Lacrosse Team Stats: Per-Game versus Tempo-Free

The captain of the College Crosse ship posted some total team statistics today and posed the following question: "What is your take [on the stats]?"

Well, here's my answer: "They're misleading and I don't particularly like them."

It's tough living a tempo-free statistics lifestyle.  People look at you funny and says things like, "Whaddya talking about, moron?  Notre Dame scores 9.6 goals per game.  That's 32nd in the country. The offense is average, stupid."  And then I flip them the bird in my mind and wonder how their state school degree is treating them in the current economic climate.

Here's my problem with per-game (or, if you prefer, "tempo-included") statistics: They tell a story, but the story isn't defined.  Everyone refers to these measures, though, so they've permeated the conversation.  I intend on refocusing the issue a little bit.

Here's an example I like to use when showing the difference between tempo-included statistics and tempo-free statistics:

Team A plays a game.  In that game, it scores six goals and yields five goals.

Team B plays a game.  In that game, it scores 10 goals and yields two goals.

QUERY: Who has the better offense?

QUERY II: Who has the better defense?

If you base your opinion on per-game (tempo-included) averages, Team B has a better offense (they're scoring 10 goals per game compared to only six).  Connectedly, Team B also has a comparatively better defense, yielding only two goals a game in contrast to Team A's five.

Simple and accurate, right?  Maybe, but what if I added these two facts:

Team A played six offensive possessions in its game and 20 defensive possessions in its game.

Team B played 20 offensive possessions in its game and 5 defensive possessions in its game.

Well, things have changed a bit, no?  It turns out that Team B only scored on half of its offensive possessions; Team A scored on all of its offensive possessions.  Now, ask yourself this question: Which offense is better -- a team that scores every time it has the ball or a team that scores only half the time it has the ball?

To me, the answer is easy: The team that scores every time it possesses the bean is better.  That's efficiency, son, and a per-game statistic can't show you that because a tempo-include statistic doesn't know how many possessions occur in a game.  A tempo-free measure cures this disability.

The same is true in the modified defensive facts. I'll value a defense that yielded a goal on only 25 percent of its defensive possessions over a defense that yielded a goal on 40 percent of its defensive possessions.  That's why I'd consider Team A's defense better than Team B's even though Team B's goals against average is better than Team A's.

Again: Possessions, possessions, possessions.

The other reason why tempo-included statistics are faulty?  They don't consider strength of competition (i.e., who did Team A and Team B play?).  Raw tempo-free statistics don't either, but mine are adjusted to fix that problem. 

So, with that backdrop, let's examine some differences between tempo-included and tempo-free measures.  We're going to look at total team defense and offense and provide some commentary on the teams with large (great than 10) rank position differences.

Let's start with offense, because, well, why the hell not?

TEAM OFFENSE: PER-GAME v. TEMPO-FREE

TEAM	G/GM.	RANK	A.O.E.	RANK
Cornell	13.1	2 (t)	39.21	1
Notre Dame	9.6	32	35.85	2
Denver	13.1	2 (t)	35.65	3
Duke	12.7	4	35.45	4
Villanova	9.9	26 (t)	35.41	5
Virginia	13.4	1	34.77	6
Stony Brook	11.5	9	34.30	7
Drexel	10.7	15 (t)	34.26	8
North Carolina	10.7	15 (t)	33.80	9
Yale	12.5	5	32.90	10
Georgetown	11.9	7	32.37	12
Maryland	12.0	6	31.89	13
Robert Morris	11.2	10	31.40	15
Harvard	11.8	8	29.67	22

The focus here is on the three teams with rank position differences greater than 10: Notre Dame, Villanova, and Harvard.

Notre Dame

So, why are the Irish so low in the per-game metric and so high in the tempo-free metric.  Well:

1. Only four teams play fewer offensive possessions per 60 minutes than Notre Dame.  When you rarely have opportunities to score (i.e., having offensive possessions), it's not surprising that your goals per game average is in the tank.  In other words, you can't score 30 a game if you only have the ball 15 times a game.
2. So, we know that Notre Dame rarely has the ball in the offensive end.  Why is the offensive efficiency rating so high?  It's simple: While they don't have the ball much, the Irish are converting on those offensive opportunities at a ridiculous rate when they actually get the bean.  Notre Dame has scored on 67 of their 197 offensive possessions.  That raw offensive efficiency value -- 34.01 -- is among the highest in the country. When you adjust the raw offensive efficiency value for strength of schedule (the Irish's is ranked as fourth-toughest nationally), you come out with Notre Dame having the second most-efficient offense in the land.

The takeaway: While the Irish don't shoot particularly well, they do score a ton when they have the bean.

Villanova

The is virtually the same situation as Notre Dame -- very few offensive possessions earned (the Wildcats are 48th nationally in number of offensive possessions per 60 minutes), but the team is converting on such possessions against a really difficult slate of opponents.

The takeaway: This is why I refer to Villanova as "Notre Dame Light."

Harvard

Ah, yes.  Quin Kessenich's darlings. Let's blow this up:

1. Harvard's strength of schedule is ranked 50th in the country on the efficiency machine.  The Crimson are 43rd in opposing defenses faced.  Of course Harvard is pumping in goals on a per-game basis.  They haven't really played anyone that could stop even average attacks.
2. Only two teams have played more offensive possessions per 60 minutes of play than Harvard this year.  Unfortunately, the Crimson aren't super efficient when they actually have the bean, only scoring on about 30 of every 100 offensive possessions they get.  So, Harvard's per-game total is showing volume aggregation rather than true performance or efficiency when they have the bean.  This is a good offense, but not a top-10 one.

OK, time for defense:

TEAM DEFENSE: PER-GAME v. TEMPO-FREE

TEAM	G/GM.	RANK	A.D.E.	RANK
Notre Dame	6.1	1	19.24	1
Syracuse	8.3	19	19.77	2
Johns Hopkins	6.4	2 (t)	20.96	3
Pennsylvania	7.6	10 (t)	21.31	4
Army	7.4	9	21.94	5
Ohio State	8.1	16	22.21	6
Bucknell	7.0	6	22.33	7
Brown	7.9	14	22.55	8
Virginia	9.3	37	22.72	9
Maryland	6.8	5	22.83	10
Hofstra	6.4	2 (t)	23.52	13
Rutgers	6.7	4	25.02	20
Yale	7.1	7	26.10	27
Fairfield	7.2	8	23.59	14
Princeton	7.6	10	23.08	11

Syracuse

Look at that! The Orange are actually a top-10 defensive team!  Here's why:

1. Nobody has played a schedule featuring better offenses than Syracuse.  So, yeah, the Orange are yielding some goals.
2. Despite that fact, Syracuse is yielding only about 20 goals per 100 defensive possessions.  That's second-best in the country.  So, while the Orange are playing a lot of defensive possessions per 60 minutes of play (only about 20 teams play more defensive possessions), Syracuse is shutting teams out at a ridiculous rate.  The per-game stuff means nothing to the Orange because they're getting it done significantly more often than not when opponents have the bean.

Ohio State

It's a pretty straightforward explanation for the Buckeyes: they've played some good offenses (15th in terms of strength of schedule -- opposing offenses faced); they're playing about 34 defensive possessions per game (right about the national average), and yet teams have only scored 81 goals on 346 defensive possessions (that's a raw defensive efficiency of about 23.41). Total it up and Ohio State is about 10 slots better than you'd think.

Virginia

The Cavaliers' situation is almost a mirror image of Syracuse (they've faced really good offenses but their goal per game average is inflated because they play so many total possessions).  The biggest difference between the Orange and Virginia is that the Cavaliers actually play more defensive possessions per game.  So, Virginia isn't shutting out opposing offenses as frequently as Syracuse in defensive possessions, but they've also had to deal with more total defensive possessions. 

This, in totem, shows that the Cavaliers' defense isn't as strong as Syracuse's, but compared to the rest of the country (e.g., teams playing fewer defensive possessions and thus limiting the number of opportunities the opposition has to score), Virginia is stopping the opposition at a greater rate.

Remember: Aggregation isn't going to tell you a story (per-game).  Rate per possession (tempo-free) will because for all teams the number of opportunities ultimately controls.  Again, Virginia is bad when you take them at the aggregation, but at a refined level, they have their act together.

Hofstra, Rutgers, and Yale

This essay is already around 1,500 words long.  Come to your own conclusions using the efficiency workbook that I've provided.