Players call it "puck luck". The direction and distance of a deflected shot. The height and energy of a bounce, the trajectory of a wobbly shot. Each of those factors can discriminate between a goal and a shot or a successful vs errant pass. The speed of the game renders these physics based variations extremely hard to predict or control. Great players can do amazing things with that frozen rubber disc but even they have their limits.
Other opportunities for luck to alter the outcome of games are injuries, illness, missed penalty calls and equipment failures. Those $300 sticks are lightweight and facilitate more powerful shots. What they don't do is vibrate like the old wooden sticks did when cracks began to form. The new composites will develop a micro crack and perform just fine until they catastrophically fail while the player attempts a slapshot. Wooden sticks would occasionally fail like that but mostly they would develop a small crack first and "buzz" when stressed. Players would recognize failure was imminent and trade their "twig" for a new one as soon as they could.
Puck luck can and does determine who wins an individual game. That is why all playoff series are best of seven. Any game in which the margin of victory is one goal may have been just a lucky outcome for the winner. Unfortunately for analysts there is almost no way to tell for certain how much luck was involved. Great goalies make plays that can be easily mistaken for luck. They also suffer from bad luck. Likewise with the players. Wayne Greztky famously said "You miss 100% of the shots you don't take", tacitly admitting that even The Great One benefited from puck luck on occasion.
Missed penalty calls and equipment failures also influence individual games, probably less so than puck luck but it is impossible to tell by how much.
Injuries and illness effect series and multiple regular season games. The effects of injuries can be estimated if an analyst wants to check the roster for every game and has accurate information about why players are sidelined. Illness is a different matter. A player too ill to play is a scratch but one that is just slightly ill or playing ill because others cannot play at all will be an easy opponent to beat.
All of this luck eventually influences the standings and can easily determine which teams make the playoffs and which don't. For instance this year Montreal won 44 of 82 games and failed to make the playoffs. The team that did make the playoffs just ahead of them is the Columbus Blue Jackets who won 47. Their regular season records for wins, losses and overtime losses are: Montreal 44, 30, 8 for 96 points. Columbus 47, 31, 4 for 98 points. Columbus won three more games than Montreal - a 6 point lead. However Montreal lost four more games in OT than Columbus did, picking up 4 points. Had Montreal lost just three more games in OT vs Regulation they would have gone to the playoffs instead of Columbus. Remember that OT games are decided by one goal. Puck Luck could easily explain all of those outcomes. Like wise regulation time wins decided by 1 goal. Since most teams will pull their goalie in the dying minutes trying to overcome 1 goal deficits, one could argue that many 2 goal margins of victory are really just the product of puck luck.
Like I wrote above, it is well nigh impossible to separate the contributions of luck from those of skill. The difference between Montreal heading for the golf course and Columbus getting the opportunity to sweep Tampa Bay could very easily be just dumb luck. Likewise for just about all of the four wild card teams. Yet all four wildcards survived the first round, a best of seven series set up to minimize the influence of luck.
The NHL really does have a high degree of parity. If they sustain it, hockey pools will never be the same.