Towards a USL League One Power Ranking

I want to put together a power ranking, but not one just based on gut feelings. In order to do that, I am utilizing the popular ELO approach. (I capitalize ELO out of habit but it really should be Elo; it’s a name not an acronym). ELO has been used in Chess for a long time, as well as many other sports.

Instead of weighing team A against team B, I am going to take the approach of looking at Teams as two parts; offense and defense — and each is going to get it’s own ELO rating. This is similar, I think, to the approach that 538 takes in their power rankings.

Advantages of the ELO rating approach to soccer

• Objective
• Gives an expected result
• Easy to update with new information

Disadvantages

• Resistant to change — “k factor” can limit rapid changes while roster turnover especially at the League One level can result in drastic changes. This is why 538s MLS rankings are always so funky at the beginning of a season; for example, why NYCFC was ranked above Columbus Crew SC in their preseason MLS rankings in 2021.

What is a Win, loss, and draw?

- Elo is designed for a zero sum game like chess where there is a clear winner and loser. Draws are frequent in high level chess, but less useful for an ELO rating system

- Rather than saying the team that scored more goals is the winner, with the offense vs defense system there are four potential outcomes for a game.

- Winning or losing against the other team is based on expected outcome — beat the expected outcome and you have “won”

How do I determine what the expected outcome is?

As always, thanks to American Soccer Analysis for the historical data.

• First, I looked at all USL League One games since the founding of the league. That sample size was fairly limited (n = 236), but the median Home xG was 1.25 and the median away xg was 1.05. On a baseline level, that seems like a good place to start.
• To get a larger sample, I also looked at all MLS games since 2013 (n = 2830). Home field advantage was more pronounced in MLS — median Home xG was 1.5, but median away xG was still 1.05.
• If you compare actual xG against median xG, you get a difference that can be used to create a normal distribution (see below). The majority (25th to 75th percentile) of games are within -0.4 and +0.5 of the median xG.

Now for the Math

The ELO ranking can be calculated after each game by adding the pre-match ELO to the k-factor multiplied by the difference between the actual and expected score.

In equation form, how to calculate ELO after a result

The expected score is where we will see the biggest departure from ELO — and the biggest departure from being an accurate predictor. Below is a table for predicting outcomes based on ELO differences. Instead of using the predicted win outcome, we will use the percentile likelihood of a victory to compare to the similar percentile rank of historical outcomes in margin vs. the median for MLS/USL. This is the area that needs the most improvement in the model.

Win probability is 50% for evenly ranked teams

Here’s an example; the ELO percentile tables indicate a 500 difference in ELO between two players means the higher ranked player will lose 5.32% of the time and win 94.68% of the time. Say Team A’s offense is ranked 500 points higher than Team B’s defense, and team A is playing at home. That would mean that Team A is predicted to generate 2.88 xG; if team A was away, it would only be 2.02.

Now assume that Team A’s defense is only 250 ELO points better than team B’s offense. That would mean Team B’s offense would be expected to earn 1.0 xG at Home, or 0.7 away.

Assuming Team A is at home, ELO the prediction would be that Team A would generate 2.88 xG to team B’s 0.7. You can further apply a poisson distribution to these numbers to determine outcome probability. Team A would be predicted to win 78.98% of the games, 11.96% would be a draw, and 9.06% would go to Team B.

Tweaking the K Factor

Now, having set up the formulas, we need to look at K Factors. I started with 50 as a constant K factor; the problem is that by the time we reached the end of the data set the average K factor difference was >800 and not even on our probability chart. I ended up setting the K Factor at 20 after testing multiple K factors for accuracy.

The disclaimer

Ideally, as you feed more info into an ELO system, it should become better at predicting outcomes over time. This was not the case. Regardless of K Factor, the formula got worse at predicting xG the more data considered. It is better than just considering the median Home and Away xG, but not by much. A K factor of 60 was the most resistant to losing accuracy over time, but a K factor of 20 had more sensitivity in the early stages (relevant for USL) and is what I will use for USL power rankings going forward.

My suspicion is that the win percentage outcomes of ELO differences is not quite transferring to soccer, and the formula will need some slight modification to be more accurate. That will come in time.

The point is, don’t take these power rankings to the bookies just yet; the correlation coefficient between predicted xG and actual xG is still just 0.38 — less than ideal.

USL League One Power Rankings:

1. Greenville Triumph SC (Offense: 1583, 3rd overall; Defense: 1649, 1st overall)
2. Forward Madison FC (Offense: 1558, 4th overall; Defense: 1611, 2nd overall)
3. North Texas SC (Offense: 1684, 1st overall; Defense: 1483, 7th overall)
4. Union Omaha (Offense: 1537, 5th overall; Defense: 1579, 3rd Overall)
5. Chattanooga Red Wolves SC (Offense: 1518, 8th overall; Defense: 1522, 4th overall)
6. Richmond Kickers (Offense: 1531, 6th overall; Defense: 1480, 8th overall)
7. North Carolina FC (Offense: 1500, 10th overall; Defense: 1500, 5th Overall)
8. Toronto FC II (Offense: 1612, 2nd overall; Defense: 1362, 12th overall)
9. Ft Lauderdale CF (Offense: 1508, 9th overall; Defense, 1441, 9th overall)
10. FC Tucson (Offense: 1521, 7th overall; Defense: 1414, 10th overall)
11. Tormenta SC (Offense: 1433, 12th overall; Defense: 1496, 6th overall)
12. New England Revolution II (Offense: 1464, 11th overall; Defense: 1399, 11th overall)

Notes:

• NCFC comes in at 1500 because that is replacement level. Drawing the toughest opponent right away means we probably won’t learn much this weekend.
• Offenses are better than defense (a sign the model needs tweaked?. A better defense, though, has an outsized impact on ranking.
• The worst USL League One team of all time was Orlando’s ill fated II team, who are now defunct.