(Potential) Power of Round Numbers

The majority of my research interests involve the relationship between words and numbers. How do words influence our (numerical) assessment of a situation? Last week, I asked what you expected a player’s shooting percentage to be when a player’s shooting was referred to as “good” vs. “not bad”. On that note, I was in New York City this weekend and heard someone refer to the weather as “not hot”. It was about 20 degrees outside. Apparently that idea plays out in the real world in terms of how people and businesses communicate. This week’s survey explores the same broad idea (linguistic influences on perception) but in a slightly different way:

What percentage of 40-yard field goals does the average college kicker make?

Similar to last week, there were multiple conditions. Some people might have seen one of the following:

What percentage of 39-yard field goals does the average college kicker make?

What percentage of 41-yard field goals does the average college kicker make?

The only difference between the conditions (i.e. what you might have seen compared to someone else who answered the survey) was the distance of the field goal. Why is that an important distinction? There is research indicating that round numbers drive behavior in unique ways. Or, similarly, approaching a milestone such as thirty changes behavior.

A recent article on NYMag.com discusses some of these unique behaviors such as more people signing up for marathons in their 9 year (ex. 29) than round year (ex. 30) or people being more likely to retake the SAT if they score under a round number. Powerful stuff. With that in mind, I wanted to build on this and explore whether it influences perceptions of chances of making the kick, difficulty, etc. Given the love for college kickers (#collegekickers) on Twitter, that seemed like an interesting way to test it.


Before I discuss the results, I want to acknowledge that not every survey I run will “work”. In other words, not every survey will have statistically meaningful differences, pretty graphs, etc. I am also trying to stay away from statistically analyzing the data and instead focus more on ideas*. The point of this blog post series is to try out, with your help, various ideas I am thinking about. The “file drawer problem” is a term used in academic circles which references studies that end up in file drawers (and not published) because the results don’t work out as planned. That won’t be the case here. If it works, I’ll talk about it and discuss why. If it doesn’t work, I’ll talk about it and discuss why. This is one of those studies that didn’t work out quite as I had planned. Nonetheless…the results:Field Goal Percentage By Distance

What do you notice?

Although the differences aren’t quite as unique as last week’s survey, there still appears to be a bit of a trend suggesting a 40 yard field goal is perceived differently than a 39 or 41 yard field goal. For example, a 40-yard field goal was perceived as more difficult (lower estimates of field goal percentage) than a 39-yard or 41-yard field goal.  Furthermore, the estimated difference between a 39-yard field goal and a 40-yard field goal was about 4 percentage points but the difference between a 40-yard field goal and 41-yard field goal was about 2 percentage points. This could have happened by chance (based on a fairly small sample size too)* so, like I’ve discussed before, don’t put too much stock into results from one study but it is still interesting to think about. In both scenarios, there is a 1-yard difference in the distance of the field goal but perceptions of how often a kicker makes the field goal are different.

What might play a role?

Power of 9 or 0. As previously mentioned, quite a few studies have shown the power of a 9 in a number and/or the power of a round number. A casual look at the graphs suggests something like this may be in play given the unique perceptions of a 40-yard field goal relative to a 39-yard or 41-yard field goal. For example, a 40-yard and 41-yard field goal are perceived similarly, yet a 39-yard field goal is perceived as much easier. Shouldn’t the perceived difference between a 39-yard and 40-yard field goal be the same as the perceived difference between a 40-yard field goal and a 41-yard field goal? These results suggest that is not the case. Why would a 40-yard field goal be perceived as more difficult than a 41-yard field goal? The milestone, based on the round number, of a 40-yard field goal appears to increase the perceived difficulty.

Knowledge. It could be that the sample that responded to this survey (presumably a lot of sports fans) are much more knowledgeable about football and thus less susceptible to any 39/40/41 bias. That being said, there does appear to be a slight perception difference due to the differences in the type of number (ex. 39 vs. 40 or 41).

 So what is the takeaway?

Think about the numbers you are using in your day to day (business) life. Multiple studies have shown how people behave different depending on whether a number ends in 9 or 0. Although this study wasn’t as conclusive as I had planned, there does seem to be a slight difference in perceptions based on the number alone. For example, in a business scenario this could apply to delivery times (9 days vs. 10 days), pricing ($1.99 vs. $2.00), the age at which someone signs up for a product (such as the 29 vs. 30 marathon example), or a host of other scenarios that are influenced by framing. Can you think of other scenarios where this type of idea might apply?

P.S. I couldn’t find any data on college kicker accuracy by distance (let me know in the comments if you know of a study) but here is an interesting article from FiveThirtyEight on NFL kicker accuracy by distance.

*This post is part of a blog series that includes my random thoughts and musings. I do not claim to be the first person to think of these things or deny that others have done research on them. I am simply discussing interesting marketing/psychology/linguistic topics that come to mind. Furthermore, I am avoiding statistical analysis as I want the emphasis to be on the ideas. I recently read (Amazon affiliate link) Paul Grice: Philosopher and Linguist and was inspired by a less statistical and more philosophical approach. Thus, the results here could happen by chance. I want to focus on thinking about, discussing and debating the ideas at a broad level rather than whether or not the differences are statistically meaningful. I typically send out a quick survey on Friday and post a follow up analysis/discussion on Monday. 


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