The Trapezoid of Excellence: Predicting the Next College Lacrosse Champion

How do you spot the next championship team?

Like most of us, I enjoy watching college basketball and its flagship event, March Madness. I also enjoy analytics, which led me to the work of college basketball content creator Ryan Hammer and his idea called the trapezoid of excellence.

The idea here is pretty simple. Hammer hypothesizes that the best teams play neither super fast, nor super slow. They have the ability to win in different kinds of games. He created the “trapezoid of excellence,” which starts with a scatter plot that pits pace (how many possessions a team plays in a game, a measure of how fast they play) against net rating (basically a combination of offensive and defensive efficiency).

Hammer draws a trapezoid near the top of the chart, which is meant to identify the best teams in the country, and others capable of making a deep run.

Here is Hammer explaining the concept:

The shape of the trapezoid is important, as Hammer hypothesizes that teams can win playing either very fast or very slow, but only if they are super elite. So teams in the top right or left corners of the chart are still included.

For reference, here was the final trapezoid of excellence from March Madness this season. This was posted before the tournament began, and includes only the 64 tournament teams.

As you can see, the final four teams were all squarely inside the trapezoid. Houston was the poster child for the idea I mentioned above. They played super slow but were so dominant that they rode that success all the way to the National Championship.

But notice also teams like Maryland and Texas Tech, slightly lower seeds who went on strong tournament runs. They were inside or around the trapezoid.

This is what the trapezoid looked like in 2024, when UConn (squarely in the trapezoid) won the national championship. The runner up, Purdue, was also inside the trapezoid.

Can This Work In Lacrosse?

So this got me thinking, what if we translated the trapezoid to lacrosse?

Before I keep going, let’s get a few things out there:

I am not a data scientist
This is my first crack at this concept, it will need to be refined
The actual trapezoid is more art than science. Whether a team is just in or just out of the trapezoid is not that important. The idea is to see (in general) which teams are in the upper middle area.
This is a chart, it does not incorporate my personal feelings towards your favourite team
No power tools

How does the Trapezoid of Excellence Work?

The first thing I needed was pace.

There are a number of great people writing about lacrosse, including and especially the good folks at lacrosse reference. Check them out and consider becoming a subscriber. They have more complex models for this stuff than I do.

I kept it simple. For a team’s offensive possessions, I added their total number of goals to the number of opponent clears. The idea is that every possession ends either in a goal or an opponent clear. Sure, there are a few exceptions to this (end of quarter for example), but they are rare enough that I chose to ignore.

This also means I ignored powerplay scenarios. This was mostly due to my own bandwidth as a data person, but it also begged the question… why should they be different? Powerplay is a part of team offence, so it should be included.

Then offensive and defensive rating were just based on goals per possession, or goals allowed per possession. A higher offensive rating is good, and a lower defensive one is good. Net Rating is created from subtracting defensive rating from offensive rating. The higher the net rating the better.

The next step was to add the ratings to pace, and to draw the trapezoid itself. Here is what I got.

Let’s discuss.

Historical Context

First of all, let’s look at some historical context for the trapezoid of excellence. This exercise is a little bit difficult in this era of super teams, but let’s take a crack at it anyways.

In 2024, Notre Dame was dominant. Here is what the final trapezoid looks like from that season.

In 2023, Notre Dame was again in a class of their own. This was also a good year to show a team like Delaware, who took the top seeded Duke Blue Devils to a one-goal game in the tournament, despite being a 16-seed.

You might be wondering if the trapezoid merely confirms that good teams perform well. But it’s true value (hopefully) lies in identifying under-the-radar contenders—teams like Delaware, whose stats hinted at their potential to challenge top-seeded Duke in a close game.

Also notice UVA here, playing easily the fastest pace in the country. They would eventually lose in the semis in the Jake Taylor twister game. Was that luck? Or does that confirm the theory of the trapezoid, that teams playing especially fast or slow will eventually lose? You tell me in the comments, but this is both science and art.

2022 was an interesting one, because Maryland really broke the chart. But notice Rutgers and Cornell hanging around the trapezoid, two teams that advanced well further than their seeds would have suggested. Then again, Georgetown lost in the first round. You still have to play the games.

Implications For This Season

Let’s get back to this year’s chart and talk about some of the results. Here it is again:

There are a few obvious ones. Cornell, Army, Princeton, Syracuse, Notre Dame and Syracuse are all inside the trapezoid. Maryland is right on the border, in the lower left portion of the trapezoid, and Ohio State is right there. Most people consider these teams to be among the title contenders.

Fans might be surprised to see inclusions like Richmond, Fairfield, and Boston University.

Richmond is only a quasi-surprise. They hung tough with several top end opponents, but by this measure figure to be a legit contender to at least make a run. Unlike the Delaware team discussed above, Richmond won’t be a 16-seed. If they win the A-10, they could possibly even be in the mix to host a game. They defeated St. Joseph’s already on Friday and look to be a strong favourite in the conference tournament.

The Cinderella season continues in Fairfield. They have the nation’s third-best scoring offence, 11th best scoring defence, and fourth best scoring margin. They lead their conference in the majority of statistical categories. Now obviously they have the 51st best strength-of-schedule, but the Stags will still have high expectations this postseason.

Meanwhile Boston University is flying under the radar just a little bit. Again, their 32nd ranked strength-of-schedule isn’t helping them, but a win over Army is better than most. The Terriers have an average offence (32nd) but their defence is good and they force opponents to clear at the fourth lowest rate in the nation, just 74%.

In total, they have forced 86 failed clears in their 14 games this season, more than six per game. That total shifts the math in their favour. Their loss to Lafayette destroyed their at-large candidacy, but they have beat Army in back to back years. If they find the magic once more in the Patriot League tournament, look out.

They also just beat Colgate, the fastest team in the country. Obviously this is a one-game sample, but it is a nice example of the thesis of the trapezoid being true. BU (who is average pace wise) was able to adapt their game to beat Colgate, who was way outside of the trapezoid range.

Who’s Out?

Now let’s discuss some omissions from the trapezoid. The most obvious is Duke, who escaped against UVA to keep themselves in the playoff hunt. The Blue Devils statistics match their eye-test this year, in that they aren’t really elite at any one thing. Their best statistical category is 13th, and that is shooting percentage. They have the 17th best scoring defence and 25th best scoring offence. Most worryingly, they clear the ball at just 83%, 55th best in the nation.

They would appear to be the biggest chasm between the polls (Duke is 9th) and the data shown here.

Maryland and UNC find themselves towards the outer edge (our slightly out) of the trapezoid. Again, the actual drawing of the trapezoid is somewhat arbitrary, but it is useful to show that both teams are playing relatively slowly. Should they get into a tournament game against, say, Army, they will have to adapt or bend the game to their will.

None of the champions listed above played on the slower side of the pace scale, but that’s not to say UNC and Maryland can’t do it.

And lastly, the entire Big East is outside the trapezoid. What a bloodbath that conference tournament will be!

What do you think of the trapezoid of excellence? What did I miss? Let me know in the comments below!