How the PivotScout Rating works

Jam-level values

pm_j = points_T_j - points_O_j. This is the team's plus/minus in jam j. It is the raw result PivotScout starts from because the rating is asking, "What happened on the scoreboard while this skater was on track?"

teammate_penalties_j = penalties by T skaters in j excluding s. This counts penalties taken by the skater's teammates, not the skater being rated. The thought process is that a skater should not get full blame for a messy jam if the lineup around them was short or disrupted by other people's penalties.

own_penalty_j = penalties by s in j. This records whether the rated skater personally took a penalty in the jam. PivotScout uses it as a gate: short-handed credit and short-handed loss relief can go to the skaters left dealing with the problem, but not to the skater who caused it.

w_j = max(0.7, 1 - (0.08 * teammate_penalties_j)). This is the jam weight. Each teammate penalty reduces the weight by 0.08, but the weight cannot drop below 0.70. That keeps penalty-hit jams in the rating while stopping one chaotic jam from overpowering the rest of the skater's game.

baseline_T = average(points_T_j) over every game jam. This is the team's normal scoring rate in that game. PivotScout uses it when judging power-jam offense, because scoring eight points on a power jam means something different for a team normally scoring two per jam than for a team normally scoring seven.

Jam score

base_j = (pm_j - team_average) * w_j. This turns the jam into a value relative to the team's normal game. If the team usually wins jams by +1.20, then a +5 jam starts as +3.80 before context. That makes the breakdown easier to read: positive means better than the team's average jam, negative means worse than the team's average jam.

+ 0.35 * max(0, points_T_j - baseline_T) if the opponent jammer was penalized. This adds power-jam-for credit only for scoring above the team's normal scoring baseline. The idea is to reward actually converting the advantage, not merely being present while the other jammer sat.

+ 0.35 * (pm_j - (-4)) if the skater's own jammer was penalized. This judges power-jam-against defense against an expected -4 margin. Holding the jam to better than -4 earns credit, because that is a good defensive result while short a jammer. Giving up worse than -4 still hurts, but the skater is no longer punished just for being in a situation where losing points is expected.

+ 0.45 * pm_j if teammates were penalized, own_penalty_j = 0, and pm_j > 0. This is short-handed adversity credit. It only appears on positive jams, and only for skaters who did not personally take a penalty, because PivotScout is trying to notice the players who still win the scoreboard while someone else has compromised the lineup.

+ 0.25 * abs(pm_j) if teammates were penalized, own_penalty_j = 0, and pm_j < 0. This is short-handed loss relief. The jam still hurts, but it hurts less for the skaters who were left trying to survive a bad situation they did not create.

Game-level conversion

relative_impact = sum(jam_score_j) / sum(w_j). This converts all of the skater's context-adjusted jam scores into a per-jam value. Because the team average was already included in each jam's base, this value is already relative to the team environment.

team_average = average(points_T_j - points_O_j) over every game jam. This is how the team performed overall in the game. It is pulled into every jam's base calculation so the breakdown shows context immediately instead of hiding the team adjustment at the end.

teammate_context = average(avg teammate VTAR in each appearance). For every appearance, PivotScout averages the VTAR values of the other four skaters on track, then averages those values across the skater's game. This estimates how much help the skater had. Stronger teammates make good results a little less surprising; weaker teammate groups make good results harder to earn.

Final rating

opportunity = (power_for_count * 0.45) + (short_positive_count * 0.85). This adds a small game-level context adjustment. Power-jam-for appearances add opportunity credit, and positive short-handed jams add extra credit because they are unusually valuable. Power-jam-against defense is handled inside the jam score against the -4 benchmark rather than as a flat game-level penalty.

vtar_signal = skater_total_avg_plus_minus * 2.5. This brings the statsbook's own VTAR signal into the rating. It is not allowed to dominate the formula, but it helps preserve useful role-aware plus/minus information that already exists in the source workbook.

rating = relative_impact * 7.5 - teammate_context * 1.4 + opportunity + vtar_signal. The rating starts at 0, which is neutral. Relative impact is the biggest lever because the core question is still scoreboard impact. Teammate context is subtracted so results beside stronger groups are discounted slightly. Opportunity and VTAR then add the smaller contextual signals. The result is not clamped, so especially strong games can go high positive and difficult games can go negative.