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The Advantage Blog

  • Jeffrey Jarman Ph.D.


Updated: Jul 14, 2023

I love sports. But I never have time to watch as many games as I’d like. In fact, I rarely find time to watch any games live, so I have to get my sports fix in other ways. I watch SportsCenter, SportsNation, and Numbers Never Lie. But I prefer the competitive banter of sports talk television – Around the Horn and First Take are my favorites.

While each of the shows embraces a slightly different tone and style, the one remarkable similarity between them is the use of evidence — sports and sports commentary are awash in statistics. My favorite recent stats involve this year’s World Series. For the first time EVER, neither team won 90 games in the regular season, and their combined winning percentage of .546 is the second lowest of all time.

These teams’ stats also show why the Royals stand a good chance of winning the World Series: the Royals have 13 stolen bases in the playoffs, while Giants’ catcher Buster Posey only throws out base stealers 29.8% of the time.

Why so much about Royals and the World Series? For one thing, I haven’t been able to talk about the Royals and the Series for 29 years, so I’m taking full advantage of it now. But more importantly, baseball stats illustrate a key strategic question when presenting information: What is the best way to show your statistics?

Consider the Royals’ stolen base total. It could be expressed as a percentage (81.25%), an absolute frequency (13), as odds (.23 to 1), or as a probability (.8125). All these numbers have the same value, but they don’t have the same meaning. Dozens of studies have confirmed that people have different perceptions of a statistic based on its format.

Which format you use depends upon what you’re attempting to accomplish. Here are some general guidelines to consider as you think about your options.

  • Small frequencies and percentages are clearer and easier to understand. We can easily understand the meaning of 1 of 10, or 10%. Most people have little experience with reading odds ratios and probabilities which can make those confusing to a jury.

  • Problems expressed as absolute frequencies are perceived as more accurate than those expressed as a probability. If you were the editor of the New York Times sports section, you wouldn’t say that .01% of the American population attended a parade to celebrate the Boston Red Sox’ victory in the 2004 World Series; that sounds boring and is difficult to visualize. Rather, you’d say that 3 million people attended the parade, making the statistic more concrete.

Attorneys must also choose how to frame the statistic. One very important framing choice involves the use of relative risk and absolute risk in the following imaginary scenario. A new drug called Royalsaminophen is being tested for use in treating Giantsphobia, a severe medical condition. It is discovered the Royalsaminophen increases the risk of vertigo from 1 in 100,000 to 3 in 100,000. The absolute risk has increased by 2 in 100,000, but the relative risk has increased to 200%. Which would be more frightening? That the risk has increased to 3 people in 100,000, or that the risk has increased by 200%.

As you can see from the above example, statistics can convey different meanings to a jury depending upon their presentation. In some cases, attorneys will want to equip the jury to see the problem as very large, and can accomplish this through the use of absolute frequencies and/or relative risk framing. In other cases, attorneys will want to minimize a problem, so here it’s more persuasive to draw upon probabilities and absolute risk.

One word of caution is in order: simply using the “right” statistic won’t guarantee that a jury will reach the “right” conclusion. In fact, the overuse of statistics could easily overwhelm a jury, especially one low in numeracy. Time and effort should go into deciding the format of the statistics that will best convey the information in the case. Jurors need to be equipped to fight for your side – that includes making sure they have access to the best statistics.

Which team will win the World Series? I’m in Kansas, rooting for the Royals. I’m comforted by the fact that they’ve already stolen 13 bases while the Giants’ catcher has a probability of .298 to throw them out. I’m worried, though, because the Royals probability of stealing a base is .8125, and the Giants have only given up three stolen bases this postseason. But what I’m most excited about is making time to watch the games! Go Royals!

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