Parcells (explained?)

In honor of March I’ve decided to do a writeup on WAB, Parcells, Pythag, and Percentile. I feel like that without a background understanding of the math involved, it can be difficult to understand what these numbers mean. First, I’m going to give a short description of what these terms are, and then I’ll try to explain how they all fit together, brick by brick. I promise to try and keep the math to a minimum.

Let’s start with WAB. WAB is short for Wins-Above-Bubble. It’s a counting stat. WAB measures how many more wins you have then we’d expect a bubble team to have against your schedule. If you’re curious how strong we’d expect a bubble team to be, this year Memphis is the closest to the bubble baseline.

Parcells is like WAB in that it measures your resume, but unlike WAB, it’s a rate stat. Also, it has no baseline. It doesn’t measure you relative to another team. Parcells measures how good you would have to be to be equally likely to have a better record than your current record as you would be to have a worse record than your current record. I’ll go into this in much greater detail in a bit.

Percentile measures how likely it is that the baseline bubble team would produce your record. A percentile of 50.00% means that the average bubble team would be equally likely to have a better record than you as it would to have a worse record than you. Most people only experience percentile when they get their SAT scores (I might be dating myself here).

Pythag is short for Pythagorean Win Expectation. It was originally developed by Bill James to measure how many games a baseball team should have won. It can serve as a descriptive measure, suggesting how many wins you should have had over the course of a season, or as a predictive measure for how good your team is. If you win a lot of close games, and get blown out a few times, you might not be quite as good as your record would suggest (see 2022 Vikings, Minnesota). Alternatively, if you lose a lot of close games, but win more than your fair share of blowouts, you could be one of those teams that ends up much stronger than your seed would suggest.

Cheat sheet:

Pythag: How good you are.

WAB: Wins-Above-Bubble (or Wins-Above-Baseline)

Parcells: How good your resume is.

Percentile: No real way to simplify this. Sorry.

The real question is: Why should you care about any of this? For me personally, the answer is: I want the 36 most deserving at-large teams to be selected to the NCAA Tournament. That’s why I started solving for WAB years ago. It’s why I created Parcells. So now, let me do a deep dive into all of these numbers. Hopefully, after reading this, all of these numbers will make sense to you.

We begin with independent power ratings. Initially, I started with KenPom. Ken Pomeroy’s work revolutionized college basketball. Using his adjusted offense, defense, and tempo ratings, I could generate projections for each college basketball game. That tool was affectionately named “The Lying Liar” by one Jon Becker (@grousehaus on Twitter).

In the beginning, KenPom’s work was so good, early adopters were able to hit Vegas and profit from their knowledge. I bring that up because the accuracy of the projections are of paramount importance to WAB.

It’s here that I should bring up statistician George Box. I suspect you’ve heard his famous quote “All models are wrong, but some are useful.”

He had some additional thoughts on the subject:

“Since all models are wrong the scientist cannot obtain a “correct” one by excessive elaboration. On the contrary following William of Occam he should seek an economical description of natural phenomena. Just as the ability to devise simple but evocative models is the signature of the great scientist so overelaboration and overparameterization is often the mark of mediocrity.”

“Since all models are wrong the scientist must be alert to what is importantly wrong. It is inappropriate to be concerned about mice when there are tigers abroad.”

I adore this and will be using reference to mice and tigers more often going forward. For now let me say I measure college basketball models by how accurate their predictions are. If your model proves sane, then I’m happy to run the numbers with it. This brings us to a pair of old masters, Jeff Sagarin and Kenneth Massey.

As good as KenPom’s numbers are, they are only one point of view on the subject. Both Sagarin’s and Massey’s work has stood the test of time. Their models are different than KenPom’s, so including them gives us a broader view.

Recently I’ve added the work of Team Rankings and Evan Miyakawa. I admit, I haven’t reviewed their work over the course of thousands and thousands of games as I have with KenPom, Sagarin, and Massey. Both of these models have passed their initial tests, and I feel it’s worth seeing what they have to say.

Let me provide an example. Tonight Arizona is facing USC in Los Angeles. The five projections:

KenPom: Arizona 80, USC 79. Arizona is 52% to win.

Massey: Arizona 77, USC 75. Arizona is 54% to win.

Sagarin: Arizona by 2.04, Arizona 52% to win, 149.02 projected points.

Team Rankings: Arizona by 1.9, Arizona 57.0% to win.

EvanMiya: Arizona 77, USC 76, Arizona 53.6% to win.

(Edit: Two additional projections since I mention them later)

Bart Torvik: Arizona 81-80, Arizona -1.1, Arizona 54% to win

ESPN BPI: Arizona 55.8% to win.

Not only do the five projection systems have slightly different projections, they also have different expected variance. For those of you who are wondering, the current market projection is roughly Arizona 78.5, USC, 76.4, Arizona 55.75% to win.

When I chose this game, I knew KenPom’s projection, but not the rest. It turns out all five agree that Arizona should be a small favorite. I’ll be DVR’ing the game tonight (ESPN, 11:00 PM ET).

One question you might have is: How do I turn these the respective power ratings into WAB. Let me go step by step throughout the process.

For KenPom, it’s simple enough: Adjusted offense and defensive ratings are available on his website for download. I’ll then apply an adjustment for home court.

Here’s where I should point out that home count advantage has drifted down a bit over the years. However, it’s also not equal across conferences. In some cases, home court advantage has proven larger than I’ve projected. If certain conferences keep that up over a period of years, I’ll modify my system to account for that.

The actual formula used to generate the Pythagorean ratings is:

Offense^11.5/(Offense^11.5+Defense^11.5).

The formula used to generate game predictions is:

(A-A*B)/(A+B-2*A*B) where A is Team A’s Pythagorean rating and B is team B’s Pythagorean rating. Again, taking home court advantage into account.

As I said, simple enough. Where it gets tricky is when you only have a power rating to go on. Thankfully, there are ways to turn power ratings into Pythagorean ratings.

As I noted earlier, different projection systems also have different expected levels of variance. I confess I am still calibrating that for Team Rankings and EvenMiya, but I should have a solid handle on that by early next week.

I promised I’d be light on the math, but I need to use some here to provide a simple example. Per KenPom, Oklahoma and Kansas have played two of the hardest schedules in college basketball this season. A bubble team would expect to be 16.5-13.5 against Oklahoma’s schedule, and 16.8-13.2 against Kansas’s. Oklahoma is 14-16, with -2.5 WAB. Kansas is 25-5, with 8.2 WAB.

Alabama’s schedule was a bit easier. They’ve gone 26-4. A bubble team would expect to go 18.2-11.8, which gives Alabama 7.8 WAB.

That’s easy enough, and I could live with WAB as a reasonable way to judge strength of record. However, I created Parcells for a reason. If you can stand a bit more math, I’ll try to make it worth your time.

To solve for Parcells you need to determine the pythag rating a team would need for their current record to be their median expectation.

It’s very tough to go 25-5 against Kansas’s schedule. For that to be your median expectation, you’d need to be a very strong team. Just how strong? You’d need a Pythag rating of 96.64%. As such, their Parcells rating would be 96.64%.

That’s impressive, but perhaps not as impressive as going 27-2 against Houston’s schedule. You’d need a Pythag rating of 97.16% for that to be your median expectation, which is to say their Parcells rating is 97.16%. Note: If Houston were currently undefeated, they’d still trail Kansas in WAB, 8.2 to 7.5.

Finally, we have Alabama. You’d need a Pythag rating of 97.26% for a 26-4 record to be your median expectation. Say it with me now: Alabama’s Parcells rating is 97.26%.

What about Charleston? They’re 28-3. It was against a fairly easy schedule though. Per the KenPom’s, you’d only need a Pythag rating of 87.63% for that to be your median expectation. Sure, that’s above the Mendoza line right now, but with a loss in their conference tournament, they’d be in rough shape.

One of the things I’d like to note is that none of this math cares about things like “Quadrants.” Quite frankly, if the NET provided a power rating, I’d run the numbers for it too.

I don’t want this to get too long, so I’ll wrap things up. What I am doing is solving for how many wins you have above a baseline-expectation, and how good you would have to be for your actual record to be your median expectation. I am solving for these things using five independent power ratings. To be clear, I am not coming up with the power ratings. I am only solving for two different resume ratings (WAB, and Parcells) with those power ratings.

One final thing I’d like to note is the math is what it is. If we had absolutely perfect power ratings for every team in every game, I could solve for WAB and Parcells with confidence that they are the absolute truth. Alas, all we have are good faith models by people doing the best they can. If all five agree that team A has a better resume than team B, then it’s reasonable to conclude it as fact. That’s especially true if other resume ratings systems such as Bart Torvik’s or ESPN’s BPI agree.

I am not a bracketologist. I don’t aspire to be one. I just want the most deserving teams to be invited to the dance. To that end, I’m willing to do the math.

Enjoy the tournament(s) y’all. 🙂