The authors have declared that no competing interests exist.

The LEGO Group has become the largest toy company in the world and they can look back to a proud history of more than 50 years of producing bricks and other toys. Starting with a simple set of basic bricks their range of toys appeared to have increased in complexity over the years. We processed the inventories of most sets from 1955–2015 and our analysis showed that LEGO sets have become bigger, more colorful and more specialized. The vocabulary of bricks has increased significantly resulting in sets sharing fewer bricks. The increased complexity of LEGO sets and bricks enables skilled builders to design ever more amazing models but it may also overwhelm less skilled or younger builders.

The LEGO Group (TLG) has become the worlds largest toy company in the year 2015. The Danish brick-maker announced in its 2014 financial report [

The brick is no longer targeted exclusively at children. It is estimated that 5% of all LEGO purchases are made by adults that consider themselves as Adult Fans Of LEGO (AFOL). This group has dramatically grown in recent years which triggered the launch of several LEGO themed magazines, such as The Brick Journal, Blocks, and Bricks. The cult of LEGO has also been the topic of recent book releases [

Scientific investigations on the development of the LEGO products remain scarce. [

At times quantitative studies are being performed to investigate common misconceptions about LEGO products. A typical misconception is that LEGO has become more expensive. [

The interest in the development of the product prices is not limited to purchasing decision for the private use of LEGO sets, such as for birthday presents. Due to a growing secondary market for bricks and sets LEGO has become the object of financial investors. The Brick Picker (

The goal of this study is to investigate further common perceptions of the LEGO bricks in particular from a historical perspective such as:

How many new bricks and sets did TLG introduce each year?

Have the LEGO products become more colorful?

Have LEGO bricks become more specialized?

Has the number of bricks that occur in only one set increased?

Do LEGO sets contain more specialized bricks?

Do LEGO sets share less bricks with other sets of the same year?

Did the number of sets that can be build by taking bricks from other sets decrease?

To address the research questions mentioned above we executed several statistical operations. Any of these statistical operations are only as good as the data upon they are used. There are some catalogs of LEGO sets available [

Our analysis was restricted to the sets which contained at least one minifigure or brick piece and which did not contain any sub-sets. There were a total of 10953 such sets, of which 5384(49.2%) contained brick pieces only, 4896(44.7%) contained both brick pieces and minifigures, and the rest contained a combination of brick pieces (P), minifigures (M), booklets (B) and gears (G). There were a total of 7593 different minifigures in the dataset, 47375 and 27303 different brick pieces with and without taking the colour into account respectively, 318 booklets and 1049 gears. A total of 130 different colours have been used throughout the years. All the data processing and analysis has been done in R using the

The trends in the number of annually released new sets and bricks (with or without taking the colour into account), and minifigures are shown in

The average size of a new set has been increasing by an average 1.9% per year (95% CI: 1.2%; 2.5%,

While the sets were becoming larger, they were also becoming more diverse in terms of the number of different brick types involved. The average number of brick types in a set has been increasing at the average rate of 2.4% per year (95%

However, that also meant that the bricks were becoming more specialized. For example, the number of sets into which a brick was expected to be included in the next of 5 years, after adjusting for the total number of sets released in that period, was estimated to decrease annually by an average of 6.6% (95%

In general, 70.6% of all minifigures were found to be unique to a single set, which was significantly higher than the proportion of unique brick pieces, which was evaluated at 53.4% and 64.9% with and without taking color into account respectively. Over the entire study period, 2776 sets were found to contain at least one unique minifigure, 4789 sets were found to contain at least one unique brick (taking color into account). The odds of a set containing unique elements have steadily increased over the years at the average annual rate of 2.9% (95% CI: 2.6%; 3.3%) for colored bricks and that of 3.5% (95% CI: 2.8%; 4.4%) for minifigures (

The number of colours used annually has also been found to increase exponentially at the average annual rate of 4.4% (95% CI: 4.1%; 4.7%, _{y}(

We plotted the number of bricks in each color across time (see

The x-axis indicates years.

Since the number of bricks available in each increased over the years it is difficult to understand how the colors used for each year have changed. We therefore calculated the relative proportion of each color for each years (see

The x-axis indicates years.

While white, grey and black seem to have remained stable over the last centuries, the primary colors of red, yellow and blue have decreased. Many new colors and shades have emerged in particular in the last ten years.

It is also interesting to note the change in the two shades of grey in the year 2003. The new cooler greys completely replaced the old greys. A similar changed occurred for the dark brown which was replaced with a brighter more reddish brown.

Our results confirm the less formal analysis of [

We first have to introduce a measure of commonality of any two sets, _{i} and _{j} are the respective sizes of the two sets, and _{ij} is the number of bricks they have in common. The index is thus closer to 1 the more bricks are shared. If one set is completely included in the other one, the index

Because, smaller sets are likelier to be one-off, we have done the commonality analysis for all 10953 sets as well as for the 8848 sets with the size of at least 10. For the sets of all sizes, a total of 10278 (93.8%) shared at least one brick with at least one other set released in the same year, and a total of 10623 (97.0%) shared at least one brick with at least one other set released in the same year or later. For the sets of size 10 or more, the corresponding figures were 8731 (98.7%) and 8793 (99.4%) respectively.

The number of the ‘exclusive’ sets, which have no pieces in common with other sets is thus very small, and has been getting smaller.

The pattern is similar for sets of size 10 and above (not shown).

For non-exclusive sets, the index of commonality was found to have decreased from an average 0.12 in 1955 to an average of 0.09 in 2015. This corresponded to an average estimated 2% annual decrease (

The number of bricks and sets that TLG produces each year has increased annually by around 7%. The size of the sets, meaning the number of bricks in each set, has also increased by an average of 1.9% per year while the number of bricks of the largest set in each year increased on average by a staggering 5.0%. There is also a significant shift towards larger sets per decade.

The sets also include more diverse bricks. The average number of brick types in a set has increased on average by 2.4% per year and the maximum number of brick types in a set has even increased by 4.1%. The bricks have also become more specialized since their expected occurrence in the five year period following the sets release has decreased by 4.8% annually.

The sets have not only become larger and more diverse, they have also become more colorful. The number of colours in a set has been increasing at the average rate of 2.4% per year and the maximum number of colours in a set has been increasing at the average rate of 3.5% per year. Overall, the number of colours has increased exponentially at average annual rate of 4.4%.

Sets have also less parts in common. The commonality has decreased at an annual rate of 2.0% and is today at an absolute value of only 0.09. This is inline with the observation that the set sizes have increased and that the bricks have become more specialized.

Overall we can conclude that the LEGO products have indeed become far more complex. While TLG is still selling a product line of “basic” bricks, the number and sizes of sets has increased significantly. Sets have become more colorful and the bricks more specialized. Sets also share less and less bricks with each other. A judgment of whether this increase in complexity is good or bad remains difficult. Anybody interested in “basic” bricks can still purchase sets that only contain those. Nobody is forced into buying specialized bricks and sets. One can, however, argue that the strong reliance on more specialized bricks in combination with strong association to licensed themes may inhibit children to take their carefully build models apart to build something completely new. On the other hand one can argue that the bricks are comparable to a language. The increase in vocabulary size only means that writers can express themselves in ever more complex and imaginative ways. The gap between master builders and instruction followers may increase. But if we learned anything from The LEGO Movie [