Goals, assists and points
A player's point total adds goals and assists together, and up to two assists can be credited on a single goal. That generosity means points accumulate quickly for anyone playing alongside a productive scorer, so the number describes a situation as much as a player.
Ice time is the necessary context. A forward on the first line with power-play duty may play twice as many minutes as a fourth-liner, and comparing their point totals without accounting for that compares roles rather than ability.
Splitting production by strength — even strength against power play — is the quickest way to see what a player really contributes. A scorer whose production collapses at even strength is a specialist, which is useful but not the same as a driver of play.
Plus-minus and why it fails
Plus-minus adds one when a player is on the ice for an even-strength goal by his team and subtracts one for a goal against. The intuition is sound and the execution is not: it ignores ice time, ignores who else was on the ice, ignores the quality of opposition, and is dominated by whether the goaltender happened to make saves.
A defenceman given the hardest defensive assignments every night will post a worse figure than a sheltered teammate who never leaves the offensive zone, and the number offers no way to tell those two apart.
It survives because it is easy to calculate and appears on every broadcast. Treat it as a curiosity, not evidence.
Possession, shot share and expected goals
The most useful development in hockey analysis was the realisation that shot attempts, counted while both teams are at even strength, describe territorial control far better than goals do. Goals are rare enough to be noisy across a game or even a month; attempts accumulate fast enough to be meaningful quickly.
Shot share — the proportion of even-strength attempts a team generates while a player is on the ice — became the standard first look at whether a player pushes play in the right direction. Its weakness is that it treats every attempt equally, when a shot from the slot and one from the boards are not remotely equal.
Expected-goal models fix that by weighting each attempt by the historical scoring rate from that location and situation. They are the current best single description of play quality, and like every model they are estimates. For goaltenders, the equivalent step is comparing save percentage to the difficulty of the shots faced, which separates a goaltender having a great season from one standing behind a great defence.