Drupal Public Data, Statistics & Silver Linings? An Exploration #3

This is part 3 of a 5-part series examining Drupal public data in search of actionable insights.

Preamble

Previously, this article presented Drupal installations data, a roster of mathematical and statistical tools, and a producer-centric innovation adoption model.  While that exercise failed to produce an accurate predictive model, it did demonstrate the power of modeling to help explain the past, narrate the present and potentially help to drive decisions about the future.  Here, we seek to reconstitute those ingredients into a new, better model and discuss whatever it uncovers.

The Futile & Wishful Thinking of the S-Curve Drupal Adoption Model

Despite the fervent desires of innovation-oriented organizations for everyone to immediately crowd into their latest innovation, we know that is not how things work in real life.  Everyone is familiar with people who are "stuck in their ways" and still using (sometimes quite proudly) antiquated technology.  Rogers recognized this fact way back in the 1950's.  In fact, it is the underlying theme behind his Innovation-Adoption Curve, and his continued urging that it be used to model adoption in a more realistic way when it comes to how people actually engage with innovation.

What Knowledge Could a "Realistic" Drupal Adoption Model Express?

One of the more powerful inferences that can be drawn from the Innovation-Adoption Curve is that half of any audience hesitates to adopt an innovation when compared to the average case.  A simple corollary is this:  Whenever a producer releases an innovation, only half of its existing audience embraces it in "a timely manner" from the perspective of the producer.  What Rogers did not explicitly mention in his model is exactly when that half-adoption occurs.  Happily, this time can be estimated using Statistics, via a sufficient number of representative samples drawn from the target population.  But the actual duration is different for every model, and even different for the same model across time itself as external conditions vary around it.

Constructing a "Realistic" Drupal Adoption Model

Despite these powerful caveats, the Innovation-Adoption Curve can still be put to some use in order to help us constitute a new model that is markedly different from the preferred S-Curve Model that innovation-oriented companies tend to use.  It might even turn out to be "better", with better defined as its ability to more tightly "fit" the numbers being used to represent observed reality.

"Realistic" Drupal Adoption Model Assumptions

Like every model, a proposed "Realistic" Drupal Adoption Model needs to be anchored to a set of assumptions to help get it off the ground.  Many, many assumptions can be loaded into a model.  Human-generated models feature hundreds or even thousands of assumptions.  AI-driven models can sometimes feature millions or even trillions of assumptions. In our case, we will use a small number of explicit assumptions, leaving the rest implicit:

• Drupal wants its audience to upgrade to newer versions of Drupal as soon as they are available.  In other words, Drupal expects Drupal 7 users to immediately adopt Drupal 8 as soon as it is made available.  This is true for every new release of Drupal.
• The typical Drupal customer has not changed their reason for choosing Drupal since their initial selection.  In other words, the typical Drupal user chooses Drupal today for the same reasons they chose Drupal yesterday.
• The audience decay function of the "More Realistic" Drupal Adoption Model mirrors the implicit assumption of the Innovation-Adoption Curve in that only half of each generation readily adopts the new version, and half do not.  This gives a decay function of y = 0.5x.
• The total number of Drupal installations (675,218) is true.
   

The "Realistic" Drupal Adoption Model Data

The following model results from the application of the assumptions to the installations total:

Criticisms of the "Realistic" Drupal Adoption Model

The "Realistic" Drupal Adoption Model can be criticized in a number of ways:

• It is almost entirely detached from reality.  It was "reverse engineered" from a single number.  Aside from that sole number, it contains no other real-world information. 
• It accepts at face value that the Rogers Innovation-Diffusion Model is correct about innovation adoption; i.e. that it distributes classically and normally.
• The growth/decay function (y = 0.5x) is patently incorrect.  This decay function does not even capture 100% of actual installations, being 5,275 installations short.  To capture all installations, y = 0.534356553428108x.
• Simple decay functions are almost useless at the extremes because they generate tiny or huge values.  For example, this model predicts that the next edition of Drupal will have an audience equal to that of the entire current installation base (675,218).  This is improbable and unrealistic.

Figure 6:  The "Realistic" Drupal Adoption Model Visualized

Here's what the "Realistic" Drupal Adoption Model looks like when presented visually:

Figure 7:  The "Realistic" Drupal Adoption Model Compared to Reality

Here's what the "Realistic" Drupal Adoption Model looks like compared to reported installations:

What Does the "Realistic" Drupal Adoption Model Reveal?

Despite its flaws, the "Realistic" Drupal Adoption Model reveals some interesting things:

1. Drupal 5 installations do not appear to line up with the model (it is at an extreme)
2. Drupal 6, 8, 9 and 10 appear to more or less line up with the model
3. The number of Drupal 11 installations seems far short of the model (it is at an extreme)
4. The number of Drupal 7 installations seems far ahead of the model

EDA #4: Why is Drupal 11 "Falling Short"?

What's going on with Drupal 11.x?  The projected number of installations given by this model (337,609) is wildly disparate from the number of actual installations (19,976).  In fact, it is only about 6% of the projected number.  So what gives?

Here are some orienting facts:

• Drupal 11.x was released on 2024-12-16. 
• The official service life of Drupal 11.x is 24 months.
• The extended service life of Drupal 11.x is 48 months.
• This article uses information published by Drupal on 2024-12-28
• When this article was written, Drupal 11.x was just twelve days old.
• When this article was written there were 19,976 Drupal 11.x installations.
• Projected installations for Drupal 11.x, according to the "Realistic" Model, is 337,609.

One of the inherent limitations of the Innovation-Adoption Curve is that it is predominantly retrospective.  In other words, it is only accurate once a suitable period of time has elapsed.  In this case, it could be argued that the prediction is wildly premature, considering that Drupal 11.x has only completed 4% (normal) or perhaps 2% (extended) of its projected service life. 

Let's look at this situation in two different ways:

The simple way to look at things is to treat Rogers' Innovators as an undifferentiated group that responds to the release of an innovation in the exact same way at the exact same time.  In this scenario, 2.5% of the population instantly adopted Drupal 11.x, giving a Day 1 install base of 8,440 (2.5% * 337,609).  The actual install base of 19,976 is actually 2.3X of projection.

A more nuanced way to look at this situation is to treat Rogers' Innovators group as a differentiated group that responds to something new using the same innovation adoption pattern as the overall group.  Yes, the Rogers model can be applied recursively.  Under those conditions we can assume that some proportion of the Innovators population would instantly embrace Drupal 11.x (I call that group Innovators2), while others took relatively more time.  Using the Innovators2 as a "heartbeat", we get 211 people (2.5% of 2.5% of 337,609) per day adopting Drupal 11.x.  Twelve times that number gives 2,532 people, making actual Drupal 11.x installations far, far ahead of projections (~7.8X).

"Realistic" Drupal Adoption Model Analysis

Many of the deviations observed in the "Realistic" Drupal Adoption Model either conform to assumptions regarding the inherent limitations of the growth factor (Drupal 5, 11 as extreme cases), or to assumptions related to the limitations of the model itself (Drupal 11 is not "finished yet").  Most of the other figures (Drupal 6, 8, 9, 10) closely conform to the shape of actual installation data.

This bodes well for the "Realistic" Drupal Adoption Model in terms of its ability to capture the present, by more or less mirroring the instantaneous reality of Drupal on 2024-12-28.  The "Realistic" Drupal Adoption model can also go further than the pie chart by presenting a model that features a "growth" narrative by way of its y = 0.5X decay function, which assumes that Drupal leaves half of its existing population behind every time a new edition of Drupal is released.

But what about Drupal 7?

The next piece in this series examines the situation of Drupal 7.  It introduces two new analytical models drawn from psychology and economics to help contextualize the situation, and utilizes those models to propose two different futures for the Drupal Project, either of them leading to a different, yet similarly promising outcome, or “silver lining”.

In 2002, Professor Graham Leach began lecturing at Hong Kong Polytechnic University, the largest school in Hong Kong, by teaching graduate level courses in the Department of Computer Science of the School of Engineering.  In 2010, he moved over to the School of Design and remained there until his retirement in 2023.   Graham currently occupies a Professorship of Entrepreneurship in the School of Business of the newest Tertiary institution in Hong Kong, Gratia Christian College.