I’ve written previously about how MOTSON relies on last season’s results for its predictions, but I wanted to do something with this season’s data now that we’re at the halfway point.

The model is simple: it’s a **generalized partial credit model** (GPCM), which is basically the same model they use for standardized tests like the SAT or GRE. I’ve written in more detail about the approach in my initial post for my blog, but the basic idea is that I treat each team as a person taking a test, and each home game as a question on the test. If you win the game, you get full credit, if you draw you get partial credit, and if you lose you get no credit. GPCM models are good because they are agnostic as to history, payroll, Big Club^{TM }status, or any of the other things that confuse regular human brains. All they know are the results that have occurred this season between the teams that have played against each other.

These models also do well with missing data, so in a half-season each team has played approximately half the other teams at home. GPCM models fill in these gaps, adjusting each team’s strength against the difficulty of the fixture.

So based on home results, here is each team’s “Strength” coefficient.

Arsenal is head and shoulders above the rest of the league, dominating at home, well above #2 Leicester City. The odd results here are Crystal Palace, who is far under-performing at home, and Swansea, who is performing at home far above their position in the table. Their positions are basically reversed, which brings me to the second part of the equation: difficulty to beat on the road.

The strength coefficient in the previous graph shows how strong each team has been at home and how good they are at beating teams on the road. As stated earlier, this is the equivalent of the score a test-taker would earn. Now we turn to the difficulty of the question being asked, or the strength of teams on the road.

The dark red point in this graph represents the strength coefficient needed for a 50% probability of the home team winning a game against the opposition (answering the question “correctly”). The blue point represents the minimum strength coefficient needed to secure a 50% probability of a draw (earning “partial credit”). Points to the left of the draw zone mean a higher likelihood of losing, points to the right of the draw zone mean a higher likelihood of winning based on results so far this season.

Interestingly, title favorites Arsenal and Manchester City are near the center of this table, seemingly weak on the road. However, when you compare their away difficulty coefficient to the home coefficients, only six teams (excluding themselves) would have a strong chance against them. This *feels *about right to me – the top 6 teams should have a good chance of beating title contenders at home, but beyond that it should be much more difficult.

On the other side, I’ve been skeptical until now, but Chelsea look to be at least a semi-legitimate relegation contender right now. They are the 6th weakest home team right now (a far cry from the undefeated season at Stamford Bridge last year), and everyone except for Aston Villa would be favored to take at least a point off of them at home. I knew they weren’t as good as MOTSON says, but this model has them in serious trouble unless they things turn around. Maybe not relegation-level, but bottom 5 wouldn’t be surprising based on the eyeball test here.

*Disclaimer: while these coefficients are accurate given results so far, we’re obviously at a very small sample size with a substantial amount of missing data that will be filled in over the next 19 weeks so these numbers could possibly change quite a bit. However, there’s a lot of logic in these numbers, and they match up at least somewhat well with my expected final table as of today. *

*Also, one can calculate predicted probabilities for each outcome (and presumably expected points over the season). off of these models. I don’t know that I’m going to do that, but if there’s interest I can probably put it together in the next couple of weeks. *