# 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.