Power Rating (PR) in NCAA Lacrosse

• Power Rating (PR) is a score-differential measure that estimates a team’s average neutral-field victory margin by adjusting for home-field advantage and capping extreme margins.
• It naturally integrates goal differentials and schedule strength, offering a robust and stable alternative to win-loss-based ratings like RPI.
• Within the Powerwise system, PR serves as a final analytic tiebreaker after head-to-head and common opponent comparisons fail to decisively rank teams.

Power Rating (PR) is the numerical rating used inside the Powerwise (PWR) system for selecting at-large teams to the NCAA Division I Men’s Lacrosse Championship. It quantifies a team’s underlying strength from game scores, and the difference $PR_i - PR_j$ is interpreted as the expected goal differential between teams $i$ and $j$ on a neutral field after adjusting for home-field advantage. Within Powerwise, PR is not the primary determinant of team selection; it functions as an analytic tiebreaker after head-to-head and common-opponent comparisons fail to separate two teams (Feldman et al., 6 Aug 2025).

1. Definition and purpose

PR is intended to estimate a team’s average margin of victory against any other team on a neutral field. Because it is built from goal differentials rather than only wins and losses, it incorporates margin of victory and implicitly incorporates strength of schedule: a team that wins by large margins against strong opponents receives a higher PR than a team with similar win totals accumulated against weaker opposition. The paper describes PR as a “simple Massey/Colley/Sagarin-like statistic” and positions it as the analytic component of a broader, explicitly hierarchical pairwise system (Feldman et al., 6 Aug 2025).

Its institutional purpose is tied to replacing the Ratings Percentage Index (RPI) inside a pairwise selection framework. The stated motivation is that RPI is based only on win-loss percentages and an opponent-based strength-of-schedule calculation, ignores score differentials, is biased in favor of teams from stronger conferences, is hypersensitive to irrelevant games, and is poor at reflecting “how well” teams actually played. PR is introduced as a score-differential-based alternative that adjusts for home-field advantage, incorporates schedule strength naturally through those differentials, and is more stable when a single irrelevant game is flipped (Feldman et al., 6 Aug 2025).

A common misconception is that PR is itself the ranking system. In Powerwise, that is not the case. On-field evidence has priority, and PR is consulted only after direct and indirect competitive evidence has been exhausted. The paper reports that historically about $40\%$ of pairwise matchups require PR after head-to-head and common-opponent checks (Feldman et al., 6 Aug 2025).

2. Mathematical formulation

The computational objective of PR is to assign ratings so that rating differences reproduce observed score differentials after home-field adjustment. In practical terms, for a game $g$ between teams $i$ and $j$, the paper describes an equation of the rough form

$PR_i - PR_j = d_g - h_g,$

where $d_g$ is the capped margin of victory and $h_g$ is the home-field adjustment, taking values $i$0, $i$1, or $i$2 depending on venue. The paper also gives a compact system-level expression and states that PRs are found by “solving a large system of nonlinear equations based strictly on game scores and an adjustment for the home-field advantage, iterating until the average difference between two teams’ Power Ratings is equal to the expected (or real) difference in scores were those two teams to play, adjusting for the home-field advantage” (Feldman et al., 6 Aug 2025).

This construction uses goal differential as the basic data unit. A one-goal win and a one-goal loss are both informative; a narrow loss to a strong team is treated differently from a blowout loss. The system therefore preserves more information than a win-loss-only formulation. The paper further notes that PR values may be scaled to roughly a $i$3–$i$4 range for readability, but the operative quantity is the difference between teams rather than the absolute level (Feldman et al., 6 Aug 2025).

To limit the influence of extreme blowouts and discourage “running up the score,” the observed margin is truncated to the interval $i$5. If the raw score difference is $i$6, the differential used in PR is

$i$7

Accordingly, wins by $i$8, $i$9, or $j$0 goals are all treated as $j$1, and corresponding losses as $j$2. The paper notes that this is analogous to the $j$3 cap once used in BCS systems and mirrors Sagarin’s use of a margin cap. It also mentions, but does not adopt, an alternative based on a nonlinear transformation such as taking an $j$4-th root of the margin (Feldman et al., 6 Aug 2025).

3. Inputs and modeling assumptions

PR is built only from final scores, team identities, and home/away/neutral designation. The data sources identified are historical game-level results from laxpower.com and more recent games from laxnumbers.com, restricted to Division I men’s lacrosse seasons under analysis (Feldman et al., 6 Aug 2025).

Home-field advantage is modeled as a single division-wide constant rather than as a team-specific parameter. The exact numerical value is not specified, but the role of the constant is explicit: if team $j$5 is home, the observed margin is adjusted in favor of the home team so that the resulting rating difference corresponds to a neutral-field expectation. Neutral-site games receive no adjustment (Feldman et al., 6 Aug 2025).

The treatment of edge cases is minimal and explicit. Ties are not discussed as a substantive modeling issue because modern NCAA men’s lacrosse rarely has ties due to overtime rules; if a tie occurred, margin $j$6 would naturally fit into the system. Missing games receive no special treatment: equations are constructed only for games that exist. Blowouts are handled exclusively through the $j$7 truncation rule (Feldman et al., 6 Aug 2025).

These assumptions make PR deliberately parsimonious. It does not use conference weights, poll inputs, or manually specified schedule-strength factors. This suggests a design preference for a score-based model whose interpretability is preserved even when the schedule graph is sparse.

4. Function within the Powerwise pairwise procedure

Powerwise resolves each ordered pair of teams $j$8 through a three-stage hierarchy:

1. Head-to-head (H2H): if the teams played, the better head-to-head record wins the Powerwise point.
2. Common opponents (CO): if H2H is tied or absent, the teams’ win-loss percentages against common opponents are compared. The paper also notes an optional rule under which a single common opponent may be ignored to avoid random noise.
3. Power Rating (PR): if neither H2H nor CO decides the comparison, the team with the higher PR wins the pairwise point (Feldman et al., 6 Aug 2025).

After all pairwise matchups are resolved, teams are ranked by total Powerwise points. PR therefore acts as a final arbiter rather than as a global ranking criterion imposed from the outset. The system imports schedule-adjusted, margin-of-victory information only where on-field comparisons are inconclusive (Feldman et al., 6 Aug 2025).

The Yale example in Appendix E illustrates the operational logic. Yale versus Brown was decided by H2H, Yale versus Delaware by common-opponent record, and Yale versus Richmond by PR because there were no H2H games and no common opponents. Over Yale’s $j$9 total pairwise matchups in that season, $40\%$0 were decided by H2H, $40\%$1 by CO, and $40\%$2 by PR. The example shows how PR fills gaps created by short seasons and incomplete schedules (Feldman et al., 6 Aug 2025).

5. Interpretation, properties, and empirical behavior

PR has a direct competitive interpretation: $40\%$3 is the expected goal margin for team $40\%$4 against team $40\%$5 on a neutral field, with capped margins in the underlying data. In Appendix B, for example, Notre Dame has $40\%$6 and Duke $40\%$7, implying an expected neutral-field margin of about $40\%$8 goals. The paper explicitly likens this to an implied point spread (Feldman et al., 6 Aug 2025).

Several desirable properties are emphasized. First, the method is framed as fair and objective because it is based purely on scores plus a transparent home/away adjustment. Second, strength of schedule is implicit rather than separately engineered: because score differentials are measured against actual opponents, strong schedules enter naturally. Third, the ratings are stable. In Appendix B, flipping the outcome of a single early-season Delaware–Lafayette game causes many top-20 RPI ranks to shift, including within the top 10, whereas the PR-based ordering changes only by a single adjacent swap around ranks $40\%$9–$g$0, and the PR values themselves change only in the second decimal place (Feldman et al., 6 Aug 2025).

Resistance to manipulation is handled through the margin cap. The $g$1 rule reduces incentives to keep scoring once a game is already decided, and it reduces the leverage of rare outlier results. The paper presents this as a partial answer to sportsmanship concerns without discarding score information altogether (Feldman et al., 6 Aug 2025).

The paper also reports an empirical selection consequence. Appendix F shows that teams selected by Powerwise, using PR only within the pairwise hierarchy, tend to have slightly better goal-differential performance against stronger opponents than historical committee selections, and that this effect remains even when the $g$2 cap is enforced (Feldman et al., 6 Aug 2025).

6. Relation to other rating systems and terminological scope

Within sports ranking methodology, PR is explicitly situated near Massey, Colley, and Sagarin. Like Massey, it ties rating differences to score differences across the full schedule; like Sagarin, it uses a constant home-field advantage, a margin cap, and an interpretation resembling a point spread. Unlike Colley, it does not discard score information in favor of a win-loss-only linear system. The paper argues that this distinction matters especially in lacrosse because seasons are short and score information is correspondingly valuable (Feldman et al., 6 Aug 2025).

The closest structural analogue identified by the paper is Division I hockey’s pairwise system, which uses head-to-head, common opponents, and RPI. Powerwise retains the pairwise architecture but replaces RPI with PR. The contrast is central: RPI is described as conference-biased, hypersensitive, and blind to margin of victory, whereas PR is intended to be schedule-adjusted, score-informed, and comparatively stable (Feldman et al., 6 Aug 2025).

Outside lacrosse selection, however, “power rating” and the abbreviation PR denote different constructs. In heterogeneously rated electric power systems, power rating refers to the machine rating parameter $g$3, which determines rating-weighted system frequency and the aggregation of inertia and damping (Paganini et al., 2017). In wind-turbine control, “power rating” is a dynamic operating rating parameterized by the power reference factor $g$4 rather than a static nameplate limit (Zalkind et al., 2021). In distribution and transmission engineering, the phrase commonly refers to thermal current or MVA capacity updated through dynamic thermal or line rating (Nourollahi et al., 2023, Dong, 2019, Glaum et al., 2022). Elsewhere, PR may denote Poisson Regression in outage forecasting (Das et al., 20 Sep 2025), Performance Ratio in photovoltaics (Milan et al., 20 Nov 2025), or Estimated Performance Rating in Elo-like systems (Ismail, 2023). This terminological breadth makes the Powerwise definition domain-specific: in the lacrosse context, PR denotes a capped, home-field-adjusted, score-differential rating used only as the final step in a hierarchical pairwise selection system.