One Million Page Views and Round Number Bias: Earlier this week, this Conversable Economist blog reached 1,000,000 pageviews. ... Of course, being me, I can 't commemorate a landmark without worrying about it. Is focusing on 1,000,000 pageviews just another example of round-number bias? Are pageviews a classic example of looking at what is easily measureable, when what matters is not as easily measurable?
Round number bias is the human tendency to pay special attention to numbers that are "round" in some way. For example, in the June 2013 issue of the Journal of Economic Psychology (vol. 36, pp. 96-102) ,Michael Lynn, Sean Masaki Flynn, and Chelsea Helion ask "Do consumers prefer round prices? Evidence from pay-what-you-want decisions and self-pumped gasoline purchases." They find, for example, that at a gas station where you pump your own, 56% of sales ended in .00, and an additional 7% ended in .01--which probably means that the person tried to stop at .00 and missed. They also find evidence of round-number bias in patterns of restaurant tipping and other contexts.
Another set of examples of round number bias come from Devin Pope and Uri Simonsohn in a 2011 paper that appeared in Psychological Science (22: 1, pp. 71-79): "Round Numbers as Goals: Evidence from Baseball, SAT Takers, and the Lab." They find, for example, that if you look at the batting averages of baseball players five days before the end of the season, you will see that the distribution over .298, .299, .300, and .301 is essentially even--as one would expect it to be by chance. However, at the end of the season, the share of players who hit .300 or .301 was more than double the proportion who hit .299 or .298. What happens in those last five days? They argue that batters already hitting .300 or .301 are more likely to get a day off, or to be pinch-hit for, rather than risk dropping below the round number. Conversely, those just below .300 may get some extra at-bats, or be matched against a pitcher where they are more likely to have success. Pope and Simonsohn also find that those who take the SAT test and end up with a score just below a round number--like 990 or 1090 on what used to be a 1600-point scale--are much more likely to retake the test than those who score a round number or just above. They find no evidence that this behavior makes any difference at all in actual college admissions.
Round number bias rears its head in finance, too. In a working paper called "Round Numbers and Security Returns," Edward Johnson, Nicole Bastian Johnson, and Devin Shanthikumar desribe their results this way: "We find, for one-digit, two-digit and three-digit levels, that returns following closing prices just above a round number benchmark are significantly higher than returns following prices just below. For example, returns following “9-ending” prices, which are just below round numbers, such as $25.49, are significantly lower than returns following “1-ending” prices, such as $25.51, which are just above. Our results hold when controlling for bid/ask bounce, and are robust for a wide collection of subsamples based on year, firm size, trading volume, exchange and institutional ownership. While the magnitude of return difference varies depending on the type of round number or the subsample, the magnitude generally amounts to between 5 and 20 basis points per day (roughly 15% to 75% annualized)."
In "Rounding of Analyst Forecasts," in the July 2005 issue of Accounting Review (80: 3, pp. 805-823), Don Herrmann and Wayne B. Thomas write: "We find that analyst forecasts of earnings per share occur in nickel intervals at a much greater frequency than do actual earnings per share. Analysts who round their earnings per share forecasts to nickel intervals exhibit characteristics of analysts that are less informed, exert less effort, and have fewer resources. Rounded forecasts are less accurate and the negative relation between rounding and forecast accuracy increases as the rounding interval goes from nickel to dime, quarter, half-dollar, and dollar intervals."
In short, the research on round-number bias strongly suggests not getting too excited about 1,000,000 in particular. There is very little reason to write this blog post now, as opposed to several months in the past or in the future. However, I hereby acknowledge my own personal round number bias and succumb to it. ...