In order to continue to help you understand how MHR works (following an introduction last week), let’s decompose two teams in the Top 25 (as reported in Padua Tourney Win Boosts Golden Bears): Toledo St. Francis and Upper Arlington. 

The RANKING is what people focus on, but to understand what is going on, we have to look at the other numbers, and more.

At a high level, Upper Arlington has a better record - 2 more wins - and a better winning percentage. So St. Francis must have a tougher schedule, according to the math, at least. That is the “Sched” number, which is the average rating of a team’s opponents.The Knight’s schedule is about 0.20 points tougher.

MHR uses the goal margin, not just W-L-T, to determine ratings. That’s AGD - average goal differential. St. Francis is scoring 0.76 more goals per game against slightly tougher opponents. So that is another reason why it is ranked higher.

The RATING number is the one to focus on. The difference in rating between two teams is MHR’s “prediction” of how many goals better the higher rated team is. The Knights are almost a goal “favorite” over the Golden Bears. 

If we added only one more result to the rankings and it was St. Francis winning by a goal over Upper Arlington, there would be almost no change in the rating for these 2 teams (or anyone else). If SF wins by a lot in this mythical game, the Knights’ rating would go up and UA’s would go down. If UA wins by a lot, UA would go up and SF would go down. How much things go up and down depends on a lot of other factors. It is not as simple as winning is worth a set number of points (like in league standings).

So, based on the data we have, MHR thinks St Francis is about a goal better than Upper Arlington. If the two teams were to play, we would have more data and the numbers would change. The more data, the better the ratings.

To really understand how MHR works, you cannot just look at these 2 teams, however: we have to look at all of their opponents. Let’s look at the 3 teams they have in common.

The “plus” number is how many goals the team won by, “minus” is goals lost by. MHR caps the margin of victory at 7.

Both teams beat St. Ed Gold by 2, so that is a wash. Both beat FIndlay, but St. Francis won by 3 more goals. The big edge in head-to-head opponents is against Olentangy Liberty, where there is an 8 point total advantage for the Knights. (SF is 1-0-1 vs. Liberty: +6 because of its win and +0 because of a tie, so +3 is the average over those 2 games.)

Even though we are only concerned with OHSAA teams, MHL includes games with USA Hockey teams, squads from other states, etc. In this case, St. Francis has a +3 win against Dayton Stealth, which is #4 in MHL. UA, by contrast, is +5 vs #19 Hilliard and +2 vs. #38 Cleveland Wildcats White. More data points that puts SF above UA.

Not all data is in St. Francis’s favor. Their losses to Gilmore A and University School knocks them down. MHR averages it all - using “fancy math” that we will not get in to yet.

The key is that when a system includes “strength of schedule” like MHR does, your rating is affected by how your opponents perform. If all of St. Francis’ opponents start losing, the Knights’ rating will go down. That Knight's win is not as impressive if other teams are beating that opponent as well.

When comparing St. Francis and Upper Arlington, what their common opponents do is not that important, however. If Findlay, Liberty and St Ed Gold go on winning streaks, both St. Francis and Upper Arlington will benefit. What matters a lot more is what their non-common opponents do. Since teams play their conference foes several times, how your counterparts in your league perform in non-conference games has a huge influence on your rating. You might win all of your league games, but if the other teams in your league lose a lot, then your first place position is not that impressive.

A common practice is to track your favorite team each week. They win but still fall in the rankings: how could that be? If your team barely wins against a team with a low rating, its rating will fall. If someone else gets a big win against a highly rated team, they will climb and may overtake your team. 

That is how a system like MHR works. Of course, what really matters is how teams perform on the ice, not what MHR predicts.

--- Keith Instone for Ohio Hockey Digest