Both baseball and poker have been televising their World Series championships, and announcers for both frequently describe strategies and tactics based on the statistics of the games. Poker announcers base their commentary and discussion on the probabilities associated with a small number of key metrics, while baseball announcers barrage us with numbers that sound meaningful but that are often pure nonsense.
Similarly, today’s web analytics give us the capability to track and report data on just about anything, but just because we can generate a number doesn’t mean that number is meaningful to our business. In fact, reading meaning into meaningless numbers can cause us to make very bad decisions.
Don’t get me wrong, I am a huge believer in making data-based decisions, in baseball, poker, and on our websites. But making good decisions is heavily dependent on using the right data and seeing the data in the right light. I sometimes worry that constant exposure to sports announcers’ misreading and misappropriation of numbers is actually contributing to a misreading and misunderstanding of numbers in our business settings.
- Selection bias
This one is incredibly common in the world of sports and nearly as common in business. Recently, headlines here in Detroit focused on the Tigers “choking” and blowing a seven-game lead with only 16 games to go. In a recent email exchange on this topic, my friend Chris Eagle pointed out the problems with the sports announcers’ hyperbole:
“They’re picking the high-water mark for the Tigers in order to make their statement look good. If you pick any other random time frame (say end-of-August, which I selected simply because it’s a logical break point), the Tigers were up 3.5 games. But it doesn’t look like much of a choke if you say the Tigers lost a 3.5 game lead with a month and change to go.”
Unfortunately, this type of analysis error occurs far too often in business. We might find that our weekend promotions are driving huge sales over the last six months, which sounds really impressive until we notice that non-sale days have dropped significantly as we’ve just shifted our business to days when we are running promotions (which may ultimately mean we’ve reduced our margins overall by selling more discounted product and less full-price merchandise).
In a different way, Dennis Mortensen addressed the topic in his excellent blog post “The Recency Bias in Web Analytics,” where he points out the tendency to give undue weight to more recent numbers. He included a strong example about the problems of dashboards that lack context. Dashboards with gauges look really cool but are potentially dangerous as they are only showing metrics from a very short period of time. Which leads me to…
- Inconsistency of averages over short terms
Baseball announcers and reporters can’t get enough of this one. Consider this article on the Phillies’ Ryan Howard after Game 3 of the World Series that includes, “Ryan Howard‘s home run trot has been replaced by a trudge back to the dugout.The Phillies’ big bopper has gone down swinging more than he’s gone deep…He’s still 13 for 44 overall in the postseason (.295) but only 2 for 13 (.154) in the World Series.” Actually, during the length of the season, he had three times as many strike outs as home runs, so his trudges back to the dugout seem pretty normal. And the problem with the World Series batting average stat is the low sample size. A sample of thirteen at bats is simply too small to match against his season long average of .279. Do different pitchers or the pressures of the situation have an effect? Maybe, but there’s nothing in the data to support such a conclusion. Segmenting by pitcher or “postseason” suffers from the same small sample size problems, where the margin of error expands significantly. Furthermore, and this is really key, knowing an average without knowing the variability of the original data set is incomplete and often misleading.
This problems with variability and sample sizes arise frequently in retail analysis when we either run a test with too small a sample size and assume we can project it to the rest of the business, or we run a properly sized test but assume we’ll automatically see those same results in the first day of a full application of the promotion. Essentially, the latter point is what is happening with Ryan Howard in the postseason. We often hear the former as well when a player is all of the sudden crowned a star when he outperforms his season averages over a few games in the postseason.
In retail, we frequently see this type of issue when we’re comparing something like average order value of two different promotions or two variations in an A/B test. Say we’ve run an A/B test of two promotions. Over 3,100 iterations of test A, we have an average order size of $31.68. And over 3,000 iterations of Test B, we have an average order size of $32.15. So, test B is the clear winner, right? Wrong. It turns our there is a lot more variability in test B, which has a standard deviation of 11.37 compared with test A’s standard deviation of 7.29. As a result the margin of error on the comparison expands to +/- 48 cents, which means both averages are within the margin of error and we can say with 95% confidence that there really is no difference between the tests. Therefore, it would be a mistake to project an increase in transaction size if we went with test B.
Poker announcers don’t seem to fall into all these statistical traps. Instead, they focus on a few key metrics like the number of outs and the size of the pot to discuss strategies for each player based largely on the probability of success in light of the risks and rewards of a particular tactic. Sure, there are intangibles like “poker tells” that occur, but even those are considered in light of the statistical probabilities of a particular situation.
Retail is certainly more complicated than poker, and the number of potential variables to deal with is immense. However, we can be much more prepared to deal with the complexities of our situations if we take a little more time to view our metrics in the right light. Our data-driven decisions can be far more accurate if we ensure we’re looking at the full data set, not a carefully selected subset, and we take the extra few minutes to understand the effects of variability on averages we report. A little extra critical thinking can go a long way.
What do you think? Are there better ways to analyze key metrics at your company? Do you consider variability in your analyses? Do you find the file to test two averages useful?