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I am asked with great frequency what it is that I have learned looking at hockey through the lens of a spreadsheet. The first part of the answer is that I have identified five important laws of hockeynomics that should shape any investigation. Failure to respect these laws will doom an analysis.
Law #1: Winning is what matters
It may seem self-evident that winning is all that matters, but a surprising number of analyses are not grounded in this law.
When measuring something, one should know the relationship of that something to winning in order to assess its usefulness. An example of statistical futility is faceoff winning percentages. These correlate very poorly with winning and are a statistic of low utility.
Some feel that winning in the playoffs is what really matters, that regular season victories don't matter much. For those people I offer up this — with 30 teams in the NHL the planets must be exceptionally well aligned for any given team to win the Stanley Cup and, in any case, the single best predictor of playoff success is regular-season success. The current Stanley Cup favourite has to be the Red Wings.
Law #2: Goals for and against are the only factors that affect winning
In any sporting event, one wins by having more credits than debits. The accounting system of some sport is complex. In hockey it is not. Hockey teams win by scoring more goals than they allow.
In a single game it is an absolute truth that the team that scores the most goals is the winner. However, over the course of a season a team with a positive average goal differential only has a tendency to win more than it loses (a consequence of Law #3).
Nevertheless the predictive power of goals for (GF) and goals against (GA) is very strong. Regression analysis tells us that about 94 per cent of winning is explained by a sophisticated model involving just GF and GA. The remaining 6 per cent seems to just be statistical noise — all other variables seem to simply drive GF or GA.
Taken together, Laws #1 and #2 tell us that 'goals are what matters'. Given that there are about six times as many goals as wins, there is much richer statistical information in the study of goals scored and allowed.
Law #3: Goals are random events
It may seem that focusing on goals violates Law #1. If a team wins a lot of games in spite of a small average goal differential, we seem to be getting mixed signals. But this is where Laws #3 comes in.
The game of hockey is played by humans at high speed in tight quarters on a slippery, but imperfect, surface with a disk made of rubber. If this does not sound like a recipe for chaotic events, watch a hockey game.
There is a great deal of statistical proof that goals occur randomly. This does not mean that skill, strategy and execution give way to luck. It means that outcomes are uncertain, influenced by a myriad of factors including skill, strategy and execution.
In fact, that is why the games are played. If variations in individual performance and conditions ('randomness') did not exist, the game would have no interest.
Most people struggle to accept this. They don't want to believe that the home team's 3-2 upset over the league leaders was a consequence of a couple of good bounces. The preference is to believe that the win came from good execution.
Humans believe in cause and effect. Yet there are too many chaotic factors in play. Randomness is everywhere in the game of hockey.
Looking lucky these days — New Jersey, St. Louis and Minnesota. These teams do not have the GF/GA records to support their winning percentages.
Law #4: Winning has a nearly linear relationship to goal differential
Below is a plot of predicted winning percentages (based on goal differentials — goals for minus goals against) versus actual winning percentages of NHL teams since 1946:
If the prediction formula was 100% accurate, all of the data (the blue dots) would have fallen on the red line. In fact the data is tightly clustered around the red line. This gives visual evidence of the very high correlation between goals and winning.
This data does have a bit of an "S" shape to it. Extremely good teams tend to under perform the prediction and extremely bad teams tend to out perform. While the linearity breaks down for extreme teams, the preponderance of the data comes from teams with winning percentages between .300 and .700. Over that range, the linear relationship between goal differential and winning is very strong.
Goal differential by itself explains about 93% of winning. We get only about 1% of extra information from a more sophisticated (non-linear) model based on GF and GA (see Law #2). This is further evidence of linearity.
Why does this matter? This 'linearity law' is a huge building block for hockey analysis. It means that goals saved and goals scored have the same kind of impact. It means that individual performances are basically additive. It means that team performances can usually be decomposed into individual contributions.
Law #5: Goal prevention is more valuable than goal scoring
"Hang on", you say, "didn't you just say that goals saved and goals scored have the same kind of impact?" Yes I did. But I did not claim that they were of equal 'value'.
Value is all about return on investment.
In statistical terms, when a process has high variation there is a greater payback associated with moving from a 'bad' to 'good' result than if the process has low variation.
Consider this example — if hockey were a game in which each team took turns skating through some pylons and shooting at a goalie cutout, you would only pay the shooters. The pylons (defensemen) and the cutout (goalies) would not earn a paycheque because they don't move the needle. They have no variation.
It turns out that goal prevention has more team-to-team variation than goal scoring. And that means goal prevention is the process with a greater payback for excellence.
Using variation analysis I estimate that goal prevention is between 55% and 60% of the game of hockey (excluding the effect of the shootout). More precisely I estimate that goaltending is about 15% to 20% of hockey and each of offense and defense are about 40% to 45% of the game.
Putting it together — the example of penalties
Penalties taken have a clear cost, a heightened risk of allowing additional goals, and a hidden cost, the loss of offense.
Consider this example: The Leafs and Senators are tied with two minutes remaining in the third period, Tomas Kaberle is sent off for holding and 20 seconds into the penalty the game winning goal is allowed. How should we see this?
Many would cry that Kaberle lost the game and charge him with the loss. But hockey events are rather random. Would you see this differently if you knew that this was Kaberle's first penalty in ten games? How about adding that Kaberle scored in the losing cause?
Clearly a game is comprised of 60 minutes and hundreds of events. Law #3 says we cannot and should not hang defeat on Kaberle's shoulders.
We need to focus the goal as a piece of the loss. It takes about 3 goals (scored or prevented), randomly sprinkled around a season, to earn an additional point in the standings (an application of Law #4). So, out of respect for our Laws, we need to see the impact of this goal as about 33% of a point.
Focusing only on the goal (not the win) one possible assessment would be the goal 'is all Kaberle's fault'. Another could be that the penalty killers blew it (most penalties end well). Or perhaps the goal was scored on a soft shot that was stoppable by the goaltender.
Another assessment is that Kaberle should be debited only with his part, taking the penalty. Most penalties (about 85%) do not result is a goal but cost two minutes of offense. His charge ought to be something like 15% of a goal plus 85% of the difference between even handed and short handed scoring rates over two minutes of hockey (roughly another 5% of a goal). In other words, his role in this is about 7% (20% of 33%) of a point. The PK team and goaltender need to be debited with the remainder (which can be separated with more information about the nature of the goal and the roles of positions on the penalty kill).
In the end it is a game played by a team of 20 over 60 (or more) minutes and played out over 82 games. Over the course of a season there are thousands of events that collectively add up to a team's success.
