Point Allocation on Defence

So far we've talked about the basis of Point Allocation in Marginal Goals, and allocating a team's offensive points to its players. All that really remains is to allocate defence amongst a team's players. This isn't as straightforward as offence, of course, and it's not helped by the fact that we don't have any defensive stats in hockey's early days.

Well, that's not entirely true. We have team defensive stats; we know how many goals each team allowed. And since Point Allocation uses a top-down approach, beginning with team results and then allocating these results to the players on that team, that's actually quite a good start. But there's no way we'll get anywhere without some judicious fudging. Remember that the system is not designed to identify who the best players are in any era; it largely assumes that those players considered to be the best were the best, and bends to make them so, to a reasonable degree. The system is meant to put players from different eras on the same relative footing, and to evaluate the players from all eras that are not among the very best. In a sense, the very best players in a particular league-season are used to calibrate the Point Allocation system for that particular league-season, via the league quality adjustment. The ratings of other players fall out of that.

Before we allocate defensive points to players, we first divide them between the team's goaltenders and its skaters. On a league-wide basis, this is done in order to make netminders (who receive no offensive points) as valuable, on average, as any other position. And then we have our first fudge factor. The reputation of a team's goaltender, versus that of its skaters, is considered when dividing defensive points among them. We can't assume a constant ratio of goalie to skaters points for every team in a league; that's just not realistic. And since we don't have anything like save percentage to evaluate goaltenders on something other than team goals-against average, we need this adjustment. Defensive Point Allocation is just full of fudgy goodness, and all the better for it.

From there, it's a simple matter to allocate points to goaltenders, if a team had more than one in a particular season. Each goaltender's Marginal Goals saved is calculated based on his GAA, and the points are allocated on that basis.

Now for the skaters, we first use the basis of the very first edition of Point Allocation from 2002 or so. That is, if we know how much a player played, and we know approximately how good he was offensively, we should be able to derive that player's approximate defensive ability, since offence plus defence should equal playing time. So when you have a player who produces a relatively low amount of offence (compared to his position, and his teammates), the system assumes he's probably a relatively good defensive player. It doesn't assume a perfect relationship between the two, of course, and sometimes this will result in some inaccurate results, but this is largely overcome by examining players by career (or at least groups of seasons) rather than by individual seasons.

The same logic is used for the amount of defence assigned to each position as a baseline. The standard defensive contribution of each position is determined based on the league-wide offensive contribution of each position, such that each position is approximately equal in overall value. On top of this, and the adjustment mentioned above, we have the other big 'ole fudge factor. Players with excellent defensive reputations have their defensive value adjusted upwards, and those with poor reputations are adjusted downwards. It's as much art as science, of course, but just doing straight computations on these numbers will produce less accurate results than if we apply what we know about these players, that is not necessarily reflected in their stats.

Oh, one final thing. Players lose points based on the penalties they take, since penalties cost your team goals. That's about it for the system. There are probably some details I've left out, which I'll mention when I think of them. Let's have a look at the complete results for the 1907 Montreal Wanderers, which we've been using for an example so far, normalized to an 80-game schedule, 20 minutes per game for forwards, 25 for defencemen and 60 for goaltenders. OP is Offensive Points, DP is Defensive Points, PP is Penalty Points, TPA is Total Points Allocated and TPAK is the same per 1,000 minutes.

1906/07 Montreal Wanderers

Player	Pos	GP	MIN	OP	DP	PP	TPA	TPAK
Russell, Ernie	5	72	1440	10.0	-0.3	-0.5	9.2	6.39
Stuart, Hod	2	64	1600	0.7	9.0	-0.5	9.2	5.75
Kennedy, Rod	1	24	600	-0.1	3.0	-0.1	2.8	4.67
Marshall, Jack	7	24	480	1.1	1.1	0.0	2.2	4.58
Hern, Riley	G	80	4800	0.0	21.1	0.0	21.1	4.40
Patrick, Lester	14	72	1720	2.7	6.2	-0.2	7.1	4.13
Johnson, Moose	6	80	1600	4.0	3.2	-0.8	6.4	4.00
Blachford, Cecil	7	56	1120	3.3	1.0	-0.1	4.2	3.75
Glass, Pud	4	80	1600	1.7	3.9	-0.4	5.2	3.25

You can see the Wanderers had two absolute superstars in Russell and Stuart, a bunch more playing at an elite level, and two others (Blachford and Glass) producing solid if unspectacular results. Little wonder the team was undefeated in 10 games.

Point Allocation on Offence

Previously we've talked about Marginal Goals, which form the basis of the historical Point Allocation system. We use Marginal Goals not only to establish a team's quality, but also to allocate this quality (in the form of points) between offence and defence. From there you merely have to allocate these offensive and defensive points to each player on the team, in a rational way, to estimate the value that each of said players contributed to the team achieving what it did.

I should say, at the outset, that Point Allocation will never by anything more than a rough estimate of a player's value, especially the further back you go in history. The surprises it uncovers will be few; those considered the best players of the day will largely be shown by the system to be great players. It's really more about trying to establish an equal footing to allow players from different eras to be compared to each other, and also to identify the value of the non-great players from any era. There are hundreds of players from history that were really good, solid players, with the level of talent that would allow a nice, long NHL career in today's world, but who are relatively unknown today because they were not among the very best players of their day. Part of the purpose of the system is to figure out approximately how good these players were.

Going back to the system, we can look at allocating offensive points, which is easier and more straight-forward than dealing with defence. Point Allocation gives offensive points to players based on their scoring point totals, as a proportion of the team's total scoring points. We don't worry about adjusting for the relative rate of assists per goal; rather we assume that the officials of the day basically knew the relative contributions of playmakers and goals-scorers at the time. There were many fewer assists awarded per goal in the pre-forward pass era, for example, and individual rushing was a more important factor in scoring goals at that time, so we figure that's alright.

We can have a look at the 1907 Montreal Wanderers again, one of the greatest teams of all time, to examine some of the details.

Player	Pos	GP	G	A	Pts	PIM	MIN
Russell, Ernie	C	9	43	4	47	26	514
Johnson, Moose	LW	10	15	5	20	42	558
Blachford, Cecil	RW	7	14	3	17	5	415
Glass, Pud	R	10	13	4	17	21	579
Patrick, Lester	P/R	9	11	3	14	21	532
Marshall, Jack	RW	3	6	0	6	0	180
Stuart, Hod	CP	8	3	2	5	20	460
Kennedy, Rod	P	3	0	1	1	2	178
Totals		10	105	22	127	124	610

Wow - this team had five Hall-of-Famers among its eight skaters (Russell, Johnson, Patrick, Marshall and Stuart), and another tending goal in Riley Hern. It was truly an all-star team that played together throughout the season.

(As an aside, you might realize that the assist totals above are completely unofficial. I compiled them by reading the game reports for all of the ECAHA games that season. I'll have a brief discussion of compiling assists like this in the next post.)

Based on the above, Ernie Russell, one of history's best pure scorers, would receive 47 out of 127 offensive points the Wanderers earned, or 37%. But it's not quite that simple. Some players produce points at such a low rate, compared to their positional norms, that they effectively costs their team goals. Remember that Point Allocation is built upon the concept of Marginal Goals, which has at its core the idea that there is a certain minimum level of performance that anyone good enough to get a sniff in a particular league will be able to contribute. This applies to individual offensive performance as well as at the team level.

For the Wanderers, this applies to only one player. Pud Glass was a hard-working, professional player and a very good defender. But in 1907 his offensive production left much to be desired, given that he played rover, which as a position scored just as much as centres league-wide. Among all centres and rovers, he places ahead of only the men from the sad-sack Montreal Shamrocks on a per-minute basis:

Player	Pos	Team	GP	Pts	MIN	Pts/60 MIN
Russell, Ernie	C	Mtl W	9	47	514	5.49
Bowie, Russell	R	Mtl V	10	47	587	4.80
Smith, Harry	C	Ott	9	25	484	3.10
Hale, Chandler	C	Mtl V	7	21	412	3.06
Jordan, Herb	C	Que	5	15	300	3.00
Sargent, Grover	C	Mtl A	9	22	538	2.45
Constantin, Charles	R	Que	7	16	409	2.35
Westwick, Rat	R	Ott	9	18	528	2.05
Smaill, Walter	R	Mtl A	10	18	578	1.87
Glass, Pud	R	Mtl W	10	17	579	1.76
Brennan, Johnny	R	Mtl S	5	7	285	1.47
McCarthy, Frank	C	Mtl S	5	4	225	1.07

The system figures if Glass can't outscore Charles Constantin, who played precisely one season of senior hockey, his offence should be knocked down a peg when deciding who contributed how much to his team's goal-scoring. So he's given 10.7 scoring points instead of 17 when allocating the team's offence. Rather than just adjust everyone's point totals to remove this "sub-marginal" level of offense, we just apply an adjustment to those below that level. Why this way and not the other? No particular reason. The effect is the same.

And don't worry. We know that Glass has a reputation for good defence, and he will earn his share of points that way, when we look at allocating defence. In fact, the system considers him the team's most valuable defensive forward. But more on that later.