Blue Jays and green beans

The Globe reported late Tuesday, on the basis of six home games, that “Rogers Centre has become a home run haven”, claiming that extra-long gophers are being hit under the don’t-call-it-Skydome at “a record-setting rate”.

Through the first homestand last week that saw Toronto win two of six games, the home side and their opponents combined for 23 homers, the most in the majors, and at 3.83 home runs per game, second in the 30-team league. Rangers Ballpark in Arlington saw four home runs per game.

The home run average across the majors the first week was 2.14 per game, so what has transpired at Rogers Centre so far represents a huge increase. Should the trend continue–a big if, considering 75 regular-season home games remain–upwards of 310 home runs stand to be clubbed at the Rogers Centre, which would set a major-league record.

That last part, of course, is sheer foolishness: almost every ballpark will have some six-game stretches in which a “record-setting rate” of home runs is achieved. This particular streak is being noticed because it came at the start of the season, a reporter took notice, and the phenomenon can be tenuously pegged to some hypothetical or downright imaginary changes in airflow and other conditions at Rogers. Fans love home runs, though, so I’d like to express the Rogers empire’s appreciation to the Globe for whipping up interest.

What I wondered, as a journalist wary of the Sin of Small Sample Size, was how much of this home-run phenomenon we can attribute to the park, as opposed to the team. The Jays, after all, went bananas with trades and free-agent signings in the offseason, and they were already a power-heavy team. The road teams visiting Rogers hit 12 home runs over the six games in 254 plate appearances. That’s a rate of 5.3%. Overall this season, non-Jays teams have hit 250 in 8,771 plate appearances outside Rogers Centre: a rate of 2.9%. The difference looks impressive, but how significant is it statistically?

By the conventional standard, the answer is “just barely”. If you run what’s called a “chi-squared test for equality of proportions”, you find that a difference of that magnitude would arise by chance only 4.875% of the time; in the sciences the usual habit is to set the significance cutoff at 5% or less. And this goes to illustrate one of the big problems with classical hypothesis testing in the sciences. If we checked all thirty big-league teams through early-season samples of similar size, and the teams all actually hit home runs at the same rate in the long run, we would still expect 5% of the 30, or one-and-a-half, to have a “significantly” unusual apparent home-run rate.

The issue is illustrated well by a famous web cartoon about green jellybeans. And that’s exactly what we have here: a big pile of green jellybeans. Unsurprisingly, it is too soon to start telling just-so stories about how balls are travelling further because of the mojito fumes from the centre-field bar at Rogers. How pleasant to think so, though.

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