Regardless of whether 2 or 1.83 is used as the Pythagorean exponent, a flaw in using runs scored and runs allowed to predict each team's record is that when it is done for every team after a season, the expected amount of wins and losses for the teams combined will probably be close but not be equal (meaning that it could give the teams a combined expected winning percentage of something like .505 instead of .500). To make an analogy, if you flip 100 coins you have over a 91 percent chance at getting at least 42 heads and at least 42 tails, but under an 8 percent chance at exactly 50 of each. The pairwise method uses the runs scored by each team against every opponent separately and calculates expected wins and losses for each team against every opponent guaranteeing that the expected wins and losses add up to the amount of games played against every opponent. The downside of the more accurate method is that a common person without statistical software could quickly calculate each team's Pythagorean record using total runs scored and allowed, but each team has 19 or 20 opponents a year depending on if your interleague rival is in the interleague division you play all five teams in, so it would be time-consuming to do that for every team.

http://content.iospress.com/articles...lytics/jsa0018 has a paper about the pairwise Pythagorean exponent.