More on Strength of Schedule

Regular Sounder at Heart readers-slash-nerds will recall the post I wrote a couple of weeks ago explaining the methodology behind the season simulation I use to calculate the Sounders playoff odds that I maintain on Seattle Soccer Scene. Dave brought up the Strength of Schedule question in a post earlier today, and that gave me a good excuse to make a few tweaks. While the sim isn't specifically designed to calculate strength of schedule, it's easy enough to adapt it to do so and the fact that it's already weighted to favor recent results and take into account home and away splits means it'll likely provide more detail than you'd get by just dividing winning percentage.

In short, since I already sim out games based on recent goals scored and allowed results, I can use those same factors to determine which teams have the best weighted goal differentials at home and away and then calculate the toughest upcoming schedules.

One way to do so is to look at the average goal differentials remaining on the schedule, and then average those out. For example, Columbus has a weighted goal differential of 1.02 at home — the second best in the league behind RSL. That means that, on average, Columbus will score just over a goal more than their opponent at home. (The worst home differential in the league, for the curious, is unsurprisingly DC United, who average 0.9 fewer goals at home than their opponents). So if I take each team's opponents for the remainder of the season and average out their goal differential at home or away, I can find the average toughest remaining schedule.

And the results might be surprising to Sounders fans. I have Seattle with the fourth toughest remaining schedule, behind only RSL, New York, and FC Dallas, with Colorado trailing just behind. Why is that? For one, the Sounders have 5 of their remaining 9 games away from home. Home field advantage is still a big factor in MLS. Only one team (DC United) has a negative score differential at home. And only two teams have a positive differential away (LA and FC Dallas). Secondly, there's that game in Columbus, which will drive the average way up. More on that in a bit. Thirdly, one of the home games is against streaking RSL and another is against the Fire, who surprisingly have the fourth best road differential in the league. Chicago doesn't get a large home field advantage, but they're a pretty good road team. And finally, the Dynamo — despite struggling mightily from a points and winning percentage perspective — are still a strong home team and shouldn't be treated lightly in Houston.

All that said, there's a weakness in this formula. Averages can be skewed by outlying values, and the fact is we can only lose to the Crew in Columbus once, so there's no need for their big home number to dominate the average. The real solution for this is to just use the sim results, but if you really want to come up with an isolated strength of schedule value, it might be better to use the median values rather than the average. By that measure, the Sounders have the 8th hardest remaining schedule, smack dab in the middle of the pack.

Here are the remaining games on the Sounders schedule, with their weighted goal differential. Higher means a tougher game for Seattle.

Remaining Sounders Matches
v Chicago Fire -0.081
@ New England Revolution 0.269
v Real Salt Lake -0.054
@ Columbus Crew 1.021
@ Chicago Fire 0.091
v Toronto FC -0.875
@ Kansas City Wizards 0.026
v CD Chivas USA -0.218
@ Houston Dynamo 0.436

And here are the full tables of team differentials at home and away and the remaining strength of schedule, first by median:

Strength of Schedule (Median)
Home Diff Away Diff Remaining
Real Salt Lake 1.867 -0.054 0.253
Chicago Fire 0.091 -0.081 0.16
CD Chivas USA 0.021 -0.218 0.16
San Jose Earthquakes 0.211 -0.149 0.086
Kansas City Wizards 0.026 -0.888 0.084
New York Red Bulls 0.147 -0.267 0.053
Colorado Rapids 0.428 -0.159 0.046
Seattle Sounders FC 0.253 -0.361 0.026
New England Revolution 0.269 -1.565 0.023
Columbus Crew 1.021 -0.22 -0.029
Toronto FC 0.82 -0.875 -0.054
D.C. United -0.893 -1.215 -0.064
Los Angeles Galaxy 0.999 0.717 -0.069
FC Dallas 0.936 0.372 -0.081
Houston Dynamo 0.436 -1.299 -0.115
Philadelphia Union 0.16 -1.278 -0.15

and by mean:

Strength of Schedule (Mean)
Home Diff Away Diff Remaining
Real Salt Lake 1.867 -0.054 0.198
New York Red Bulls 0.147 -0.267 0.197
FC Dallas 0.936 0.372 0.087
Seattle Sounders FC 0.253 -0.361 0.068
Colorado Rapids 0.428 -0.159 0.062
Chicago Fire 0.091 -0.081 0.028
San Jose Earthquakes 0.211 -0.149 -0.019
Columbus Crew 1.021 -0.22 -0.029
New England Revolution 0.269 -1.565 -0.06
Toronto FC 0.82 -0.875 -0.097
Kansas City Wizards 0.026 -0.888 -0.141
Philadelphia Union 0.16 -1.278 -0.143
D.C. United -0.893 -1.215 -0.146
CD Chivas USA 0.021 -0.218 -0.175
Los Angeles Galaxy 0.999 0.717 -0.189
Houston Dynamo 0.436 -1.299 -0.31

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