Easy as 1.121: How some nerdy strength of schedule stats will make you happy about Austin FC's last 15 matches

If you have this nagging sense that Austin FC's had a really difficult season to date, and that it can only get easier from here, do we have some stats for you.

This journey started a couple of days ago when I began pondering Austin's strength of schedule over these first 19 games – including a winless-in-league-play May – and how it compared to the strength of schedule Austin will face in the remaining 15 games. With names like CF Montréal, St. Louis, SKC, and the hapless Galaxy on the schedule to come, it's got to be easier down the stretch, right?

That's when I checked in with Chase Hoffman, who brought me into the American Soccer Analysis fold a while back, telling me about the perspective-shifting (or at least reinforcing) conference I attended at the start of this year. If I need to get to a next level of numbers nerdery, Chase is one of the first people I check in with.

I'd initially run some numbers to attempt a strength-of-schedule calculation, using points per game as the metric. I found that if you took Austin FC's first nineteen opponents – that includes counting Vancouver, San Diego, Minnesota, and Portland twice, as Austin's played each of those teams home and away already — added all opponents' current points per game (starting with adding 2.06 to 2.06 to get Vancouver's lofty contribution), and divided the total by 19, Verde's opponents have an average 1.425 PPG in that half-plus-two-games so far this season.

In May, Verde played seven league matches; opponents they faced that month had a 1.571 PPG average. If those seven teams were an MLS Voltron getting that PPG over a whole season, it works out over a full season to be a little over 53 points. (Our Voltron would have been good enough for 6th in the East or 4th in the West last season.)

But Verde's average PPG for the remaining 15 matches? 1.121 PPG.

The question I threw out to Chase was how that compares to other MLS teams.

He came back, after some math, with charts and talk about standard deviation, which I surmise collectively makes us fun at parties, but only certain kinds of parties.

Can I interest you in some charts to show how good Austin FC might have it?

Some charts

Here's the first encouraging visual to show you how an opponent group averaging 1.121 PPG (like playing 2023 Austin over and over[[1]]) shapes up.

And then, also, here's a quick and dirty table to show the march Verde has been on up to this point.

Yep, that's the second-hardest schedule in the West, only "bested" by the Galaxy, who are clearly having a time of it this season.

Conversely, look at the top four in the West, who happen to occupy four of the seven lowest opponent PPG spots. Maybe there's a correlation between San Diego FC looking so good and the teams they've had to face so far?

In a chart involving just the West teams, here's what's come before compared to what's coming next.

For LAFC and Minnesota, it's about the same. For San Diego and Portland, it's appreciably harder.

For 8th-place San Jose, who Austin still has to play twice in league matches, including on Decision Day (and, of course, once in the Open Cup), it gets harder. It also gets harder for FC Dallas, in 10th place, and Austin will play that rival twice. Austin also has to play 6th-place Seattle twice, including on Saturday night in Seattle, catching them at potentially the best possible time to catch them in Lumen Field[[2]] — though Seattle's schedule also eases up post-Club World Cup compared to pre-Club World Cup (and certainly during the Club World Cup).

And then just for fun, here's how home vs. away looks down the stretch.

An away opponent average PPG of less than 1? Yes, please!

You're following me so far? Let's get into standard deviations now, which I'm only now getting better at understanding, which will help us grasp how remarkably significant the lower strength of schedule number down the stretch is.

Let's get really nerdy

Here's a good definition of standard deviation from the National Library of Medicine:

"A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low, or small, standard deviation indicates data are clustered tightly around the mean, and high, or large, standard deviation indicates data are more spread out. A standard deviation close to zero indicates that data points are very close to the mean, whereas a larger standard deviation indicates data points are spread further away from the mean."

Then we've got to cover Z-score, which is, per Investopedia,

"a statistical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean."

Following so far?

"Z-score is a statistical measure that quantifies the distance between a data point and the mean of a dataset. It's expressed in terms of standard deviations. It indicates how many standard deviations a data point is from the mean of the distribution.

"If a Z-score is 0, it indicates that the data point's score is identical to the mean score. A Z-score of 1.0 would indicate a value that is one standard deviation from the mean. Z-scores may be positive or negative, with a positive value indicating the score is above the mean and a negative score indicating it is below the mean."

Now here's another Z-score tidbit to keep in mind.

"In most large data sets (assuming a normal distribution of data), 99.7% of values lie between -3 and 3 standard deviations, 95% between -2 and 2 standard deviations, and 68% between -1 and 1 standard deviations."

Here's where that comes into play, starting with standard deviation.

See how that falls off a cliff when it gets to Austin? And look at St. Louis at the mean, and how more than half the MLS teams are above the mean in their remaining games.

And now, this!

Remember that 95% of datasets typically have between Z-score values from 2 to -2. Austin's very close to a Z-Score of -3. In other words, that's highly unlikely variance from the mean. In this case, it works in Austin's favor as the opposing strength of schedule is almost three times easier per the stats math.

Or, at least it has the potential to be that. Austin has to play the games, first of all.

Keep in mind how the strength of schedule looks now will look at least slightly different by the end of the season due to teams getting hot or cold adding or shedding points to affect their overall PPGs.

Also, because it's MLS, teams can change their composition about 2/3 of the way through their seasons — due to a transfer window scheduled when most of the world's leagues are between seasons.

So, let's say Antoine Griezmann decides he really wants to play in San Jose under Bruce Arena[[3]], and moves there in the summer transfer window. Even with the challenge it takes some players to adjust to MLS from overseas leagues, I'd hazard a guess that a Quakes team with Griezmann is better than a Quakes team without him.

Certainly, at least some teams will pick up difference-making new players in the summer transfer window. Some of those teams will get better and play better than their late June PPG average indicates. We just don't know which teams those will be.

Who knows – one of those teams might even be Verde.

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[[1]]: Sorry to bring that up, but that team was at 1.15 PPG, and you're all familiar with how that looks.

[[2]]: Considering they just crashed out of the Club World Cup with three straight losses, albeit to PSG, Atlético Madrid, and Botafogo, which are difficult teams.

[[3]]: For illustrative purposes, of course, though the prospect of this happening is certainly worth entertaining just for the sensible chuckles.