Developing Better Box-Score Metrics: Introducing Yardage-Based Plus/Minus

How can we develop a better measure of overall impact based on a simple ultimate box score?

January 31, 2020 by Paul in Analysis with 0 comments

We have long decried relying on goals and assists to assess individual game play and yet they remain the default metric by which performances are judged. Even when combined with turnovers and blocks in a “plus/minus” metric, we still live in a goals and assists dominated stats universe.

One approach to this problem is to develop a comprehensive metric based on the situation of every action in the game, including more complex defensive assessments, such as Ultiworld’s “Expected Contribution” metric, developed by Childers, Weiss, and Carnegie. A complementary approach is to develop simpler—yet better—integrated box-score metrics that anyone can calculate by looking at summary game data.

With announcements by the AUDL and Ultiworld to provide more yardage data in 2020 comes the opportunity to fix a key problem with plus/minus and more fairly assess individual player contributions to game outcomes (even if still primarily an offensive metric). We present preliminary results for a yardage-based plus/minus (YPM) metric. Based on this model, a second option is presented that seeks to replicate the yardage-based model without the need to collect yardage.

The Plus/Minus Problem

Consider the contributions of two Empire players in the AUDL Championship Game, Jack Williams and Matt Weintraub. Williams had three assists and one turnover; Weintraub had one assist. On a plus/minus basis, Williams had a marginally better game, 2-1, but considering that Williams played three times as many points (28 vs. Weintraub’s 9), one could even suggest that Weintraub was more efficiently productive—until you see the yardage stats: Williams: 15 touches, 321 total yards (throwing + catching); Weintraub: 1 touch, 8 yards.

Goals and assists are not irrelevant, but they are insufficient to determine a player’s impact on a game. Plus/minus relies on goals and assists as proxies for all offensive contributions, but there are not enough goals and assists to adequately serve this function for twenty players on a team. (One question not addressed here is how many games are required before such a proxy relationship is dependable, if ever.) We’ve seen attempts to mitigate this problem by adding hockey assists. This probably helps a little, but only because it expands the number of offensive actions (slightly), not because it has been demonstrated that there are players who are disproportionately high-volume dishers of hockey-assists relative to their assists or total throws.

The proposition here is that plus/minus is salvageable if one also includes highly dynamic measures of total activity. Yardage is likely the best. However, when yardage is not available, another factor appears useful for a quick-and-dirty adjustment of plus/minus. These new metrics don’t fix the problem of measuring off-disc contributions, improve the consideration of defense, or any other shortcoming of current box-score stats, but they can alleviate the goal/assist-dominance problem.