Filling in the untracked two-thirds

Every count on the page comes from Corey’s All Three Zones project: zone entries and exits, retrievals, and the passes that lead to shots, recorded game by game from video. It is licensed to Post Hockey and shown only to active patrons of his Patreon; we do not sell access to it, and nothing here is served outside that gate.

For a player p in a game g Corey did not track, the expected count of a metric is

mu_pg = TOI_pg × r_pN × exp(c + β · x_pg)

r_pN  his rate per hour of 5v5 in SEASON N, shrunk toward the
      position prior:  (Y/φ + a) / (E/φ + b)
Y, E  his tracked count and 5v5 hours, that season at full weight
      and his other seasons at ρ^(years apart); where a context
      term ships, each tracked hour counts as exp(c + β · x) hours,
      so the rate is what is left once that night's context is out
φ     how much one game's total varies per unit of its mean: 1 for
      a count, about an eighth for the xG-created columns
x_pg  what the play-by-play saw that night: usage, on-ice attempts,
      zone starts, own events, rush-shaped sequences, score state,
      quality of competition and teammates, opponent strength

Season estimate = tracked count + Σ mu_pg over untracked games

The player’s own tracked rate carries most of the information. The context term is a ridge Poisson regression fitted with player effects absorbed, so it only explains why one of his games differed from another; it cannot invent a rate for a player Corey never saw. Position groups (forwards, defence) get separate priors and coefficients.

The competition is a baseline that ignores context entirely: shrunk rate × TOI. Thirty percent of tracked games were hidden, by game, so every player in a hidden game was hidden together. Each metric ships the context model only where it beat the baseline on those games and its level was right; otherwise it ships the baseline and says so here.

A few percent of deviance is not a transformation. It fits an earlier finding on this data, that shot-level proxies built from the play-by-play recover only about a tenth of what the tracking knows about a shot. The player’s tracked rate does the work; the context term trims the games where he played more, or less, or against different people than usual.

Split-half reliability of the raw per-60 rates within a player-season, tracked games divided at random, Spearman-Brown corrected to the full tracked sample. Low numbers mean the metric needs many games before it says something about the player rather than the games.

The lists are in the appendix.

Corey chooses which games to track, so the tracked third is not a random draw. On the things the play-by-play can see, the difference between a player’s tracked and untracked games is:

The context features exist partly to absorb this: if his tracked games ran hotter than a player’s season, the model sees the lower on-ice attempts and TOI in the untracked games and scales down. It cannot absorb selection on things the play-by-play does not record — which is why the table below exists.

Whom he tracked them against. The check above covers quantities the play-by-play carries for every game, so the model can already see those skews. This one covers the opposition in Corey’s own terms, which it cannot. Each row is the difference between the opponents faced in his tracked games and in the untracked ones, as a share of the untracked mean and as a fraction of the spread between teams.

The columns above count what Corey tracked. This section predicts something else entirely: the player’s real NHL box score. It exists because the two got confused once, and the confusion was ours.

The obvious move is to add up the expected goals on the shots a player set up and call the result expected assists. We did, briefly. Measured against actual 5v5 assists it came in at 0.65 for primary and 0.45 for secondary, and the band around the implied point total missed the real figure far more often than it should. The cause is not a modelling error and no modelling fixes it: Corey records a primary passer on about 74% of the shots he tracks and a secondary on about 38%, while the NHL awards a primary assist on nearly every goal. A pass nobody wrote down cannot be credited to anyone.

expected total = c_G · (own xG) + c_1 · (xG created, 1st pass)/(fill1 · match)
                              + c_2 · (xG created, 2nd pass)/(fill2 · match)

fitted per quantity, non-negative, identity link: points really are
goals plus assists, so a model that multiplies them is harder to check

Validation is leave-one-season-out, because the job is to price a season the model was not fitted on. Holding each season out in turn, the league level lands between 0.92 and 1.10 and the 80% band contains the player’s real total between 77% and 85% of the time, against a nominal 80%, across all twelve quantities and five seasons (research/a3z_xpoints.json).

Below five tracked games the model runs about 14% high, because the estimate feeding it falls back to a positional average. Those cells are left blank. An empty cell is honest; a number is not.

• The expected box score predicts NHL totals and is calibrated to them. The xG created columns count danger created on the passes Corey recorded, and sit about a third below real assist totals by construction. Do not read one as the other.
• Regular season, 5v5, 2021-22 onward. Earlier seasons use different workbook layouts and are not standardised yet.
• Thirty-two counts, twelve percentages and three derived counts (shot, rush and forecheck contributions, each a shot total plus its shot assists). Corey tracks more still; these are the ones with enough events per game to estimate. Percentages are ratios of two estimated counts and are shown as points, not intervals.
• Pass types split his primary shot assists by where the pass came from, so they sum to his shot-assist total rather than adding to it. Entry defence now carries the outcome of a target as well as the denial: carried in, passed in, and whether it became a chance.
• A player with no tracked games gets the position prior and a wide band, and is hidden by the default minimum of five tracked games.
• Opponent strength is the opponent’s full-season 5v5 xG rate, which includes games after the one being estimated. It is a mild look-ahead about team quality, not about the target.
• The context term is fitted to Corey’s definitions as he applies them; if his tracking changes, the model is refitted, not patched.