I mentioned that the chance of any person in our group slipping into the electric fence was very small, say 1 in 100, which was not too worrying. But, then I mentioned that there are 29 people in our group, so you have a 1 in 4 chance of someone slipping into the electric fence with somewhat unpleasant consequences! The leader of our group asked me how I worked this out, and I replied as follows.
“If it were just you and I on this walk, then we would both need to not slip. If I have a 1% chance of slipping, I would then have a 99% chance of remaining upright. However, we would both need to remain standing and the chance of that is 99% of 99%, which is 98%. Not quite as unlikely, but still not a cause for concern. But, for the walk to occur without incidents, then all 29 people in the group would need to not slip. The chance of this is 0.99 multiplied by 29 times, which is 0.74. Meaning there would be a 26% chance of at least one person slipping.”
At this point, she ordered me to walk at the back!
Joking aside, this simple principle, where a small risk can become compounded into a much bigger risk occurs many times in everyday life. Flying is one of the safest modes of transport (per mile at least) and the chance of a crash on a flight is very low. However, the regular traveller or (more so) cabin staff takes numerous flights in a year. They would need to avoid crashes on every single journey and, therefore, their risk over a period would become significantly greater than those flying occasionally. That is not to say that their risks would be great in absolute terms (they would probably be more likely to succumb to a critical illness, as any person could) or that they should change their careers. But, interestingly it seems to be the infrequent flyers, who carry the much smaller risk, who appear to fear flying the most.
Taking this a step further, one can start to see where large discrepancies between actual risk and perceived risk can come about. There may be many people around who think twice about making a trip to popular parts of city centres because of what they hear on the news, but may not think anything of driving home from an evening out having had that extra drink.
This principle of compounding or multiplying out probabilities is something that Ipsos regularly applies in its surveys as a core part of media measurement. An important measure of an advertisement or campaign is the reach. This is the number of different individuals in a population who are likely to see or be exposed to a campaign. Measuring the number of impacts or sightings of a campaign is relatively easy, but the reach is a more complex measure and probably the more useful. Reach correlates with the number of people acting, making a purchase or contributing to the profit margin of the advertised organisation. A person may read eight issues of a monthly magazine over a year, which amount to eight impacts, but the reach will only be one person. Two people reading four issues each will still be eight impacts, but the reach will be two.
Estimating and modelling reach is an important activity in predicting how many people are likely to see a campaign, and hence act. This is figure that in turn effects the investment in the campaign. How geographically widespread should it be and for how long? This is where the “mudslide principle” I mentioned above becomes relevant.
Depending how fast they walk and how close they get, a person walking past a billboard or poster in a station might have a 40% chance of seeing the message and a 60% chance of missing it. If later in the day, that person walks past the same poster at the same speed and closeness (or a 2nd poster showing the same message), then there would be again a 40% chance of seeing it.
For them not to be “reached” after two passes, they would need to not see the poster on both occasions. If their chance of viewing the message on the 2nd pass is not influenced by whether they saw it on their first, their chance of missing it both times is 0.6x0.6 = 0.36. Consequently, the chance of seeing the message on at least one or other of these occasions is 1-0.36 = 64%. After three passes this will go up to 78%, and after four 87%. After that, although the number of impacts continues to increase, the reach probability will “saturate” at just under 100% after that person has passed the poster lots of times.
To optimise reach, the planners must ensure that the campaign is viewed by as many people as possible. When one considers different individuals, one can start adding the reaches and the total reach can continue to rise. Ten people seeing the poster twice will yield a reach of 10 x 0.64 = 6.4. Whereas two people, even if they see the poster ten times each, will give a reach that would not exceed 2.0.
Reach calculations are not always straightforward as there are additive and multiplicative components coming into play, but this type of work is commonplace for Ipsos’ Data Scientists and Researchers working on the large-scale media measurement surveys. Knowing which measures provide the most valuable insights for your business and how to measure them accurately and effectively, can help you focus your resources and achieve a better ROI. The combined experience and expertise of Ipsos Connect’s Data Science team can help you understand just how many people are being reached by your advertising and the impact this can have on your business.
As for the mudslide situation, it is probably a good thing that there were no posters attached to the electric fence. If these posters were to have any reach or viewing probability, then the slip risk of at least one person in the group would have increased to almost certainty!