Quantitative Lacrosse Rankings: Brown is really good

By Austin Tymins

In a previous post of mine, I introduced the method of Pythagorean expectation to college lacrosse. While this was a marginal improvement over simple winning percentage, it is possible to go even further into the depths of rankings systems to find more tenable results. Based on the relative shortage of data in college lacrosse, it is probably fair to say that this is the most advanced ranking system possible until the quality of data improves.

I’m going to develop a Simple Rating System similar to those used in every major sport today. This article at Pro Football reference describes the general SRS methodology, but I will restate some of the gory details below. For the less mathematically-inclined readers, feel free to skip directly to the results section.

Methodology

At the basic level, NCAA men’s lacrosse has 70 Division I teams and thus we have a system of 70 equations and 70 unknowns. Using the Ivy League as an example, here are a few sample equations:

 SRS_Harv = 0.989 + (1/n) (SRS_Yale + … + SRS_Princ)

SRS_Yale = 3.778 + (1/n) (SRS_Harv + … + SRS_Princ)

SRS_Prin = -2.224 + (1/n) (SRS_Harv + … + SRS_Yale)

Where 0.989, 3.788, and -2.224 are the corresponding average margin of victories for Harvard, Yale, and Princeton and n is the relevant number of games. The equation basically states that the team’s ranking should be the average point margin adjusted for the caliber of the opponents. Thus, an SRS of 0 implies a perfectly average team after adjusting for strength of schedule.

It would be exceptionally easy if we knew each of the opponent’s ratings and could do one iteration to find SRS. But of course, the opponent ratings are based on the ratings of whom they’ve played and so on and so forth. This recursive property means that I’ll need to use a computer to solve the 70-by-70 matrix that includes every game of lacrosse in 2016. My goal is to ultimately disaggregate the strength of schedule from margin of victory to more fully understand the underlying ability of the team. The results of this method are easily interpreted, and have been shown to be predictive rather than just retrodictive.

Results

The following SRS scores are based on the most recent data and therefore include the results from this weekend’s first round playoff matchups. Here are the SRS results from 10,000 iterative processes for the 2016 NCAA Men’s Lacrosse season:

Team

MOV

SOS

SRS

Brown 8.106 -0.067 8.039
Syracuse 4.011 0.584 4.595
Notre Dame 3.156 1.401 4.557
Duke 3.358 1.156 4.514
Maryland 3.258 0.962 4.220
Denver 4.136 -0.074 4.063
Yale 3.949 -0.171 3.778
Stony Brook 3.886 -0.202 3.685
Albany 2.875 0.650 3.525
Villanova 2.929 0.440 3.368
North Carolina 2.320 0.897 3.217
Loyola 2.511 0.595 3.107
Towson 3.543 -0.543 3.000
Army 3.282 -0.420 2.862
St Josephs 4.136 -1.298 2.839
Navy 2.493 0.265 2.757
Bryant 2.426 -0.077 2.349
Harvard 0.989 1.322 2.310
Johns Hopkins 0.814 1.374 2.187
Marquette 1.188 0.895 2.082
Bucknell 1.920 0.017 1.937
Air Force 2.333 -0.616 1.717
Penn State 0.853 0.571 1.424
Richmond 1.617 -0.424 1.193
Quinnipiac 2.049 -0.955 1.094
Hartford 0.934 -0.288 0.646
Rutgers 1.500 -0.856 0.644
Virginia 0.026 0.607 0.633
Drexel 0.662 -0.106 0.557
Hofstra 1.386 -0.926 0.460
Ohio State 0.093 0.342 0.435
Fairfield -0.424 0.835 0.411
Vermont 1.777 -1.447 0.330
Marist 1.213 -0.962 0.251
Robert Morris 1.564 -1.474 0.090
Penn 0.053 -0.070 -0.017
High Point 0.080 -0.182 -0.102
UMass -1.837 1.733 -0.104
Cornell -1.016 0.559 -0.456
Boston University -0.614 -0.025 -0.639
Bellarmine -0.293 -0.383 -0.676
Lehigh -0.520 -0.288 -0.808
Providence -1.114 0.098 -1.016
Monmouth 1.214 -2.558 -1.344
Hobart -0.670 -0.999 -1.669
Holy Cross -2.520 0.782 -1.738
Mount St Marys -0.399 -1.480 -1.880
Binghamton -2.471 0.381 -2.090
Mercer -1.600 -0.571 -2.171
UMBC -2.714 0.502 -2.213
Princeton -3.601 1.377 -2.224
Canisius -1.951 -0.437 -2.387
Michigan -3.292 0.692 -2.600
Delaware -2.186 -0.774 -2.961
Colgate -2.929 -0.078 -3.007
Georgetown -4.101 1.037 -3.064
Detroit -3.349 -0.050 -3.399
Furman -3.215 -0.220 -3.435
Siena -2.845 -0.667 -3.511
Jacksonville -3.246 -1.009 -4.256
Wagner -1.614 -2.738 -4.352
UMass Lowell -3.125 -1.251 -4.376
St Johns -5.114 0.537 -4.577
Lafayette -3.786 -0.831 -4.617
Sacred Heart -4.828 0.134 -4.694
Dartmouth -5.870 -0.250 -6.121
Manhattan -5.159 -1.037 -6.196
NJIT -7.371 -1.259 -8.631
VMI -7.636 -1.269 -8.905

 

Firstly, it is important to note that I calculated and then adjusted every game result for homefield advantage. The regression showed that home field advantage is worth 2.41 goals per game or that the home team should win ~57% of the time based on the standard deviation of 6.40. This is nearly identical to the home field advantage in the NFL and is slightly less than that found in the NBA.

The MOV column is constant and represents the average margin of victory/loss. SOS is the strength of schedule and is positive for teams that played a more difficult schedule than the average team. The final column is the SRS, or final rankings.

Of the remaining teams in the tournament, Brown appears to be the clear favorite. They would be favored by approximately 3.5 goals in any matchup—equivalent to a 61% win probability on a neutral field. In addition, they will face off next round against Navy, the worst remaining team in the field as judged by SRS. Some of the other matchups appear to be more closely contested however, such as the Maryland (1) vs. Syracuse (8) matchup in which Syracuse is actually favored. In my next post, I’m going to apply these predictions to the remaining games in the NCAA Championship.

 

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