# You are more likely to retweet HubSpot post than this …

The post is titled, “10 horrifying stats about display advertising”. In a attempt to tell stories or relate arcane data to something common the author goes on to make some likelihood comparisons

You are more likely to complete NAVY SEAL training than click a banner ad.

You are more likely to get a full house while playing poker than click on a banner ad.

You are more likely to get a full house while playing poker than click on a banner ad.

You are more likely to birth twins than click a banner ad.

You are more likely to get into MIT than click a banner ad.

You are more likely to survive a plane crash than click on a banner ad.

It is pointless and simply wrong to make such comparisons based on respective frequentist probabilities. Let us say there is a one tenth of one percent of people who see  display ad click on it. Let us us say one percent of people who sign up for Navy SEAL complete the training.

That does not mean these two are comparable nor can you say that chances of  ANYONE completing Navy SEAL training is far better than clicking on display ad. What is missing here are the hidden hypotheses we take for granted (the context).

Think of those who sign up for Navy SEAL. Consider their drive, motivation, physical fitness, mental strength, initial screenings they survived to get to training stage. You already have weeded out people like us. If indeed 1% of people who attempt SEAL training complete, it is the conditional probability

P(Complete SEAL training | Passed all screenings and have wherewithal to complete it)

This is not the probability of any random person you pick from street, which is highly likely close to 0.

It is indeed horrifying that they would compare such unrelated events and their conditional probabilities to make their case about display advertising.

Now to the title of this article. Determining whether or not this is relevant comparison of likelihoods is left as an exercise to the reader.