one does), and came across Darth Vader's Meditation Chamber (75296), which is newly available for preorder.

My first thought was "this looks nice, but $69.99 feels a bit steep for 663 pieces." Being both a Lego and data nerd, I decided to see how good or bad this price actually is compared to other sets.

Most of my Lego collection

I searched for a freely available source of data on Lego set prices, but didn't find any that were suitable to answer my question. After a few hours of frustration, I wrote a small Python script using Beautiful Soup to scrape brickset.com's historical data on Lego sets dating back to 1980. Out of respect for the hard and excellent work of the Brickset team, I won't be sharing the scraper code, but I have made the data set (scraped on June 1, 2021) publicly available. This is the first post in a series analyzing this data.

In [1]:
DATA_URL = 'https://austinrochford.com/resources/lego/brickset_01011980_06012021.csv.gz'

First we make some standard Python imports and load the data.

In [2]:
%matplotlib inline
In [3]:
import datetime
from functools import reduce
from warnings import filterwarnings
In [4]:
from matplotlib import MatplotlibDeprecationWarning, pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns
In [5]:
filterwarnings('ignore', category=MatplotlibDeprecationWarning)
In [6]:
plt.rcParams['figure.figsize'] = (8, 6)

sns.set(color_codes=True)
In [7]:
def to_datetime(year):
    return np.datetime64(f"{round(year)}-01-01")
In [8]:
full_df = (pd.read_csv(DATA_URL,
                       usecols=[
                           "Year released", "Set number",
                           "Name", "Set type", "Theme", "Subtheme",
                           "Pieces", "RRP"
                       ])
             .dropna(subset=[
                 "Year released", "Set number",
                 "Name", "Set type", "Theme",
                 "Pieces", "RRP"
             ]))
full_df["Year released"] = full_df["Year released"].apply(to_datetime)
full_df = (full_df.set_index(["Year released", "Set number"])
                  .sort_index())
In [9]:
full_df.head()
Out[9]:
Name Set type Theme Pieces RRP Subtheme
Year released Set number
1980-01-01 1041-2 Educational Duplo Building Set Normal Dacta 68.0 36.50 NaN
1075-1 LEGO People Supplementary Set Normal Dacta 304.0 14.50 NaN
1101-1 Replacement 4.5V Motor Normal Service Packs 1.0 5.65 NaN
1123-1 Ball and Socket Couplings & One Articulated Joint Normal Service Packs 8.0 16.00 NaN
1130-1 Plastic Folder for Building Instructions Normal Service Packs 1.0 14.00 NaN
In [10]:
full_df.tail()
Out[10]:
Name Set type Theme Pieces RRP Subtheme
Year released Set number
2021-01-01 80022-1 Spider Queen's Arachnoid Base Normal Monkie Kid 1170.0 119.99 Season 2
80023-1 Monkie Kid's Team Dronecopter Normal Monkie Kid 1462.0 149.99 Season 2
80024-1 The Legendary Flower Fruit Mountain Normal Monkie Kid 1949.0 169.99 Season 2
80106-1 Story of Nian Normal Seasonal 1067.0 79.99 Chinese Traditional Festivals
80107-1 Spring Lantern Festival Normal Seasonal 1793.0 119.99 Chinese Traditional Festivals

Most of the fields are fairly self-explanatory. RRP is the recommended retail price of the set in dollars.

For fun, I have also exported my Lego collection from Brickset and load it now.

In [11]:
MY_COLLECTION_URL = 'https://austinrochford.com/resources/lego/Brickset-MySets-owned-20210602.csv'
In [12]:
my_df = pd.read_csv(MY_COLLECTION_URL)
In [13]:
my_df.index
Out[13]:
Index(['8092-1', '10221-1', '10266-1', '10281-1', '10283-1', '21309-1',
       '21312-1', '21320-1', '21321-1', '31091-1', '40174-1', '40268-1',
       '40391-1', '40431-1', '40440-1', '41602-1', '41608-1', '41609-1',
       '41628-1', '75030-1', '75049-1', '75074-1', '75075-1', '75093-1',
       '75099-1', '75136-1', '75137-1', '75138-1', '75162-1', '75176-1',
       '75187-1', '75229-1', '75243-1', '75244-1', '75248-1', '75254-1',
       '75255-1', '75263-1', '75264-1', '75266-1', '75267-1', '75269-1',
       '75273-1', '75277-1', '75278-1', '75283-1', '75292-1', '75297-1',
       '75302-1', '75306-1', '75308-1', '75317-1', '75318-1'],
      dtype='object')

We add a column to full_df indicating whether or not I own the set represented by each row.

In [14]:
full_df["austin"] = (full_df.index
                            .get_level_values("Set number")
                            .isin(my_df.index))

Exploratory Data Analysis

First we check for any missing data.

In [15]:
full_df.isnull().mean()
Out[15]:
Name        0.000000
Set type    0.000000
Theme       0.000000
Pieces      0.000000
RRP         0.000000
Subtheme    0.241825
austin      0.000000
dtype: float64

About a quarter of the sets do not have a Subtheme, but each set has data for every other column. We see below that most sets are classified as "normal" building sets, but there are some books and other types of sets present in the data.

In [16]:
ax = (full_df["Set type"]
             .value_counts(ascending=True)
             .plot(kind='barh'))

ax.set_xscale('log');
ax.set_xlabel("Number of sets");

ax.set_ylabel("Set type");

For simplicity, we will focus only on "normal" sets.

In [17]:
FILTERS = [full_df["Set type"] == "Normal"]
In [18]:
df = full_df[reduce(np.logical_and, FILTERS)]

We still have information on over 8,000 sets.

In [19]:
df["Pieces"].describe()
Out[19]:
count     8163.000000
mean       265.848095
std        489.269642
min          1.000000
25%         34.000000
50%        102.000000
75%        310.000000
max      11695.000000
Name: Pieces, dtype: float64

The set with the most pieces is the recently released World Map, (31203-1).

In [20]:
df.loc[df["Pieces"].idxmax()]
Out[20]:
Name            World Map
Set type           Normal
Theme                 Art
Pieces            11695.0
RRP                249.99
Subtheme    Miscellaneous
austin              False
Name: (2021-01-01 00:00:00, 31203-1), dtype: object

I love the idea of a Lego world map, but I'm not in love with the ocean color, so I'll probably pass on this beast.

We see below that here are many sets with very few pieces (presumably replacement parts, minifigures, and promotional sets).

In [21]:
max_pieces = df["Pieces"].max()
plt_max_pieces = 1.1 * max_pieces

ax = sns.kdeplot(data=full_df, x="Pieces",
                 label="All sets")
sns.rugplot(data=full_df, x="Pieces",
            c='k', alpha=0.1, ax=ax);

THRESHES = [1, 10, 25, 50, 100]

for thresh in THRESHES:
    sns.kdeplot(data=full_df[full_df["Pieces"] > thresh],
                x="Pieces",
                clip=(thresh, plt_max_pieces),
                label=f"Sets with more\nthan {thresh} pieces",
                ax=ax);

ax.set_xscale('log');
ax.set_xticks(THRESHES + [10**3, 10**4])
ax.set_xlim(0.9, plt_max_pieces);

ax.set_yticks([]);
ax.legend();

We filter our analysis to sets with more than 10 pieces.

In [22]:
FILTERS.append(full_df["Pieces"] > 10)
In [23]:
df = full_df[reduce(np.logical_and, FILTERS)]

Note that by using FILTERS.append the order of execution of cells in this notebook becomes very important (notebooks are bad, etc., but I love them anyway).

We now examine the distribution of sets across themes.

In [24]:
(df["Theme"]
   .value_counts()
   .describe())
Out[24]:
count    134.000000
mean      52.992537
std       94.157163
min        1.000000
25%        7.000000
50%       19.000000
75%       52.500000
max      556.000000
Name: Theme, dtype: float64
In [25]:
n_theme = df["Theme"].nunique()

N_THEME_PLOTS = 12
N_THEME_COLS = 2
n_theme_rows = N_THEME_PLOTS // N_THEME_COLS

n_themes_per_plot = int(np.ceil(n_theme / N_THEME_PLOTS))
In [26]:
fig, axes = plt.subplots(nrows=n_theme_rows, ncols=N_THEME_COLS,
                         sharex=True, sharey=False,
                         figsize=(16, n_theme_rows * 6))

theme_ct = df["Theme"].value_counts()

for i, ax in zip(range(0, n_theme, n_themes_per_plot),
                 axes.flatten()):
    (theme_ct.iloc[i:i + n_themes_per_plot]
             .plot(kind='barh', ax=ax));
    
    ax.set_xscale('log');
    ax.set_xlabel("Number of sets");

    ax.invert_yaxis();
    ax.set_ylabel("Theme");

fig.tight_layout();

Unsurprisingly, the Star Wars theme has the most sets historically. That Duplo comes in second is interesting. We filter out Duplo sets, service pack, and bulk brick sets from our analysis.

In [27]:
FILTERS.append(full_df["Theme"] != "Duplo")
FILTERS.append(full_df["Theme"] != "Service Packs")
FILTERS.append(full_df["Theme"] != "Bulk Bricks")
In [28]:
df = full_df[reduce(np.logical_and, FILTERS)]

Set Price

We now turn to the question that prompted this work, whether or not Darth Vader's Meditation Chamber is overpriced. Our set data spans 1980-2021, and we see that the number of sets released has been increasing fairly steadily over the years.

In [29]:
ax = (df.index
        .get_level_values("Year released")
        .value_counts()
        .sort_index()
        .plot())

ax.set_xlabel("Year released");
ax.set_ylabel("Number of sets");

Since the data spans more than 40 years, it is important to adjust for inflation. We use the Consumer Price Index for All Urban Consumers: All Items in U.S. City Average from the U.S. Federal Reserve to adjust for inflation.

In [30]:
CPI_URL = 'https://austinrochford.com/resources/lego/CPIAUCNS202100401.csv'
In [31]:
years = pd.date_range('1979-01-01', '2021-01-01', freq='Y') \
            + datetime.timedelta(days=1)
cpi_df = (pd.read_csv(CPI_URL, index_col="DATE", parse_dates=["DATE"])
            .loc[years])
cpi_df["to2021"] = cpi_df.loc["2021-01-01"] / cpi_df
In [32]:
fig, (cpi_ax, factor_ax) = plt.subplots(ncols=2, sharex=True, sharey=False,
                                        figsize=(16, 6))

cpi_df["CPIAUCNS"].plot(ax=cpi_ax);

cpi_ax.set_xlabel("Year");
cpi_ax.set_ylabel("CPIAUCNS");

cpi_df["to2021"].plot(ax=factor_ax);

factor_ax.set_xlabel("Year");
factor_ax.set_ylabel("Inflation multiple to 2021 dollars");

fig.tight_layout();

We now add a column RRP2021, which is RRP adjusted to 2021 dollars.

In [33]:
full_df["RRP2021"] = (pd.merge(full_df, cpi_df,
                               left_on=["Year released"],
                               right_index=True)
                        .apply(lambda df: df["RRP"] * df["to2021"],
                               axis=1))
In [34]:
df = full_df[reduce(np.logical_and, FILTERS)]

Here we plot the most obvious relationship pertinent to my initial question about Darth Vader's Meditation Chamber, price versus number of pieces.

In [35]:
ax = sns.scatterplot(x="Pieces", y="RRP2021", data=df, alpha=0.1)
sns.scatterplot(x="Pieces", y="RRP2021",
                data=df[df["austin"] == True],
                alpha=0.5, label="My sets");

ax.set_xscale('log');

ax.set_yscale('log');
ax.set_ylabel("Retail price (2021 $)");

The relationship is fairly linear on a log-log scale, which will be important in subsequent posts when we introduce more complex statistical models. The sets in my collection are highlighted in this plot.

We can also highlight certain themes of interest to see where the sets from those themes fall.

In [36]:
PLOT_THEMES = [
    "Creator Expert",
    "Disney",
    "Star Wars",
    "Harry Potter",
    "Marvel Super Heroes",
    "Ninjago",
    "City",
    "Space",
    "Jurassic World"
]
In [37]:
grid = sns.relplot(x="Pieces", y="RRP2021", col="Theme",
                   data=df[df["Theme"].isin(PLOT_THEMES)],
                   color='C1', alpha=0.5, col_wrap=3, zorder=5)

for ax in grid.axes.flatten():
    sns.scatterplot(x="Pieces", y="RRP2021", data=df,
                   color='C0', alpha=0.05,
                   ax=ax);
    
    ax.set_xscale('log');

    ax.set_yscale('log');
    ax.set_ylabel("Retail price (2021 $)");