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.