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The Pythagorean Theorem and the Birth of the "Johnson Effect"

A journalist named Bryan Johnson was a reporter/columnist for the Toronto Globe and Mail in the late '70s and early '80s. I don't know what Johnson's doing now, or even if he’s still alive, but at one time he was known in sabermetric circles for the "Johnson Effect": that is, the idea that teams who outperform or underperform the record that their runs for-runs against ratio predicts will basically revert to that level the next year, all else being equal.

Looking around online, it seems few remember Johnson now, so I thought I'd discuss him a little bit here. I rooted around some archives and found the Johnson "Inside Baseball" column that apparently debuted the "Johnson Effect." It came out on Thursday, October 14, 1982. Some relevant excerpts:

 

In the euphoria of a 78-win season, Toronto Blue Jays' rosy future seems to be regarded as a virtual certainty. Media analysts have already zeroed in on their many close losses (30 by a single run, 17 by two runs) to prove that just a few changes will reap enormous dividends. One Toronto columnist traced this "painful" statistic to a lack of home-run power, concluding that the problem could be "turned around" by adding a slugger. . . .

Doesn't anybody bother to read the team's statistics? The fact is that the Jays were superb in close contests this year - playing significantly better than they did in other games. They won more close games than before, and, far from offering a chance to move up, their excellent 1982 record in tight situations may pose the greatest single danger for a major backslide next season.

The numbers could hardly be clearer. Toronto was 28-30 in one-run and 19-17 in two-run games, for a .500 mark in those "painful" tight games. They played .456 ball the rest of the season. In addition, the team, which entered 1982 with an abominable 24-45 (.348) record in extra-inning games, had a fine 10-5 record in those contests this year. . . .

Without an off-season infusion of talent, the law of averages will have a lot to say about the Jays' success in 1983, and its pendulum is swinging against them on almost every front.

First of all, there is a simple formula that computes a team's probable winning percentage from its runs-scored and runs-allowed totals. Unfortunately for the romantics among us, such dull-sounding mathematics play an enormous role in the year-to-year success of any team, since it is virtually impossible to vary more than four or five wins from the "projected" results. Think of it as the ghost inside the machine, a shadowy win number that sits inside your stats and dares you to mock it.

Occasionally, someone does push the ghost around a bit, and promptly feels its wrath. Possibly because of the players' strike that interrupted the 1981 season, Cincinnati Reds finished a full nine games above their projected win total last year. But that only meant the Reds appeared to be nine games better than they actually were - a theory borne out by this season's resounding crash into the basement.

The 1982 Jays aren't nearly that over-rated, but the projected win mark for their 651-701 runs total is 75 games, three fewer than they actually won. Essentially, that means that if they went out tomorrow and duplicated this season's bottom-line numbers, they probably would win 74 to 76 games, and they are no more likely to win 78 again than 72 - which all observers, including the Jays themselves, probably would view as a disappointing season.

 

Then, on Thursday, April 14, 1983, in a column titled "Blue Jays will win more games - it's in the numbers," Johnson followed up:

 

It is flattering to be named in Bill James' latest Baseball Abstract as inventor of something called the "Johnson Effect." Now all I have to do is refine the theory advanced here last October . . . while somehow tip-toeing away from its original conclusion.

Most readers have long forgotten my first column six months ago, which used a Pythagorean formula to explain why Toronto Blue Jays would slide backwards in 1983 if they tried to stand pat. But it apparently struck a chord in the fertile mind of Mr. James.

His exhaustive research has turned my idle speculation into a proved theorem.

The formula (which predicts winning percentage from runs scored and allowed) indicated the Jays' 78 wins last season were three more than they had earned. So I concluded that, even if they precisely duplicated their runs this year, they'd probably win 75 games - and were as likely to get 72 as another 78.

James, of course, has risen to prominence as baseball's statistical guru mainly by demolishing the easy myths of daily journalism. And he wasn't about to accept my reasoning at face value. "Is it not possible," he asks himself in the '83 Abstract, "that getting more wins than your share out of a given number of runs is in some way a talent, and thus something which is steady from year to year?"

No, apparently, it is not. James used a computer printout of won-lost percentages for 80 years to test the theory. Of the 42 teams that did far better than their Pythagorean projections, 29 declined the next season, while only 13 improved. And even the smaller margins - such as the three- game bulge of the '82 Jays - produced the same results. Of 50 American League teams that had a similar record since 1960, two-thirds declined the next year, with a net loss of 203 games.

"Johnson certainly seems to have a point," concludes the Abstract. "Teams which win more games than their Pythagorean expectation are lucky, by and large, and their luck does not hold up from year to year. . . . So, the Blue Jays are 2-to-1 favorites, essentially, to win fewer than 78 games in 1983." . . .

My own best estimates rank the improved Jays four or five games above last season. But, since I also accept that Pythagorean projection as their true level in 1982, that would place them at 79 or 80 wins this time. They could defy the mathematical odds once again to reach higher, but even then it's stretching things to look above 83 or 84.

 

Johnson's "Inside Baseball" column was apparently the first regular, in-depth statistical/sabermetric column to appear in a North American newspaper (I believe it came out either every Thursday or every other Thursday). You can also read excerpts from him talking about Range Factor in 1983, his take on the meaning of the 1982 Bill James Baseball Abstract, and him getting criticized by one Globe and Mail reader. By the way, in 1983 the Blue Jays went 89-73 (88-74 under the Pythagorean method), starting their run as probably baseball's best team over the 1983-1993 period.

 

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