This is not a conventional fight 

Comics fans love crossovers. And a key part of most crossovers is providing an answer to the “who would win?” question. So who would win out of Captain America and James Bond?

They are both meant to be icons of their respective cultures; the US v the UK; brash individualism v sophisticated charm; red, white and blue v black tie. Both are physically at the pinnacle or beyond human ability, but neither has an actual “super” power as such, unless you count Cap’s ability to throw a shield in a trajectory that defies physics or Bond’s casual misogyny as superpowers.

But this post is not actually about who would win a fight between Captain America and James Bond. I’m sure everyone has their own opinion, and I don’t want to start a fight of my own.

This blog is about the movie franchises — it’s MCU v Bond. And the the MCU (Marvel Cinematic Universe) kicks Bond’s butt.

A quick recap can confirm that: as of writing, the recorded worldwide box-office for the MCU was more than $18 billion, whereas Bond tops out at around $7 billion. Even adjusted for inflation, the MCU wins handily.

So … if the winner is so obvious, then this is a really short post?

Not really. What I wanted to look at are some of the reasons why the MCU is so much more than Bond. Obviously part of that story is just the quality of scripts, acting, direction and so on. I’m not really qualified to comment on those except at the level of personal preferences.

What I can comment on is how the overall structure of the franchises differ, and I think that is the critical distinction. The little piece of magic that elevates the MCU above its rivals.

The Structure of a Franchise 

The obvious pieces of property in a franchise are

  • the movies themselves

  • the characters

and the overall setting in which they live. This latter is important, but since most modern franchises sit in some variant of the world we live in, it isn’t the detail that matters most I think.

Bond has 26 movies (inc. non-canon films). The MCU has only 23 movies (inc. the two yet to appear this year). So superficially Bond wins on number of films, but the number doesn’t tell the story.

The Bond movies are based on about a dozen novels plus some short stories by Ian Fleming. There are quite a lot of later books by some 8 or 9 other authors, and a relatively recent series of comics. Altogether it’s quite a substantial corpus, but it pales before Marvel’s. They have tens of thousands of individual media (mostly comics, but also novels, histories and so on). So there is a depth to the Marvel universe that the Bond universe lacks, but Bond makes up for it perhaps on consistency? The Marvel universe has multiple timelines/dimensions/planets in every variation they could think of. It’s a crazy, creative soup. Maybe the structure of the Bond movies is better because it comes from a single consistent world?

However, when you look at them, the Bond movies are only loosely connected. They share some characters and concepts, but most are not even traditional sequels. That is, they don’t share direct references to plot elements. There are sub-sequences (for instance the Daniel Craig sequence of Bond Movies: Casino Royale, Quantum of Solace, Skyfall and Spectre) that are such, but they are almost independent of the prior movies. Some are also direct remakes (Never Say Never Again and Thunderball). John Griswold has constructed a “high-level chronology of James Bond’s life”, but he notes that there are difficulties even with the Fleming books by themselves.

Fleming … loved to put real events in the his stories even they were out of synchronization with with the story being told.

Other problems include Fleming ret-conning Bond’s birth-date for artistic reasons, and in other places he just seems careless of details.

On the other hand, the MCU (as opposed to the wider Marvel universe) is linked together by a complex timeline. It isn’t entirely consistent either, but it’s a good deal easier to trace than the Bond world. We’ll go into more depth on the structure of the movies in later posts, but for now something simpler.

The MCU is working with a much larger set of heroes and supporting characters than Bond. Arguably, there are about 20 heroes in the MCU and only 1 in the Bond movies. Both have casts of supporting characters, but again, a fan of the MCU could probably list 20 or 30 important side characters in the MCU, and only about a dozen regulars in the Bond universe (assuming we ignore the seemingly disposable Bond girls).

The Bond universe does have a nice set of villains, and actually reuses villains (for instance, the iconic Blofeld) more than the MCU. This is a little strange – comics are famous for the reuse of villains, but the only villains to get much more than one movie are Loki (who is a bit of a flip-flopper), and Thanos, who is only in the background in most of his appearances.

However, that is all pretty vague. This is a data-science blog, so let’s try to be a little more quantitative.

The simplest thing we can do is perhaps to count how many movies each character appears in. The data comes from IMDb (through IMDbPY – see this post for more details). The resulting frequency for each name character are here for Marvel and Bond, and the top-10 are displayed below.

You can see each character’s position and number by moving your mouse over the plot (if you have javascript enabled, in particular PlotlyJS). The two franchises have a similar number of overall character appearances (618 for the MCU and 584 for the Bond movies), but otherwise they differ tremendously:

  • The Bond movies have a small, core set of characters (the eponymous hero plus ’M’, ‘Q’ and Miss Moneypenny) who appear in almost every movie, and then the number of movies any other character appears in drops very rapidly.

  • The MCU movie characters are in, at most, 10 movies (Iron Man, Captain America and Nicky Fury achieve this, though many of Fury’s appearances are very brief cameos), but the rest of the top 10 are not far behind. No.10, Pepper Potts, is still in 7 movies.

This difference persists. We can look at the distribution of appearances per character over all named1 characters. All the usual problems apply to determining which movie a character appears in, but I have covered most of that in a previous post. Once we have collated them all we can plot a full distribution of the number of appearances per character below. Data for the frequency histogram counts are available here for Marvel and Bond.

The plot shows the distribution of the number of characters to make a given number of appearances. The axes are both log-axes, so that we can see the whole range clearly (there is another reason to use log axes that we will get into in a second).

The two empirical distributions are very different. The full distribution exacerbates the phenomena already described. Bond has a small set of characters that appear often, and almost every other character is in only one movie. The MCU has a much more consistent form.

In fact the form of the MCU distribution is very close to a straight line on the log-log axes (see the fitted curve). A straight line would correspond to a power-law or Pareto distribution. The Marvel data fits that law (to some extent2) and the Bond data very much doesn’t. Let’s look at why that is interesting.

Power Laws and Human Behaviour 

A power-law is where one variable – call it \(Y\) – is related to another, \(X,\) by a function of the value that looks like \[ Y \propto X^{-s}. \]

For a probability distribution we might have, for instance, a probability density function that takes the form \[ f(x) = \frac{\alpha x_m^{\alpha}}{x^{\alpha+1}}, \] for \(x \geq x_m.\) The distribution above is called the Pareto distribution after Vilfredo Pareto an economist and sociologist who first noticed that the distribution appeared when looking at peoples’ incomes.

In our case, we are looking at a variation in which the variable of interest (the number of movies a character appears in) takes discrete, integer values. The discrete variant is often called a Zipf distribution.

Power-law and Zipfian distributions have some interesting properties:

  • Power-laws are commonly associated with the 80-20 rule (80% of everything is caused by 20% of people), but power-laws generalise this rule, e.g., in many societies, the top 10% of wealthiest people control roughly half the wealth, and you can look at other such ratios.

  • Power-laws are scale invariant, i.e., when you change the scale, the law is not changed, e.g., if \[ f(x) \propto x^{-s}, \] and then we scale by a constant \(c\) \[ f(c x) \propto c^{-s} x^{-s} \propto x^{-s}, \] the law is unchanged.

  • Power-law distributions can lack standard “moments”. The moments are standard statistical measures of a random variable, e.g., the mean and variance. For instance, the Pareto distribution with \(\alpha \leq 2\) has infinite variance, a phenomena which breaks a great deal of statistical intuition. For example, the Central Limit Theorem doesn’t apply! That’s a big problem because this theorem underlies a lot of other assumptions made in statistical or data-science analyses.

Despite their “weird” properties, we see power-law distributions all over the place:

  • the magnitudes of earthquakes

  • the distribution of incomes

  • word frequencies and other analyses of media.

In fact they are almost so ubiquitous in nature that the “normal” distribution is not normal at all! They are particularly common when examining human behaviour.

One of the places we see them is in human relationships. For instance, the number of contacts between people in a social network is often modelled this way.

Several data scientists have noticed that power-law distributions appear in the context of the myths, legends and stories that have survived to the present. In particular:

Both find that when you look at the network structure of (Western) myths and legends you commonly see power-laws (in the node-degree distribution). These networks have other features in common with social networks, but the power-law is the feature I am focused on today.

Power-laws have also been noticed in the superhero world before. The following two references look at the much larger Marvel universe (around 96,000 appearances of over 6,500 characters in about 13,000 comics).

They also observe (truncated) power laws in this larger dataset, so it is not surprising that the MCU emulated it, but there is a deeper idea in play here.

It seems that human constructs (stories in particular) that survive the test of time are complex enough to mimic the real world, for instance mimicking features such power-law distributions. So it isn’t surprising (to me at least) to see some trace of this in the Marvel universe, but it fails in the Bond world. We don’t see even a trace of a Pareto-like distribution.

That seems, to me, to be a big difference, and part of what sets the MCU apart.

Fitting curves in Julia 

Before finishing, it seems worth a brief note on fitting distributions in Julia.

Julia has a nice set of packages for working with probability distributions and statistics. They mirror, in some respects, the equivalent packages in R, the programming language of choice for many statisticians these days.

My code works by loading the files (see Marvel CSV and Bond CSV) with the histogram data into a data frame, creating a new data frame of log10 of the data, and then fitting a linear model to that data. The syntax for fitting the linear model, and the approach (using a data frame) is very reminiscent of R, as is the output.

julia> using CSV
julia> using DataFrames
julia> using StatsModels
julia> using GLM
julia> mcu_hist ="cast_movie_count.csv")
julia> mcu_data = DataFrame(X=log10.(mcu_hist[:N]), Y=log10.(mcu_hist[:F]))
julia> mcu_ols = lm(@formula(Y ~ X), mcu_data)

The function lm fits a linear model (it performs simple least-squares regression) on the log-data. Its output is

Formula: Y ~ 1 + X

             Estimate Std.Error  t value Pr(>|t|)
(Intercept)   2.37665  0.126716  18.7557    <1e-7
X            -2.22627  0.175468 -12.6876    <1e-5

which tells us that the slope of the linear curve (which gives the exponent in the power law) is -2.2, leading to a power law with infinite variance, such as we commonly see in real social network data.

Note, though, that in this work I am fitting to only a few points, so we should take these results with a very big pinch of salt, except that they reinforce the findings of the much larger data analyses mentioned earlier.


So, that’s the story for this week. The MCU has at least traces of a hidden power-law built into its structure, and this is one of the features that distinguishes it from the more staid and traditional movie franchises.

No-one is saying that the peeps at Marvel sat down and worked this out. It happened (I think) because they are trying to build something complex and human and wonderful, and in doing so they naturally mimicked nature.


  1. Here we use the term "named" character to mean a character that has a proper name, not just a job description or other place holder. We do so for two reasons, one philosophical and the other practical. (i) At a practical level, placeholder 'names', e.g., "SHIELD Agent" are non-unique3, and so identifying these between movies is impossible. (ii) At a philosophical level, if a character is not important enough to the script to be given a name, they are not important enough for us to include in our analysis. Some cases are borderline however. For instance, we exclude characters named by reference "X's husband". However, we do allow a small number of particular 'unnamed' cases where a well-known role was not named in the credits, the most obvious cases being several of the Bond girls who were named thing like "Log Cabin Girl" (in *The Spy Who Loved Me*).
  2. It should be noted that the fit here is to only a few data points, and as such must be taken with a pinch of salt. Fits to power-law distributions, to be convincing, should cover more than 1 decade (we see here only 1). Moreover, the last few data points (e.g., the number of characters in 10 movies) do not fit the overall law. Ideally a larger data set is needed, but we are constrained here by the number of movies produced -- it will be interesting to see how this plot evolves.
  3. Unfortunately even character names are not always unique. We know of several instances in the Bond movies -- e.g., Patricia -- where the same name is used for two different characters. A considerable effort went into resolving names that appeared more than once, checking that they really were the same character. We make no guarantee that the effort was 100% successful though. If you want to check, then the name/alias list for the movies are here along with all of the other data. There are two files for each movie `alias_list.csv`, which provides a list of aliases for more important characters, and `extras.csv` which is a list of minor characters that appear in only one movie. A small amount of additional coding is needed to separate character names that are not unique.