Eight to Late

Sensemaking and Analytics for Organizations

Trumped by conditionality: why many posts on this blog are not interesting

with 15 comments

Introduction

A large number of the posts on this blog do not get much attention – not too many hits and few if any comments. There could be several reasons for this, but I need to consider the possibility that readers find many of the things I write about uninteresting.  Now, this isn’t for the want of effort from my side: I put a fair bit of work into research and writing, so it is a little disappointing. However,  I take heart from the possibility that it might not be entirely my fault:  there’s  a statistical reason (excuse?)  for the dearth of quality posts on this blog. This (possibly uninteresting) post discusses this probabilistic excuse.

The argument I present uses the concepts of conditional probability and Bayes Theorem. Those unfamiliar with these may want to have a look at my post on Bayes theorem before proceeding further.

The argument

Grist for my blogging mill comes from a variety of sources: work,  others’ stories, books, research papers and the Internet.  Because of time constraints, I can write up only a fraction of the ideas that come to my attention.  Let’s put a number to this fraction – say I can write up only 10% of the ideas I come across.  Assuming that my intent is to write interesting stuff, this number corresponds to the best (or most interesting) ideas I encounter.  Of course, the term “interesting” is subjective – an idea that fascinates me might not have the same effect on you.  However  this is a problem for most qualitative judgements,  so we’ll accept this and move on.

If we denote the event “I have an interesting idea” by I and its probability by P(I), we have:

P(I) = 0.1

Then, if we denote the event “I have an idea that is uninteresting” by U, we have:

P(U) = 0.9,

assuming that an idea must either be  interesting or uninteresting (no other possibilities allowed).

Now, for me to write up an idea, I have to find it interesting (i.e. judge it as being in the top 10%). Let’s be generous and assume that I correctly recognise an interesting idea (as being interesting) 70% of the time. From this, the conditional probability of my writing a post given that I encounter an  interesting idea, P(W|I),  is:

P(W|I) = 0.7,

where W is the event that I write up an idea.

On the flip side, let’s assume that I correctly recognise 80% of the uninteresting ideas that I encounter as being no good.  This implies that I incorrectly identify 20% of the uninteresting stuff as being interesting. That is, 20% of the uninteresting stuff  is wrongly identified as being blog-worthy. So, the conditional probability of my writing a post about an uninteresting idea, P(W|U), is:

P(W|U) = 0.2

(If the above values for P(W|I) and P(W|U) are confusing remember that, by assumption, I write about all ideas that I find interesting – and this includes those ideas that I deem interesting but are actually uninteresting)

Now, we want to figure out the probability that a post that appears on my blog is interesting – i.e. that a post is interesting given that I have written it up. Using the notation of conditional probability, this can be written as P(I|W).  Bayes Theorem tells us that:

P(I|W) = \displaystyle\frac{P(W|I) * P(I)}{P(W)}

P(W),  which is the probability that I write a post,  can be expressed as follows:

P(W) = probability that I write an interesting post+ probability that I write an uninteresting post

This can be written as,

P(W) = P(W|I) * P(I) + P(W|U) * P(U)

Substituting this in the expression for Bayes Theorem, we get:

P(I|W) = \displaystyle \frac{P(W|I) * P(I)}{P(W|I) * P(I) + P(W|U) * P(U)}

Using the numbers quoted above

P(I|W) =\displaystyle \frac{0.7*0.1}{0.7*0.1+0.2*0.9}=0.28

So, only 28% of the ideas I write about are interesting. The main reason for is my inability to filter out all the dross.  These  “false positives”   – which are all the ideas that I identify as interesting but are actually not –   are represented by the P(W|U) * P(U) term in the denominator. Since there are way more bad ideas than good ones floating around (pretty much everywhere!), the chance of false positives is significant.

So, there you go: it isn’t my fault really.🙂

I should point out that the percentage of interesting ideas written up will be small whenever the false positive term is significant compared to the numerator.  In this sense the result is insensitive to the values of the probabilities that I’ve used.

Of course, the argument presented above is based on a number of assumptions. I assume that:

  1. Mostreaders of this blog share my interests.
  2. The ideas that I encounter are either interesting or uninteresting.
  3. There is an arbitrary cutoff point between interesting and uninteresting ideas (the 10% cutoff).
  4. There is an objective criterion for what’s interesting and what’s not, and that I can tell one from the other 70% of the time.
  5. The relevant probabilities  are known.

…and so, to conclude

I have to accept that much of the stuff I write about will be uninteresting, but  can take consolation in the possibility that it is a  consequence of conditional probabilities. I’m  trumped by conditionality, once more.

Acknowledgements

This post was inspired by Peter Rousseeuw’s brilliant and entertaining paper entitled, Why the Wrong Papers Get Published. Thanks also go out to Vlado Bokan for interesting conversations about conditional probabilities and Bayes theorem.

Written by K

March 17, 2010 at 10:43 pm

15 Responses

Subscribe to comments with RSS.

  1. Your posts are fine. You would get more attention if your RSS feed was full-text. Read “Truncated RSS Is A Bad Business Decision” http://bit.ly/bQ5X9Z

    Like

    Chuck

    March 17, 2010 at 11:07 pm

  2. Chuck,

    Thanks for the feedback and suggestion – I really appreciate it. I’ve changed my feed settings to full text, but it doesn’t seem to be working right. Will look into it tomorrow (getting late here…)

    Regards,

    Kailash.

    Like

    K

    March 17, 2010 at 11:25 pm

  3. Kailash, I randomly found your blog a while back and have been a keen reader since. I greatly appreciate the depth you dive into your subject matter and the quality of your writings.

    Some of the material I requires background reading to comprehend (e.g. crack open an old uni. textbook).

    Keep up the great writing!

    Like

    Evan Wise

    March 18, 2010 at 4:02 am

    • Evan,

      Thanks so much – I really appreciate the feedback.

      Regards,

      Kailash.

      Like

      K

      March 18, 2010 at 6:56 am

  4. Kailash,

    I read your blog regularly, partially for the ideas and how you carefully, and methodically explain the reasoning for your often very interesting conclusions.

    There are a couple points I think are relevant/might be helpful in facilitating feedback (comments) and getting readers(for each article).

    1. Your writing style is very academic and realistically at a higher level than many (most?) blogs out there that aren’t on a pay subscription basis as an example.

    This means (in my personal opinion) diving into your blog entries would be more challenging for a new user and realistically isn’t as broad of a target audience as many others.

    Not suggesting you change this (I actually love it for this very reason) but it’s something that means ‘comparing’ against other blogs/sites might not be a fair comparison unless the material and style is much similar.

    2. To get feedback sometimes it’s great to make a very opinionated statement, or to ask a question. In many of your posts you clarify, report on, or break down a concept, but I wouldn’t say it always facilitates that ‘desire’ for feedback.

    As an example as a reader I often read the blog posts and think: I gained something from this, but much less often do I say to myself: I can add real value to this article with more information (again keeping in mind the nature of the material you cover and the style).

    Not saying this is an issue (I actually enjoy reading the entries again, and often really don’t have much to add beyond your observations because we often share opinions) – Just that it may influence the number of comments?

    3. The conclusion or summary is the best part – Maybe put a highlight or brief summary at the start of each article? Since the length is greater people may be more intrigued and want to see how you came to the reasoning after briefly reading that statement. I could see this helping with first time readers for certain.

    Hope this helps, and isn’t annoying feedback as I haven’t really re-read or validated all my statements, just thought I would share some relatively unstructured thoughts that came to me as I read this entry.

    A reader who finds pretty much everything you post interesting,
    Richard Harbridge

    Like

    rharbridge

    March 18, 2010 at 4:28 am

    • Richard,

      Thanks for your thoughtful and very kind words. Yes, I realise that my writing style is academic; journalese is a hard language to unlearn, but I’ll keep trying. 🙂

      The point you’ve made in (3) is very helpful – I’ll try to do this on some of my more involved posts.

      I also take your point about making opinionated statements to get more feedback, but that’s something I feel uncomfortable doing (ex-academic’s caution, I guess).

      Finally, thanks so much for all the airtime you’ve given my posts on twitter.

      Regards,

      Kailash.

      Like

      K

      March 18, 2010 at 7:06 am

  5. I agree with rharbridge on points 1 & 2. I love to read most if not all of your posts. However, I never really think about what more can add through feedback.

    Like

    Courtney

    March 18, 2010 at 4:47 am

    • Courtney,

      Thanks so much!

      Regards,

      Kailash.

      Like

      K

      March 18, 2010 at 7:08 am

  6. I wouldn’t deprecate yourself based on probability. The very fact that you turned a post about uninteresting posts into an interesting post using probability that actually showed that the posts ARE uninteresting was quite amazing! For me, this is analogous to an out-of-work musician who wrote a hit-song about the fact that nobody liked his music anymore. It’s just unfortunate that you don’t receive royalties every time someone reads your posts (interesting or otherwise).

    Like

    Nick

    March 18, 2010 at 11:23 am

    • Thanks Nick,

      Royalties – now that would be nice….

      Regards,

      K.

      Like

      K

      March 18, 2010 at 5:03 pm

  7. I notice you use various forms of the word “assumption” seven times. This is basically seven times you could have potentially screwed this up (if you made an incorrect assumption). If you’re generous and assume that you have a 50% chance of making a valid assumption then using the binomial distribution you have only a 0.08% chance of being correct. So I’d say it’s safe to assume that more than 28% of your articles are interesting. I wouldn’t like to guess what percentage of them are correct though…

    Like

    Kane

    March 24, 2010 at 2:45 pm

    • Kane,

      Thanks for raising an excellent point – you’re absolutely right, there are several assumptions in the argument. These have been highlighted in the post.

      A couple points in response to your comments:

      1. I had to pick numbers to arrive at a numerical value for the final conditional probability, hence my assumptions for numerical probabilities. Obviously, the final value of 28% is as arbitrary as my choices for the input probabilities. However, the numbers don’t really matter; the proportion of interesting posts will be small as long as the proportion of false positives is large (the second term in the denominator).

      2. In principle one could obtain P(I|W) for empirical data. Here’s how: one could add a 5 point scale at the end of each post, inviting readers to rate how interesting they found the post. The resulting data could be used to evaluate P(I|W) directly.

      Regards,

      Kailash.

      Like

      K

      March 24, 2010 at 9:06 pm

  8. Kailash

    The quality and depth of your posts doesn’t invite much discussion. What more can we add to such great analysis?

    I get most of my blog comments when I says something stupid or poorly thought through. People love to correct you!

    I agree with the comment about the RSS feed. I scan the RSS reader almost daily and there is a lot to trawl through. And even though I do click through to your site 90% of the time, it’s a barrier to further engagement with the content.

    Lastly, you are writing for a smaller audience than someone who writes for first time PMs, so naturally the audience is smaller. My reckoning is that the people who read this material are seeking to move from intermediate to advanced skills and knowledge levels.

    You are simply aiming at a higher point in the knowledge pyramid than many others (including me I think.)

    Anyway, this is one of my top 5 blogs. I love your work.

    Like

    Craig

    March 24, 2010 at 6:59 pm

    • Craig,

      Thanks so much for the kind words.

      I’ve changed my feed settings to full text. However, it seems to work in some browsers (e.g. IE) but not others (e.g. Firefox). Seeing how important this is, I’ll try to sort this out.

      The comments I’ve received from you and others in response to this post have been very encouraging. I truly appreciate your taking the time to comment.

      Thank you!

      Regards,

      Kailash.

      Like

      K

      March 24, 2010 at 9:17 pm

  9. […] couple of years ago I wrote a piece entitled, Trumped by Conditionality, in which I used conditional probability to show that majority of the posts on this blog will be […]

    Like


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: