By Jared Young (@jaredeyoung)

Major League Soccer has updated their playoff format for 2019 to a March Madness style single elimination tournament that will take roughly a month play out. The prior competition used a combination of single elimination and home and away ties over a month and a half period, and had long breaks in the action. The one clear benefit of this change is the shortened duration of the tournament. Avoiding the November international window will create a compact and uninterrupted tournament that should improve the momentum of the story lines that emerge.

The new format is also supposed to benefit the higher seeds, as the single elimination games will give advantage to the home teams, versus the old method of home and away legs for each team. This seemingly makes regular season games more important. More Victory! [Insert scratching record sound here]. These types of simplifying statements make my geek antenna start to hone in on theoretical galaxies of mathematics. Sadly, the only off switch I have for my antenna is my keypad and a Google docs session. So let’s dig in and deconstruct this new tournament bracket and see who benefits and who does not, and if indeed the regular season matters more.

**Starting in theory**

Tournament analysis can get complicated quickly, so let’s start with a very simple model. Let’s assume that all the teams that enter the playoffs are exactly as good as one another. Yes, that’s a dramatic simplifying assumption, but it will be loosened later. The benefit of looking at a tournament this way is that it isolates the idiosyncrasies of the competition structure itself. In other words, it lays bare any fairness issues and doesn’t let the fact that better teams are at the top cover those issues.

Next we need to estimate what home field advantage is worth for an average team. To do this we’ll estimate the probability team will win at home. I took the average of three different results to determine this probability. MLS single game playoffs have been won by the home team 64% of the time. Last season, the home team won 65% of the time, if you split the draws in half. I also ran a Poisson based simulation of thousands of games using the expected goal differences for home and away teams observed on average over 2018, which projects a 60% home team win probability. The average of those observations is 63% which is what was assumed in the analysis below.

We also need to estimate any advantage for the two game tie. This is simple in this situation because we’re assuming the teams are even. Therefore, both teams in a two game tie have a 50% chance of winning.

Now we need to play out each tournament format using the probabilities above. The results below show the probabilities of winning the conference by seed between the old and new formats. The reason that we’re focusing on just winning the conference is because the MLS Cup Final portion of the tournament remains unchanged as a single elimination game.

The first thing that jumps out is that all of the value in the new structure has been transferred to two teams - the first and seventh place teams. The seventh because they weren’t in the tournament in the old format, and the first because they are now the only team with a bye. The seventh place team now has a 5% chance of winning the Conference. There is now significantly more incentive to finish first. The top team is 15% more likely to win the conference. All the other seeds - two through six - have seen their chances take a hit between 3% and 6%.

The old format had a stepwise incentive structure. Finishing first or second was important because of the bye. Finishing third or fourth was important because of the home field advantage in the knockout stage. Removing for quality of competition those were the only incentives. The new format definitely has a more linear incentive system. Your odds move up with each seed with one exception. There is actually a negative incentive to finish fifth instead of sixth. This is because the new format does not reseed teams between rounds. That means that the fourth or fifth seed are guaranteed to play a second round away game, while there is a chance that the sixth seed could still get a home game (in the event the seventh seed upsets the second best team).

In other cases, some seeds have less incentive to move up than they had in the prior format. For example, the three seeds have less incentive to become two seeds than they previously had. In the old format their probability of winning the conference would go up 9%, but now it’s only worth 5%. A similar story is true when moving from fifth to fourth.

Does the new format increase the importance of the regular season? It depends on where you sit in the standings. If you are pushing for the first or seventh seed - absolutely. If you are pushing for the second or fourth seed, not so much. And you’re actively not interested in the fifth seed if you are sitting in sixth. But the chances of winning only marginally change (and in fact have gone down) for most teams. All of the value now rests in becoming the top seed, and that race will likely only involve two or three teams at most.

**Introducing some reality**

Okay, but some of these teams are actually better than the others. It’s better to be a fifth seed than a sixth because you get to play a four instead of a three, right? Maybe. Going back to 2011 here is the expected goal difference by finish, averaging the Eastern and Western conferences together.

Historically the top seed has been a quarter of a goal per game better than the two seed, but after that the teams are roughly equal. That is, until the new seventh seed is introduced, which will likely be significantly worse than the rest of the field. So here again, it’s good to be king, but after that the theoretical probabilities above won’t be too far off from reality.

Before completing the picture let’s look at the value of home games versus home and away ties. When introducing different team quality, how do these two concepts fare? Using that Poisson based simulation of average home versus away expected goal differences, this is how the two forms of elimination play out:

The way to read this chart is that if one team has a 0.75 better goal difference per game than their opponent then there is no value difference between one home game or a home and away tie. The probability of either team winning is the same. Home field advantage is obviously a big factor for evenly matched teams, but as the quality of the two teams separate, the two forms of elimination don’t share as much difference in expected outcomes. This is likely due to the fact that the better team ultimately has more time to exert their “betterness” over their opponent, and the home field advantage on either end is less of an issue relative to time on the field. The lines actually do cross for extreme differences in team quality.

The blue circles, where a one seed versus four or five matchup rests on the spectrum, is not that far up the curve, so in most cases a tournament won’t have a situation where home field advantage is actually a disadvantage versus a home and away tie.

Putting it all together, the final outcome doesn’t look much different than the initial one.

The number one seed advantage isn’t quite as big, but it’s still enough to perk up the antenna of, say, an Arthur Blank or other wealthy owner. The stakes just got higher for winning the Conference in the regular season. But in general the new format does little to change the perspective of most of the teams, unless you are one of the owners who are “broke” or cheap, because they can now sell a little hope too. But beware the five seed, if you are in the sixth spot be sure to not work too hard.