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Ranking Parenting And Mummy Bloggers In The UK: A Mathematical Model

07 January 2019 by Babios
Ranking Parenting And Mummy Bloggers In The UK: A Mathematical Model
  1. Introduction

We recently published an article analysing parent and mummy bloggers in the UK. The objectives of the study are as follows:

  1. Exhaustively analyse data across a wide range of key performance metrics related to mummy bloggers in the UK (stage 1 of the study).
  2. Develop advanced mathematical models that objectively benchmarks and ranks bloggers (stage 2 of the study)

The first stage of the study is complete, which can be found at Parenting And Mummy Bloggers In The UK - A Statistical Analysis

We are now in stage 2 - the development of mathematical models that objectively ranks parenting and mummy bloggers. According to the feedbacks we had so far from bloggers, there is a consensus that blogging should not be a mere number game. It’s not quantity that counts its quality. So, what’s wrong with the current methods and approaches used in the industry to benchmark and rank bloggers? 

  1. Limitation of Conventional Influencer/Blogger Benchmarking Methods

In the influencer marketing industry, ranking is typically based on reporting average values (e.g. average number of likes, comments), number of followers, and authority scores. This type of conventional ranking is myopic and performance indicators such as simple ratios, counts and averages can be misleading, when in fact performance should be determined by interrelated multifactorial processes, i.e., rather than relying on single measures a much wider range (or series) of factors should be considered. The blogger and influencer marketing industry is currently not responding to these issues and robust mathematical models should be developed to assist businesses make informed decision about the influencers they could potentially work with.

A commonly used measure of efficiency is the output to input ratio, which is widely used in benchmarking systems and processes to identify best practice. Let’s use one input and one output as an example. Suppose a mummy blogger posts 200 blogs per year (an input) generating around 200,000 engagements (an output). The output to input ratio is 1000 (200,000/200).

Embedding interrelated multifactorial processes (i.e. many inputs and outputs) further complicates the mathematical model, so it’s not a simple ratio analysis. The example above was just to illustrate the definition of ratios.

Procedures referred to as ‘efficiency benchmarking’ are instrumental for guiding both the influencers/bloggers and businesses. It will enable bloggers to be efficient with respect to minimising inputs (e.g. number of posted articles) and maximising outputs (e.g. engagement rate), and help businesses find a group of efficient and effective bloggers to work with. Note that the relationship between efficiency and effectiveness is not linear but efficiency (low waste) is associated with high effectiveness (i.e. high attainment). The ratio between effectiveness and efficiency is called productivity. In this context, significant developments have been made with the efficiency and benchmarking methods known as data envelopment analysis.

The Mathematical Model in Layman Terms: Data Envelopment Analysis

Data Envelopment Analysis (DEA) is a performance measurement technique used for comparing the performances of organisations. For example, we can compare all the McDonald’s franchises operating in London to find out which outlet is doing good and which one is not and then recommend some actions to bad ones to perform better.

DEA is a popular theme around operations research and statistics, where institutions and organisations such as schools, hospitals, and companies are ranked in order to measure performance and productivity. So, why can’t bloggers be ranked just like hospitals and schools? They are no different, an entity just like organisations with clear inputs, sharing and promoting blogs within their community, working with brands, which then leads to outputs, such as authority, value added to brands and community, and level of engagement on social media platforms. 

The mathematical theory behind DEA is far too technical and can be discouraging (unless you are mathematically competent), so to minimise confusion I’m going to keep it really simple, and try to explain this in layman terms. I hope I won’t fail.

Here is a small sample of mummy bloggers (see Table 1). The blue column signifies inputs for mummy bloggers, e.g. the number of blog articles published in the last 12 months (A1). The pink column are the outpatient variables, e.g., total number of blog engagements (last 12 months).

Table 1: A sample of parenting and mummy bloggers input/output variables

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INPUTS: T1 = Number of Twitter Followers, T2 = Twitter Account Age (yrs), A1 = No. of published blog articles (last 12 months), FB = No. Facebook Followers, I1 = Number of Instagram Followers. OUTPUTS:  T3 = Retweet Ratio, T4 = Twitter Reply Ratio, T5 = Average Retweets, T6 = Twitter Social Authority (0-100), A2 = Total Blog Engagements (last 12 months), A3 = Average Blog Engagement (last 12 months), I2 = Instagram Engagement Rate (%), I3 = Average No. of Instagram Likes, I4 = Average Number of Instagram Comments.

It is important to distinguish input variables from outputs. An input must lead to an output, for instance, posting blogs on a regular basis leads to blog engagements. Note that there are series of inputs and outputs, hence DEA reduces the danger of relying on one performance indicator, instead it utilises many inputs and outputs generated by the blogger. Therefore, the methodology eliminates the need to use average values and counts that many of the industry tools heavily rely on for ranking purposes.

The basic principle of DEA is ratios. Typically the methodology takes the combination of output measures and divides it by the input measures. DEA then produces an “EFFICIENCY” score for each blogger ranging from 0 – 1, one been the most efficient blogger. For instance, if a blogger is able to generate a higher ratio of outputs using fewer inputs, then it is considered to be efficient. So, it’s not a NUMBER GAME for DEA, it’s all about efficiency. If a blogger has large numbers of fake followers, then DEA is also able to pick this up, and gives a score less than 1 (meaning inefficient). The choice of the inputs and outputs does matter and one needs to be cautious and ensure that a wide range of variables (or data) are considered.

  1. Application to Mummy/Parenting Blogger Data

We next apply our DEA model to a sample consisting 1,188 mummy bloggers in the UK. Over a period of six months, relevant data was extracted using various websites, some publicly available and others through paid platforms. This is a large sample size thus the analysis can be deemed to be nationally representative, reliable and accurate. An exhaustive analysis of the data can be found at Parenting And Mummy Bloggers In The UK - A Statistical Analysis

Given that there are far too many bloggers we will only be showcasing the results for the top 225 bloggers. See Table in the Appendix for final rankings (column 8). We will be sending out emails to top 100 ranked parenting/mummy bloggers, where names will then be published upon receipt of consent.

The Mathematical model categorises bloggers into two groups, namely efficient and non-efficient bloggers. Table 2 illustrates a comparative analysis between the efficient (efficiency scores > 1) and non-efficient mummy bloggers (scores < 1). We examine the variation between the two groups in terms of the inputs and outputs. To do this the data is further split into two (efficient vs. non-efficient) where the percentile distribution is calculated for each input/output.

For example, the top 25% of the efficient group of mummy bloggers generates 26% higher average blog engagement rate by posting far fewer blogs (i.e. 21 blogs) compared to the top 25% of the non-efficient group (61 blogs). Therefore, higher output is achieved amongst the efficient mummy bloggers as a result of posting fewer blogs.

According to the 50th percentile distribution, the efficient group has 8% higher Twitter authority score (52 vs. 48) with only half the number of non-efficient influencer group Twitter followers (10,100 for non-efficient vs. 5,100 efficient). Again, the efficient group has achieved higher authority score with far fewer Twitter followers. The same argument applies for Facebook and Instagram. Therefore, if there are any fake accounts or bots, the model is able to account for such activities.    

A marked difference is observed in the Instagram metrics too. With almost the same number of Instagram followers, the 75th percentile distribution (9,200 vs. 9,250 Instagram followers) shows that the efficient group has 2.4 times the engagement rate of the non-efficient group (2.70% vs. 6.38%). 

Table 2 A percentile distribution of inputs and outputs comparing efficient vs. non-efficient mummy bloggers.ES = Efficiency score, I = Input and O = Output.

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After posting our first blog, a mummy blogger shared the following, and here I quote: “I find it so frustrating the brands and ad agencies favour their ambassador opportunities and sponsored posts to who they prefer to work with, merely on vanity numbers”. We can confirm that this is not the case according to our findings above.

Here’s another one: “So much of the engagement is fake. Does the survey take into account bloggers who use comment threads and Instagram like pods to artificially inflate their engagement figures, i.e., they join a thread where everyone likes everyone else’s photos on Instagram or retweet a specific twitter post. This is really widespread”. I have also picked this is up myself and was wondering whether the Mathematical model has. So, I went back and deep dived into the program and examined the relative importance of inputs/outputs, i.e., how much weight has the model given to “comment/like” engagement oriented output variables. The short answer is very little. It concentrates around efficiency and not just on mere numbers.

What’s next?

We will soon be sending out emails to top 100 mummy bloggers ranked according to our mathematical model. Upon receipt of consent we will compile together all names and publish accordingly.

Future works

The development of mathematical models for benchmarking bloggers and influencers is in its infancy. There are plenty of work to do, including the testing of novel methods/approaches with new data variables. Additional data will include Pinterest metrics; site visits (including number of visitors, average session duration, bounce rate, on-site SEO score);  Vlogging stats, YouTube metrics, and Instagram Stories.

Academic rigour is essential here, which takes time, effort (and financial investment too), so please bear with us. We will continue to share our findings as and when results are statistically verified and validated. Upon completion, we anticipate that our methodology will have significant impact on the influencer marketing industry, particularly around ranking and assisting businesses and individuals looking to work with the most appropriate influencers in the UK and other parts of the world.


Table Results for additive DEA model and additive super efficiency DEA model. CRS = Constant return to scale, VRS = Variable return to scale, Inf = Infeasible. a = the rankings for additive DEA model under CRS assumption for inefficient mummy bloggers only, where ‘-‘means efficient with an efficiency score of 1. b = the rankings for additive DEA model under VRS assumption for inefficient mummy bloggers only. c = the rankings for additive super efficiency DEA model under CRS assumption including efficient parenting bloggers exceeding efficiency score of 1. All influencers ranked from 1 (the most efficient) to 225 (least efficient).

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Jax Blunt
28 January 2019
You worked from a sample of 1100 bloggers, and my blog for example was excluded as older than any others you considered. Seems a flawed starting position.



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