After reading Moneyball I got thinking if hockey could be similarly quantified. I think to some extent it can. This isn't fully thought through and others have spent a lot more time on this than me. Still here goes.
Reduced to simpler situations it can be quantified and expected value can be used. Suppose there is a two on one. The puck carrier would like to pass to his teammate for a one timer. The defenceman can choose to cut off the pass and let the puck carrier go in on a clear breakaway, or he can cut off the puck carrier and try to break up the one timer pass. What should the defenceman do?
To find the correct move we need some more data. Let's say that the goalie stops 3 of every 5 breakaways. However on one timers the shooter will score 3 times out of 5. The defenceman can break up a one time pass 3 times in 10.
Now it becomes clear what to do. On a breakaway the puck carrier will score 40% of the time, for an expectation of 0.40 goals. One the one timer the pass gets through 70% of the time and the shooter scores 60% of the time, or an expectation of 0.7 * 0.6 = 0.42 goals. So the correct play is for the defence to cut off the pass and allow the breakaway- the fans might not like it but it's the best outcome for the defence in this situation.
Now hockey, like football and basketball, is different from baseball in that a team in a positive scoring situation can end up being scored upon. Power play is around 20% effective so drawing a penalty may be worth 0.2 goals. However there may be around 2% shorthanded goals. So the value of the power play may be 0.18 of a goal. In baseball only the team at bat can score so it is easier to consider offence separately from defence.
So how do you win a hockey game? Well the team that scores more goals wins. Of course there's more to it than that, as in that case teams would just pull their goalie for the entire game and add another skater to increase scoring. In a "fluid" game like hockey and basketball you need to both score more and prevent fever scores. There's value in offence and defence up to a point of diminishing returns.
I think Ted Sator way back had some good ideas. He was perhaps a bit ahead of his time. Today with access to big data there may be some applications to possibly determine value of things like blocking a shot, winning a faceoff in the offensive zone, a defenceman joining a rush, superior rebound control. The applications might be in building a winning roster, identifying underpriced or overpriced players, or predicting the number of goals that will be scored in a game or a more probable range of goals for each team.