More on Defence in Point Allocation

Friend and colleague Rob Vollman had some questions about the Point Allocation system when it comes to defence. At his suggestion, here's some more detail with regard to a particular era of hockey history, using the 1925/26 Ottawa Senators as an example.

This team makes for an effective example for two reasons. First, they were an extremely good team but also an extremely defensive one. They finished first overall in the NHL with a winning percentage of .722, even though they scored a below-average number of goals. Only one of seven teams that season scored fewer than Ottawa's 77, yet the Sens finished comfortably ahead of the second-place Montreal Maroons. They won so many games by allowing only 50.6% of the league average in goals against. That would be something like recording 128 points in the 2010/11 NHL season by scoring 213 goals and allowing 116.

Second, the Senators had a very clear delineation between starting players and substitutes. I've written before about the transition between starter-sub to rolling-lines systems, and the Senators were still very clearly in the former at this time. Just look at their traditional counting stats; it's absolutely clear that the starting line (Frank Nighbor, Hooley Smith and Cy Denneny) and defencemen (George Boucher and King Clancy) played far more minutes than any other players on the team. (Note also that all five of these men, as well as netminder Alec Connell, are in the Hall of Fame).

Player	Pos	GP	G	A	PTS	PIM
Denneny, Cy	6	36	24	12	36	18
Smith, Hooley	7	28	16	9	25	53
Nighbor, Frank	5	35	12	13	25	40
Clancy, King	3	35	8	4	12	80
Boucher, George	3	36	8	4	12	64
Kilrea, Hec	65	35	4	0	4	12
Gorman, Ed	7	23	2	1	3	12
Finnigan, Frank	7	36	2	0	2	24
Graham, Leth	6	1	0	0	0	0
Duggan, Jack	3	27	0	0	0	0
Smith, Alex	3	36	0	0	0	36
Total		36	76	43	119	339

The starting forwards scored 86 points and recorded 111 PIM, the subs had 9 and 48. Starting defencemen had 24 and 144 versus zero and 36 for subs. There is obviously a great disparity between their relative playing times, much moreso that we see in the modern game between first-liners and fourth-liners.

Rob's question is, basically, how does Point Allocation avoid seeing the substitute players as historically-great defensive players? If you look at Hockey Reference's Point Shares results for this team, for instance, you get the following:

Player	OPS	DPS	PS
Connell, Alec	0.0	11.1	11.1
Denneny, Cy	7.6	1.5	9.1
Boucher, George	2.0	5.9	7.9
Clancy, King	2.1	5.7	7.8
Smith, Hooley	5.0	1.1	6.1
Nighbor, Frank	3.8	1.4	5.2
Smith, Alex	-1.4	5.9	4.5
Gorman, Ed	0.0	3.8	3.8
Duggan, Jack	-1.0	4.4	3.4
Kilrea, Hec	-0.8	1.4	0.6
Graham, Leth	-0.1	0.0	-0.1
Finnigan, Frank	-1.9	1.5	-0.4
Total	15.3	43.7	59.0

Where OPS, DPS and PS are Offensive Point Shares, Defensive Point Shares and Point Shares. Notice in particular that Alex Smith, spare defenceman, is considered to be just as important to the team defensively as Boucher and Clancy, two giants of hockey history. Jack Duggan also looks right good, but they have him as a defenceman rather than a winger.

Since Point Shares is intended to measure the same thing as Point Allocation, you might not be surprised to find that in most cases, the results are quite similar, at least on the surface:

Player	OP	DP	TPA
Connell, Alec	0.0	24.3	24.3
Denneny, Cy	4.5	1.8	6.4
Boucher, George	2.0	9.0	10.7
Clancy, King	2.0	7.3	9.0
Smith, Hooley	3.3	1.7	5.0
Nighbor, Frank	2.5	3.7	6.8
Smith, Alex	-1.0	5.8	4.8
Gorman, Ed	0.8	2.8	3.6
Duggan, Jack	-1.1	0.8	-0.3
Kilrea, Hec	0.5	2.3	2.6
Graham, Leth	-0.1	0.0	-0.1
Finnigan, Frank	-0.8	1.7	0.9

Although most of the differences are relatively minor, that's actually an illusion, and the mirage is revealed by examining Connell's results. In terms of raw Point Allocation results, Connell is actually credited with 11.4 points, which is extremely similar to the Point Share results. This is because the Point Shares are presently wholly on a raw basis, while the Point Allocation numbers above are based on adjusted games and minutes. Point Shares uses only games played to allocated defensive points, while Point Allocation uses (estimated) minutes played. Connell has 11.4 defensive points in 2,251 minutes, which translates to 24.3 in 4,800 minutes, the basis on which his numbers are presented in Point Allocation.

Realistically, Alex Smith probably played only about 500 minutes in 1925/26, while Boucher played over 1,600; yet Smith is credited with equal defensive points to Boucher. This means that Smith must have been three times as good, on a per-minute basis, than George Boucher. This, of course, is just plain nuts.

Point Allocation therefore has Alex Smith with 5.8 defensive points, but in 2,000 minutes. That's 2.9 per 1,000 minutes (compared to 4.5 for Boucher), while the Point Shares results in about 11.71 defensive points per 1,000 minutes. The Point Allocation numbers are probably a bit high for Smith (remember to look at a player's career, or at least blocks of years instead of a single season), but the Point Shares results are completely unrealistic and totally misleading, in this case.

So, in addition to the defensive fudge factor which I've talked about before, the fact that Point Allocation uses estimates of minutes played also plays an extremely important role in reasonably crediting defensive points. It'll never be more than an estimate, as I've said many times before, but estimating minutes is far more accurate than not doing so, ironically. Now that I'm thinking about it, it's actually the more important factor of the two, and as such I should have mentioned before now. Sorry about that.

Just to illustrate the fudge factor, though, let's look at the Point Allocation results if it were not included. You'll see historic greats Boucher, Clancy and Nighbor much closer to the lesser players defensively, and that's the entire reason for the fudge. Also see Alex Smith being overrated, because the system interprets his lack of offence as an indication of good defence:

Player	OP	DP	TPA
Connell, Alec	0.0	24.3	24.3
Boucher, George	2.0	7.8	9.8
Clancy, King	2.0	7.5	9.5
Smith, Alex	-1.0	8.6	7.6
Denneny, Cy	4.5	2.0	6.5
Gorman, Ed	0.8	5.3	6.1
Smith, Hooley	3.3	1.6	4.9
Nighbor, Frank	2.5	2.2	4.7
Kilrea, Hec	0.5	2.9	3.4
Finnigan, Frank	-0.8	2.3	1.5
Duggan, Jack	-1.1	1.6	0.5
Graham, Leth	-0.1	0.0	-0.1

The final results are surely much more accurate than these. By combining the fudge factor and the ice time estimates, Point Allocation produces reasonably accurate results, which other systems may not.

1907 ECAHA Point Allocation

Yesterday I posted the Point Allocation results for the 1906/07 Montreal Wanderers of the ECAHA, which looked remarkably like this:

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

So it's only appropriate that I post the rest of the league as well. So here we go. Enjoy.

Montreal Shamrocks

Player	Pos	GP	MIN	OP	DP	PP	TPA	TPAK
Kavanagh, Frank	4	16	320	1.1	-0.1	-0.1	0.9	2.81
Murphy, Joe	7	64	1280	1.8	-0.2	0.0	1.6	1.25
Baxter, Quigg	5	40	1000	1.2	0.1	-0.1	1.2	1.20
Mulcair, Jack	6	56	1120	1.4	-0.1	0.0	1.3	1.16
Hewitt	1	48	1200	0.3	1.1	-0.4	1.0	0.83
Grannery, Fred	2	40	1000	-0.1	0.6	-0.1	0.4	0.40
Brennan, Johnny	47	80	1800	0.3	1.0	-0.7	0.6	0.33
Currie, Neil	G	80	4800	0.0	-0.1	0.0	-0.1	-0.02
Armstrong, Walter	5	8	200	-0.1	0.1	-0.1	-0.1	-0.50
DeGray, Lawrence	6	24	480	-0.3	0.0	-0.1	-0.4	-0.83
McCourt, Bud	5	16	320	-0.3	0.0	-0.1	-0.4	-1.25
McCarthy, Frank	5	40	800	-0.8	-0.1	-0.4	-1.3	-1.63
Tigh, Oliver	5	32	640	-1.0	-0.9	0.0	-1.9	-2.97
McMillan, Reddy	7	8	160	-0.4	0.0	-0.1	-0.5	-3.13
O'Leary, Bob	4	8	160	-0.6	0.0	0.0	-0.6	-3.75

Montreal Victorias

Player	Pos	GP	MIN	OP	DP	PP	TPA	TPAK
Bowie, Russell	4	80	1600	9.6	-0.3	-0.3	9.0	5.63
Hale, Chandler	5	56	1120	4.3	0.5	-0.2	4.6	4.11
Russel, Blair	6	80	1600	5.3	0.3	-0.1	5.5	3.44
Eveleigh, Joe	5	40	800	2.2	0.6	-0.2	2.6	3.25
Davidson, Gordon	1	40	1000	0.4	3.2	-0.4	3.2	3.20
Major, Billy	1	56	1400	-0.2	5.2	-0.6	4.4	3.14
Frye, Nathan	G	80	4800	0.0	12.7	0.0	12.7	2.65
Gilbert, Raleigh	7	72	1440	1.9	1.8	-0.3	3.4	2.36
Howard, Cavie	2	64	1600	-0.7	4.8	-0.4	3.7	2.31
Campbell, Duncan	2	16	400	-0.3	1.2	0.0	0.9	2.25

Montreal Winged Wheelers

Player	Pos	GP	MIN	OP	DP	PP	TPA	TPAK
Sargent, Grover	5	72	1440	3.8	0.2	0.0	4.0	2.78
Smaill, Walter	4	80	1600	2.0	0.8	0.0	2.8	1.75
Cameron, Doc	2	64	1600	0.6	2.2	-0.3	2.5	1.56
White, George	G	80	4800	0.0	5.1	0.0	5.1	1.06
Horsfall, Bert	1	8	200	-0.1	0.3	0.0	0.2	1.00
Masson, Charles	6	80	1600	1.3	0.7	-0.6	1.4	0.88
Brownrigg, William	1	72	1800	-0.9	2.1	0.0	1.2	0.67
Chipchase, Bill	7	80	1600	-0.3	0.6	0.0	0.3	0.19
Kerwin, George	4	24	480	-0.3	0.0	0.0	-0.3	-0.63
Hanrahan	5	8	160	-0.3	-0.2	0.0	-0.5	-3.13

Ottawa Senators

Player	Pos	GP	MIN	OP	DP	PP	TPA	TPAK
Pulford, Harvey	2	80	2000	-0.9	9.6	-0.8	7.9	3.95
Snelling, Charles	5	8	160	0.6	0.1	-0.1	0.6	3.75
LeSueur, Percy	G	80	4800	0.0	16.7	0.0	16.7	3.48
Westwick, Rat	4	72	1440	2.4	2.7	-0.2	4.9	3.40
Baird, Billy	1	48	1200	-0.1	4.5	-0.5	3.9	3.25
Spittal, Baldy	1	16	400	-0.2	1.8	-0.3	1.3	3.25
Smith, Alf	7	72	1440	4.1	0.9	-0.4	4.6	3.19
Moore, Art	2	8	200	-0.1	0.7	0.0	0.6	3.00
Ryan, Jack	2	8	200	-0.1	0.7	0.0	0.6	3.00
Smith, Harry	5	72	1440	4.9	0.4	-1.0	4.3	2.99
Shore, Hamby	6	80	1600	3.4	1.7	-0.4	4.7	2.94
Williams, Jack	4	8	160	-0.1	0.2	0.0	0.1	0.63
Westwick, Tom	5	8	160	-0.3	0.1	0.0	-0.2	-1.25

Quebec Bulldogs

Player	Pos	GP	MIN	OP	DP	PP	TPA	TPAK
Doddridge, Harry	G	32	1914	0.0	8.8	0.0	8.8	4.60
Jordan, Herb	5	40	800	2.6	0.0	0.0	2.6	3.25
Constantin, Charles	4	56	1120	2.7	0.1	-0.2	2.6	2.32
Gale, Alfred	7	8	160	0.4	0.0	-0.1	0.3	1.88
Power, Joe	24	64	1480	1.4	1.0	-0.1	2.3	1.55
McDonald, Jack	6	72	1440	1.5	0.6	-0.2	1.9	1.32
Blair, Harold	1G	80	2024	0.0	2.4	-0.2	2.2	1.09
Baxter, Bert	2	32	800	0.4	0.6	-0.2	0.8	1.00
McDermott, Ed	1	8	200	-0.1	0.2	0.0	0.1	0.50
Leonard, George	7	64	1280	0.3	0.5	-0.2	0.6	0.47
Moran, Paddy	G	48	2862	0.0	-0.8	0.0	-0.8	-0.28
Power, Chubby	4	8	160	-0.1	0.0	0.0	-0.1	-0.63
Gillespie, Jim	6	8	160	-0.2	-0.1	0.0	-0.3	-1.88
Baptiste, Gladstone	5	16	320	-0.6	-0.4	0.0	-1.0	-3.13
Morency, Len	5	24	480	-0.9	-0.6	0.0	-1.5	-3.13

Oh, and as a bonus:

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.

Pro or Am?

One thing that will often come up when discussing players from the early era of hockey is the concepts of amateurism and professionalism. Specifically, the idea that amateur hockey is somehow more pure or honourable than the professional game which began to emerge in the early 1900s. Pro players are sometimes portrayed as greedy, money-grubbing blackguards who care not one whit for the integrity of the very endeavor which fills their dirty little pockets! Phew, I think I had an attack of the vapours, there. I'll just go have a little lie down on the chaise longue.

That's better. Read biographies of certain early hockey players and you'll see references to them remaining "staunchly amateur" throughout their careers, possibly even turning down offers to turn professional at times. The implication is always that this is a noble character trait, that is says something about the player's makeup that he wasn't willing to sully the wholesome sport with filthy money and all it brings. This is ridiculous. Whether a player remained amateur throughout his career is a mark neither for nor against him. There is nothing inherently despicable about professional sports.

Arguments that amateur players played solely for the love of the game don't really hold water. Amateur hockey leagues were rife with arguments, petty squabbles and politics. Hardly a week would go by without some game or another being protested by the losing team on some (often frivolous) grounds or another. Nobility went out the window as teams and players traded barbs, each accusing the other of misdoings. Sometimes a team would refuse to play a game due to some unresolved issue. Sometimes a team or teams would quit the league entirely over some apparently minor thing. At least in the professional arena, teams had incentive to play every game they were supposed to, since there was money on the line.

Ultimately the distinction between amateur and professional sports comes down to class, a social concept given a great deal of import in the Victorian era when organized hockey was developing. Amateurism was considered to be the ideal, at least by those in the influential upper classes, because only those in the upper classes could devote a great deal of time to sport without expecting recompense for it. If you were in the working class, it was more difficult to take enough time away from work to become one of the very best in a particular sport, without being able to make money doing it. The origin of the special place amateurism is supposed to hold in the sporting realm is very much elitist in nature. It was intended to keep the riff-raff out.

I think (or hope) that we're beyond that now. You do need to consider a player's status when analyzing their careers, of course, in the sense that amateur players tended to have shorter careers, since they had less incentive to keep playing as they aged, and this shouldn't be held against them. But there's nothing inherently good about being an amateur, and nothing inherently bad about being a professional.

Putting Some Numbers on Hobey

I've written about Hobey Baker before, more specifically whether he belongs in the Hall of Fame. A quick summary goes something like this: he was a very good player, had superficially impressive numbers, but due to the low level of competition he played against, that's not enough to merit induction into the Hall of Fame. His tragic death is likely what got him in. Also, the lack of quality competition means that people had only reports to know how good he was; he never faced the best players of his time which might have revealed the flaws in his game that were not apparent when opposing lesser teams.

And Baker did have flaws. Although he was a gifted shooter, passer, and (especially) skater, possessing blinding speed, he was also a floater. Descriptions of his play make it clear that he did very little backchecking, instead waiting for his defencemen to recover the puck from the opponents and get the offence started so Baker could make another of his dandy rushes. Now, being purely an offensive player does not make you a bad player, as I mentioned when discussing Harry Smith. But the existing writing on Baker rarely implies anything other than his perfection as a player. He has been heroicized to the extent that objective discussion of his abilities as a hockey player is difficult.

One of the reasons for the development of the historical Point Allocation system is to allow us to compare players from different times and leagues to estimate how much they contributed to their teams' success, and including an adjustment for a quality of the league. The league quality adjustment allows us, in theory, to produce Point Allocation numbers for any player in any league. This means we can determine numbers for Hobey Baker, not only for his two seasons in the American Amateur Hockey League (AAHL), but also his three years at Princeton. So the new year bring the first look at a player's career Point Allocation results:

Season	Team (League)	Pos	GP	MIN	OP	DP	PP	TPA	TPAK
1912	Princeton Tigers (NCAA)	4	80	1600	10.0	-3.3	0.0	6.7	4.19
1913	Princeton Tigers (NCAA)	4	80	1600	5.6	-2.7	0.0	2.9	1.81
1914	Princeton Tigers (NCAA)	4	80	1600	7.1	-2.2	0.0	4.9	3.06
1915	New York St. Nicks (AAHL)	4	80	1600	10.8	-2.9	0.0	7.9	4.94
1916	New York St. Nicks (AAHL)	4	73	1460	2.4	-0.7	0.0	1.7	1.16

Point Allocation results are normalized to an 80-game schedule, and forwards are normalized to 20 minutes per game played. The table above show Baker's Offensive Points (OP), Defensive Points (DP), Penalty Points (PP), and Total Points Allocated (TPA). The final column, TPAK, is TPA per 1,000 minutes, which is used to compare the performances of players at different positions.

Of course, at this time you have no point of reference for the above numbers. Is a TPAK of 4.94 impressive? If so, how impressive is it? To get an idea, we have to look at results for more recent players, for whom we have better ideas of how good they were. So, here are the top 30 players for the 1967/68 NHL season, by TPAK:

Player	Team	Pos	GP	MIN	OP	DP	PP	TPA	TPAK
Beliveau, Jean	MTL	5	64	1280	6.6	1.4	-0.1	7.9	6.17
Gamble, Bruce	TOR	G	57	3364	0.0	21.0	0.0	21.0	5.93
Bower, Johnny	TOR	G	58	3422	0.0	20.7	0.0	20.7	5.85
Tremblay, J.C.	MTL	3	79	1975	2.2	9.3	0.0	11.5	5.82
Esposito, Phil	BOS	5	80	1600	7.3	1.3	-0.1	8.5	5.31
Ratelle, Jean	NYR	5	80	1600	7.1	1.4	-0.1	8.4	5.25
Cournoyer, Yvan	MTL	7	69	1380	5.7	1.4	-0.1	7.0	5.07
Laperriere, Jacques	MTL	3	78	1950	1.6	8.5	-0.3	9.8	5.03
Neilson, Jim	NYR	3	72	1800	3.0	6.3	-0.3	9.0	5.00
Goyette, Phil	NYR	5	79	1580	6.6	1.3	-0.1	7.8	4.94
Williams, Tommy	BOS	5	74	1480	6.4	1.0	-0.1	7.3	4.93
Bucyk, Johnny	BOS	6	78	1560	6.6	0.9	0.0	7.5	4.81
Gilbert, Rod	NYR	7	79	1580	6.3	1.2	0.0	7.5	4.75
Howe, Gordie	DET	7	80	1600	6.7	1.0	-0.2	7.5	4.69
Brown, Arnie	NYR	3	80	2000	2.2	7.2	-0.3	9.1	4.55
Tremblay, Gilles	MTL	6	77	1540	4.0	3.0	0.0	7.0	4.55
Howell, Harry	NYR	3	80	2000	2.1	7.2	-0.3	9.0	4.50
Rousseau, Bobby	MTL	7	80	1600	5.5	1.6	-0.1	7.0	4.38
Favell, Doug	PHI	G	56	3350	0.0	15.7	0.0	15.7	4.37
Mikita, Stan	CHI	5	78	1560	5.3	1.5	0.0	6.8	4.36
Harris, Ted	MTL	3	72	1800	2.2	6.0	-0.4	7.8	4.33
Hodge, Ken	BOS	7	80	1600	6.1	0.8	-0.1	6.8	4.25
Provost, Claude	MTL	7	79	1580	3.9	2.9	-0.1	6.7	4.24
Hull, Bobby	CHI	6	77	1540	5.0	1.7	-0.2	6.5	4.22
Stanfield, Fred	BOS	6	79	1580	5.8	0.8	0.0	6.6	4.18
McKenzie, John	BOS	7	80	1600	6.2	0.9	-0.5	6.6	4.13
Delvecchio, Alex	DET	5	80	1600	5.5	1.2	-0.1	6.6	4.13
Ullman, Norm	DET	5	63	1260	4.7	0.5	0.0	5.2	4.13
Prentice, Dean	DET	6	75	1500	5.3	1.0	-0.2	6.1	4.07
Green, Ted	BOS	3	78	1950	3.9	4.3	-0.4	7.8	4.00

So a TPAK of 4.94 is close to the level of being the very best in the NHL, which is impressive indeed. If Baker had been able to produce at that level for his career, he would have a strong argument for the Hall of Fame, even with his short career. But he didn't, of course. His second-best season was 4.19, which is still plenty good. However his third-best was only 3.06 (1967/68 equivalents: Earl Ingarfield or Ed Westfall), the level of a very solid NHLer but not a star. Then we get 1.81 (Claude Laforge or Pat Hannigan), and 1.16 (Billy Harris or Wally Boyer), which are not numbers recorded by Hall of Famers.

Especially when examining players of Baker's era, it's important to look at their career results rather than just a single season. Since they played such a low number of games per season, it's much easier for normal variance in performance to creep its way into seasonal results (although it is easy to overstate the importance of the number of games played; Baker may have only played eight games per year, but he was playing 60 minutes per game, and the minutes are really what matters for variance purposes). Baker's average season was just over 3.00 TPAK, meaning that if he did play in the NHL he would have been a very good player, contributing a lot to his team's success. But he would not be one of the very best players, not one who you would expect to see in the Hall of Fame when his playing days were done.

No disrespect intended to the man or his legacy, of course. But no one should be above rational analysis. Even heroes are subject to reality checks.

P.S. Here are renditions of the sweaters Baker wore during his career. They don't add anything to our knowledge of Baker, but they're fun.

Some Old Linkies

Years ago (nearly a decade ago, in fact) I used to write some articles at a site called HockeyZonePlus. Most of the articles I wrote there don't fit with the subject matter of this blog, but there is one that does:

The Quality of Hockey

And at my old site, we've have a couple more relevant links:

Player Comparisons

Greatest Teams of All Time

Hmm. When I started this post I would have sworn there would be more relevant links. Ah well.

Here's one final link, which discusses some theory relevant to the use of Point Allocation, since we've been talking about that recently:

Win-Things Theory

Review at your leisure. Especially the player comparisons one, and the win-things one. Or don't. Live your own life!

Positional Notation

A short one today.

As regular readers (I know you're out there; I can hear you yawning) will know, I'm fixin' to publish the result of the historical Point Allocation system in the relatively near future. In order to do that, I wanted an efficient means to indicate a player's position.

The typical system for modern players is simply G, D, C, LW and RW. Sometimes LW and RW are written as L and R instead. Of course, these are not the only positions we need to worry about when discussing historical stats. We also have the point, cover-point and rover. These could be written as P, CP and R respectively. But then, in order to use R for rover, we would not be able to use it for right wing, forcing us to use RW and LW for the wings.

Two-letter codes for the positions are undesirable, because they're not efficient. What if a player split time between cover-point and left wing? Should we write that LW/CP, using five characters to show something that we should be able to do in two? I don't think so.

That's why I settled on a (mostly) numerical code to show the positions.

Code	Position
G	goaltender
1	point
2	cover-point
3	defence
4	rover
5	centre
6	left wing
7	right wing
8	wing
9	forward

So LW/CP can now be written 62. The goaltender position is different enough from any of the skaters that it need not conform to the system; in fact goaltender stats will be presented separately from skater stats so that position does not need to be included in the codes.

What are the 8 and 9 for? Well, often in game reports newspapers would list the goaltender, point, cover-point, rover, centre and two wings, but would not specify which side each player played. Code 8 is for that type of player. The 9 is for cases, mostly in the very early years of the game, when the four forwards would be listed only as forwards, not by individual position. Players such as that get a 9 in this system.