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In the midst of the muggy swelter of July, it’s not just baseball aficionados who look forward to the crisp, cool days of October. But with twice as many wild cards this year, fully one third of all major league teams will be suiting up when the season ends, giving fans an additional reason to anticipate the autumn. But which teams are we likely to see in the playoffs, and which ones will be watching it on TV with the rest of us?

Pythagorean winning percentage was created by Bill James to estimate the number of games a team should have won based on their runs scored versus runs allowed. It was so named because of its resemblance to the Pythagorean theorem.

James’ original formula was:

W = RS2 / ( RS2 + RA2)

where W is expected wins, RS is runs scored, and RA is runs allowed.

The formula has been tweaked over the years for greater accuracy. The version I’ll be using in this article is the one used by Baseball Reference:

W = RS1.83 / ( RS1.83 + RA1.83)

The difference between actual wins and expected wins is referred to by the technical term luck. A team is “lucky” if their actual wins exceed their expected wins, and “unlucky” if their actual wins are less than their expected wins. Over the course of the season most teams’ luck evens out and their actual winning percentage moves closer to their Pythagorean winning percentage.

For example, in 2005—the Washington Nationals‘ first season after moving from Montreal—the Nationals led the NL East by 2 ½ games at the All-Star break; they were 16 games above .500, yet their Pythagorean winning percentage was only .495. In the second half Washington faded, ending the season at 81-81. At the opposite end of the spectrum, the 2008 Cleveland Indians found themselves mired in last place at the All-Star break, 12 games below .500, despite having a .509 Pythagorean winning percentage. In the second half the Indians moved up and also managed to finish 81-81.

Note, however, that Pythagorean winning percentage is not fate. Occasionally a team can defy the odds for an entire season. The 2007 Arizona Diamondbacks rode all the way to the National League Championship Series despite having a sub-.500 Pythagorean winning percentage. But they are the exception rather than the rule.

Personnel changes, too, can affect a team’s chances of winning. Last year the Detroit Tigers came out of the All-Star break leading the AL Central despite a .491 Pythagorean winning percentage. Second half trades brought them Doug Fister, Delmon Young, and Wilson Betemit to shore up weaknesses, and the Tigers finished the season outscoring their opponents 787 to 711 for a .546 Pythagorean winning percentage. In the end they won 95 games and the division.

Injuries can make a difference as well. Last year’s Pittsburgh Pirates were only a game out of first at the All-Star break, but were beset by injuries throughout the second half of the season. They acquired Derrek Lee and Ryan Ludwick at the trade deadline, but even these two players spent time on the disabled list. As the injuries piled up, so did the losses, and the Pirates finished the season at 72-90.

But generally, the Pythagorean winning percentage can give us a good idea where a team will end up.

The following analysis combines each team’s first-half record with second-half projections based on their Pythagorean winning percentage to this point.

AL East

As strong as this division is, the Yankees are head and shoulders above the rest. The other four teams will likely spend the rest of the season fighting for a wild card spot.

The surprise of the AL East is Baltimore, which was expected to finish last place but was actually in first as late as June 7. Unfortunately, their Pythagorean winning percentage suggests that despite their strong start, they are still expected to finish last in this competitive division.

Boston has been one of the unluckiest teams in the major leagues, but they are still in the thick of it, and once their luck turns around they have a good chance of joining the Yankees in the playoffs.

The Chicago White Sox were expected to be contenders…a year ago. After a disappointing 2011, the White Sox faced low expectations for this year. But they have rebounded and are having the kind of season last year was supposed to be. What’s more, luck has been against them. The White Sox have actually played better than their record indicates. Meanwhile, the second-place Indians have been lucky so far.

Despite adding Prince Fielder to last year’s division title team, the Detroit Tigers are stuck in the middle of the pack. A five-game winning streak just before the break pulled both their actual and Pythagorean winning percentages above .500, but they will have a hard time catching Chicago at this rate. Unless something changes, the White Sox should win this division by a wide margin.

AL West

This division is pretty simple. The defending American League champion Rangers are the clear favorites. The Angels are on pace to win 90 games, and should be the favorites to host Boston in the Wild Card Playoff.

NL East

All three NL division winners from 2011 are under .500 this year, but none have sunk further than Philadelphia. The Phillies’ situation is actually not as bad as it looks, because they have been among the unluckiest teams in the majors, while Miami in 4th place has been one of the luckiest. With a more regular distribution of runs, these two teams would swap places in the standings. Still, at this point the Phillies might be too far behind to get out of last place, especially if they sell off pieces of the team to reduce payroll.

Washington has been a surprise in 2012 after six consecutive losing seasons. With the only pitching staff in the major leagues that has allowed fewer than 300 runs to this point, the Nationals are on target to win 95 games—which would tie the franchise record set in 1979 as the Montreal Expos—and finish a full season in first place in for the first time. (The Expos won the 2nd half of the 1981 season and were leading the NL East in 1994 when the season was suspended.)

This is the closest of all the division races, with three teams within 2 ½ games of first. It’s all the more close because first-place Pittsburgh has been lucky and third-place St. Louis has been unlucky. The Pirates and Cardinals—as well as the Reds—are on a pace to win 90 games this season. This division could easily produce both National League wild card teams.

NL West

The Dodgers have exceeded expectations this year, while the Giants have been lucky just to stay in the hunt. That’s not the way these teams were picked at the start of the year, but the Giants’ sub-.500 Pythagorean winning percentage indicates that they have some work to do if they want to remain competitive in the second half of the season.

The table below shows the teams most likely to make the playoffs, based on first-half results and Pythagorean projections for the second half.

The Orioles, Indians, and Giants are all in second place at the moment, but they have done it while being outscored by their opponents for the season. They will need to improve on this if they want to stay competitive.

So who will be the actual playoff teams? We won’t know until the end of the regular season. Statistics can give us probabilities, but they never tell the whole story. In baseball, on a given day, anything can happen. That’s what makes the sport so fascinating.

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