Analyzing chances of winning a two-leg aggregate series

In 2003, Major League Soccer introduced 2-game aggregate series into the MLS Cup playoff structure. For that first season, "golden" goals in 2nd leg extra time could end the game. In 2014, the league adopted the current practice of using away-team goals as an end-of-180-minutes tiebreaker. If we ignore these nuances, the league has completed 12 years of 2-game aggregate playoff rounds, and played 54 unique series over that span... but 54 games is not enough to predict anything about a winner...

The chart above plots the goal differences (high seed minus low seed) of the first leg, second leg, and full 2-game aggregate against the teams' respective performances over the course of the regular season. "Projected goal difference" is the GD for the higher seed projected over 180 minutes, minus the lower seed's GD. Neither this metric nor the ppg difference between teams are particularly predictive of success in the 2-game series or even in any individual leg therein (the best fit of the omitted linear regression lines presented an r-squared value of ~0.016, and all trendlines except the top left have negative slope). Establishing superior play over a full season seems to matter little when it comes to the home-and-away sequence, and the lower seed has advanced to subsequent rounds on 23 of 54 occasions (42.6%). Perhaps the requirement that the higher seed play first on the road does indeed outweigh any extra time advantage in the second leg (as might be expected from the characteristic success of home teams in league play).

But that was not the question eight teams want answered this week: once the first leg has been played, how much do we know of the end result?

The better fit here is no surprise (given that the x-axis value is a component of the y... if one plots 1st leg performance vs. 2nd, the 2 games show no relationship in results), but illustrates the basic point that a first leg win makes a great deal of difference to the series. The higher seed has headed home for the second leg playing from behind on 25 occasions in MLS Cup play and advanced 10 times. The higher seed has advanced on 8 of 16 occasions (50%) heading into the second leg with a 1-goal deficit. Rewinding the exciting end to Sunday's game a bit...

The higher seed has advanced 10 of 15 times (66.7%) following a drawn first leg.

The higher seed has advanced from a first leg advantage 11 of 14 times (78.6%). Andreas Ivanschitz and Clint Dempsey took 23 minutes to improve Seattle's chances of advancing to a coin flip, based on MLS history (this comports fairly well, incidentally, with the ASA projection of 0.524 based on expected goal distributions).

Of course, both MLS history and the teams' respective 2015 performances will mean little in Frisco if Seattle fails to contain the Dallas offense. Fabian Castillo was able to create half-chances at will on Sunday when isolated with Tyrone Mears or Zach Scott, and Oniel Fisher had shaky moments attempting to contain Michael Barrios on the other side of the field. Without bunkering too early, the Sounders will have to defend well enough to capitalize on their advantage, and that very likely requires a better performance than Sunday.