In my early years, when others were working on more fruitful endeavours like the development and analysis of shot-based statistics like Corsi, catch-all statistics like GVT, or shot quality work like expected goals, I was trying to develop a defensive statistic. 

At first, I looked at the plus/minus statistic, under the mistaken belief that if I could adjust it for the various factors that impact it (which was my first co-publication, with Iain Fyffe, in the Hockey Research Journal in 2001), and then removed the offensive component, then I would be left with the defensive component. 

Sadly, I learned that the best defensive players allow the most goals, because they're up there against top opponents, while the weakest defensive players allow very few, because they're only out there against the fourth lines, and tasked with playing low-event hockey. 

For example, in Ken Daneyko's prime, he was -22 with the New Jersey Devils in 1988-89, while the defensively suspect Tom Kurvers was +11. Now that the NHL has this information online, we know that Daneyko was on for 74 goals against at even strength that season, and Kurvers was on for 71. So, essentially any use of plus/minus to measure defensive play is a dead end.

Iain proposed another way to measure a player's defensive play. He figured that every player was on the ice for a reason, and if that opportunity couldn't be explained by his scoring (or something else that was measurable), then it must have been because of his defensive play, or some other intangible. That formed the basis of the defensive component of his own catch-all statistic, Point Allocations.

So to answer today's question, let's apply Iain's ideas to the AHL. I've got all the player data from 2005-06 to 2016-17 handy, so here's what I did.

1. First, I figured out how many goals were prevented, league-wide. Under the assumption that offense and defense are equally important, the number of goals prevented is equal to the number of goals scored. Bear in mind, this isn't an actual count of goals prevented (which would be a highly subjective exercise anyway), but rather a "thing" that we're going to call goals prevented.

2. Then, I figured out how many goals were prevented by each team. Assuming that the opportunity to score is equal in all games, that means that this can be calculated by adding together the league average goals scored and goals prevented (which is just double goals scored), and then subtracting the actual goals that a team allowed. In theory, this could result in a negative number, but in practice it should result in a distribution that is exactly the same as goals scored.

3. Then, I set aside the goals that were prevented by the team's goalies. But, just how many is that? First of all, the common perception is that goalies are responsible for roughly half a team's goals prevented, or maybe a third.

However, most of the models I've seen peg a goalie's contributions somewhere between 20 and 30 percent. In this case, I arbitrarily decided to assume that a quarter of all goals prevented should be credited to the goalies. 

Side Note: There is the argument that defensemen are more valuable than forwards, because they play more minutes. So, you could add up all the goals created by forwards and assume that an equal number of goals were prevented among all defensemen. The results will be 50 percent higher, because those goals were created by three forwards and the equal number of goals prevented are being dividing up among two defensemen. That will make defensemen far more valuable than forwards. While I don't necessarily disagree with that assessment, I opted for the simpler approach this time around.

5. Ok, so now I finally assigned a team's goals prevented to its forwards and to its defensemen. Here, I did so on an equal basis, with the exception that forwards and defensemen were being weighted differently, as computed in step four. 

Side Note: For fun, I used this to figure out which players were frequently on particularly good or bad defensive teams. All I did was add up a player's goals prevented over the entire time span (2005-06 to 2016-17), and divided it by their games played to create a "base team index" that might become useful later. At the very least, it indicates whether a player has played on particular strong or weak defensive teams, which is useful information in and of itself. For example, defensemen Ryan Lannon and Aaron MacKenzie often found themselves on good defensive teams, as did forwards like Matt Mangene and Nate Thompson. They were either really lucky, or doing something right. On the flip side, scoring-line forward Derek Grant and enforcer Darren Kramer were on some awful defensive teams, as was defenseman Ryan Murphy -- that's either bad luck or bad defense.

So what I need to do is to make a second pass through this data, and try to get a distribution of goals prevented among the different types of players. That is, even among the higher-scoring players, there needs to be a wider distribution of goals prevented. Yes, their average goals prevented per game should still be lower than the average among lower-scoring players, but the distribution should allow for lots of overlap. Having done this first pass, this could be achieved by simply widening the distribution among each tier of players. 

Furthermore, there are a ridiculous number of reasonable but completely unproven assumptions throughout this process, not to mention a number of reasonable but completely arbitrarily chosen numbers. Each step along the way can be improved by proving these assumptions, and calculating the correct numbers.

But, what I have done is enough for the first pass to kill time on a snowy Saturday, so I'll just leave this here for now, pause to reflect on the next step, and save the hard work for later.