Points Above Replacement

[Czech Your Math]

I've had a metric in the back of my mind that relates to career scoring. We all know that a shorter, brilliant career (like Bossy, Orr, Lindros, Forsberg) is often perceived to be of equal or greater value to many longer careers with much lower peaks (e.g., Dave Andreychuk). So my idea was to give players credit only for production that exceeds the production which teams couldn't otherwise replace (with another available player of replacement level and/or through increased opportunities such as more and better ice time for the remaining players).

Since it seems to be the most commonly accepted standard for such purposes, I will use VsX as the basis for converting both an individual player's points for the season and the replacement level for that season to a standardized number that should be comparable across seasons.

The tricky part is determining what replacement level should be, especially as actual replacement level and effective level are different. Since we will be analyzing players that played most or all of their careers on the first and/or second lines (with the exception of some high-scoring defensemen), deducting a player of that caliber from a team would result in more opportunities for at least some of the other forwards on that team, which should lead to increased production for at least some of them.

Absent a better method of determining what the effective replacement leve is, I'm using an arbitrary method for now: The average of the last 6th N & first 7th N scorers in the league each season (where N = the number of teams, so in a 31 team league it would be the 186th & 187th ranked scorers... in a 21 team league, the 126th & 127th scorers... in a 6 team league, the 36th & 37th scorers). So basically, the median forward if teams are rolling four lines (slightly higher than that actually, since there are many defensemen that will finish in the top 6N scorers... maybe it's closer to the median 6thN forward or even on the cusp of 5thN/6thN). Production is highly dependent on opportunity and first/second line ES ice time and power play time is restricted proportionally to the number of teams, hence that is the basis of our replacement level standard.

I am using seasons from 1943 to present and calculating a player's Points Above Replacement (PAR) score for each season as follows:

PAR = (Points - Replacement Level)/VsX Standard

Then I just summed the seasons to get a career score. One final note: No season score can be negative, if it calculates as such, then it is given a score of zero.

I included adjusted points and career VsX for comparison. The ranks are among those players I analyzed, so those which played mostly after WWII. I apologize for any players that may have been accidentally omitted from the study. When the ranking is blank, it just means I was too lazy to keep adding to the ranking list for that metric.

It helps players with a lot of good to very good scoring seasons, but without long careers. It hurts compilers, players who had very long careers and lots of decent but not very good scoring seasons, or who missed substantial portions of many seasons with injuries.

Feel free to comment. I'm particularly interested in ideas for alternative methods of determining and calculating the effective replacement level. Looking at the results, my initial inclination is to raise the replacement level standard a tad higher, but given that the original standard I have used has no exact basis, I obviously have no other basis for this.

PLAYER PAR Adjusted VsX Score Rank Points Rank Career Rank Gretzky 1,585.5 1 2,475 1 2,327 2 HoweG 1,300.0 2 2,190 2 2,444 1 Jagr 1,056.5 3 2,080 3 1,921 3 Esposito 917.0 4 1,508 12 1,609 6 Sakic 838.4 5 1,679 7 1,534 10 Lemieux 836.4 6 1,540 11 1,409 18 Dionne 793.6 7 1,493 13 1,484 14 Crosby 789.1 8 1,484 14 1,391 20 Ovechkin 770.5 9 1,482 15 1,372 22 Mikita 769.7 10 1,478 16 1,610 5 Thornton 761.6 11 1,682 6 1,580 8 Yzerman 743.7 12 1,650 8 1,529 11 Francis 735.6 13 1,711 5 1,588 7 Messier 715.1 14 1,732 4 1,620 4 Beliveau 713.4 15 1,385 25 1,519 12 HullBobby 702.6 16 1,239 37 1,376 21 Selanne 678.3 17 1,565 10 1,415 17 HullBrett 654.7 18 1,390 24 1,271 28 Sundin 645.7 19 1,410 20 1,284 26 Kane 644.7 20 1,254 35 1,175 41 RichardM 641.0 21 1,229 39 1,403 19 Oates 628.0 22 1,396 22 1,282 27 Recchi 606.8 23 1,569 9 1,438 15 Delvecchio 604.4 24 1,427 18 1,575 9 Iginla 603.0 25 1,445 17 1,343 23 Bucyk 600.3 26 1,391 23 1,519 13 Ullman 588.9 27 1,300 32 1,434 16 Malkin 579.5 28 1,231 38 1,141 47 Robitaille 571.7 29 1,354 27 1,250 35 Coffey 557.9 30 1,347 28 1,258 30 Bathgate 557.7 31 1,113 67 1,226 38 Modano 555.8 32 1,408 21 1,286 25 Lafleur 554.7 33 1,161 53 1,158 45 Turgeon 546.1 34 1,315 31 1,200 39 Shanahan 540.0 35 1,376 26 1,257 31 Ratelle 539.6 36 1,191 46 1,251 33 Hawerchuk 539.3 37 1,189 47 1,119 50 St. Louis 537.0 38 1,166 52 1,083 62 Trottier 534.2 39 1,177 50 1,159 44 Lindsay 533.8 40 1,109 69 1,255 32 BackstromN 526.2 41 1,117 66 1,056 71 Bourque 520.5 42 1,426 19 1,338 24 MahovlichF 519.0 43 1,146 58 1,260 29 Orr 518.5 44 878 137 940 95 Alfredsson 510.3 45 1,261 33 1,162 43 Hossa 505.5 46 1,257 34 1,178 40 Bossy 499.7 47 906 123 894 105 Kurri 496.6 48 1,185 47 1,113 53 Kopitar 496.5 49 1,133 62 1,061 69 Gilmour 494.1 50 1,321 30 1,227 37 Perreault 493.4 51 1,134 61 1,145 46 Fedorov 489.0 52 1,226 41 1,113 54 Fleury 483.7 53 1,111 68 1,011 77 Roenick 482.9 54 1,228 40 1,128 48 Clarke 480.7 55 1,062 78 1,087 60 Forsberg 475.2 56 977 96 882 108 Kariya 473.6 57 1,078 74 970 88 SedinH 472.5 58 1,181 49 1,115 51 Staal 461.2 59 1,154 54 1,098 57 Marleau 459.6 60 1,325 29 1,239 36 Giroux 455.7 61 984 94 939 96 Stamkos 455.5 62 1,000 92 931 97 StastnyPeter 451.6 63 1,001 91 957 92 Spezza 447.1 64 1,060 79 996 82 Getzlaf 447.1 65 1,099 71 1,036 74 SedinD 446.5 66 1,154 54 1,084 61 Gilbert 445.6 67 1,005 89 1,072 65 Tavares 444.9 68 950 103 904 101 Damphousse 438.5 69 1,193 45 1,096 58 SavardD 438.3 70 1,123 65 1,060 70 Zetterberg 433.7 71 1,069 76 1,005 80 Tkachuk 432.6 72 1,150 56 1,038 73 Datsyuk 426.5 73 1,026 86 956 93 Sittler 424.6 74 959 99 973 86 Elias 422.4 75 1,144 59 1,070 66 Kessel 420.3 76 1,032 84 976 85 RichardH 420.1 77 1,131 63 1,251 34 Kovalchuk 419.8 78 969 98 880 111 Geoffrion 418.8 79 982 95 1,093 59 Brind’Amour 410.6 80 1,210 42 1,100 56 RichardsB 409.8 81 1,032 84 967 90 Lindros 406.3 82 942 107 840 128 Mogilny 399.2 83 1,054 80 958 91 McDavid 396.2 84 Weight 392.3 85 1,099 71 1,003 81 Lidstrom 385.7 86 1,204 43 1,102 55 Wheeler 383.7 87 926 110 880 109 Nicholls 383.7 88 1,068 77 994 83 Gartner 382.8 89 1,142 60 1,077 63 Naslund 376.8 90 940 108 862 118 Nieuwendyk 376.0 91 1,124 64 1,031 75 Lecavalier 375.4 92 1,051 82 967 89 MacInnis 375.4 93 1,200 44 1,114 52 Toews 371.1 94 925 111 864 116 Bure 369.5 95 Marchand 369.3 96 Kovalev 367.3 97 1,107 70 1,009 78 Federko 366.6 98 917 116 892 106 Leetch 360.6 99 1,039 83 956 94 Bergeron 360.4 100 1,026 86 973 87 Heatley 358.8 101 Pavelski 356.5 102 959 99 909 100 Andreychuk 353.3 103 1,250 36 1,165 42 Lach 352.4 104 930 98 LaFontaine 351.3 105 902 124 Goulet 350.3 106 938 109 903 102 Yashin 350.3 107 LeClair 348.4 108 893 129 Ciccarelli 343.1 109 1,052 81 983 84 Amonte 341.8 110 953 101 875 112 Benn 341.7 111 Keon 338.4 112 975 97 1,064 68 Larmer 332.7 113 Palffy 327.9 114 Hodge 327.4 115 898 103 Tanguay 324.2 116 952 102 897 104 Seguin 324.0 117 Perry 323.9 118 920 113 868 114 Voracek 321.0 119 Bondra 320.6 120 947 105 864 117 Housley 318.3 121 1,148 57 1,066 67 Lemaire 316.7 122 Doan 310.8 123 1,077 75 1,006 79 Kucherov 310.3 124 Draisaitl 309.7 125 Cournoyer 309.6 125 883 107 Mullen 306.9 126 918 115 858 120 Kennedy 303.5 127 Anderson 296.0 128 918 115 869 113 Moore 295.6 129 Potvin 294.6 130 882 134 880 110 MacKinnon 293.9 131 Kelly 292.4 132 1,003 90 1,127 49 [TBODY] [/TBODY]

[TBODY] [/TBODY]

Click to read more...

 

[plusandminus]

I think this is an interesting approach. I've thought about it too, and was inspired by the "discounted career points" thread by @Hockey Outsider.

If it's easy to do, you could add columns for Seasons and GP. I mean, for example, "How many seasons are counted for each player?", and "How many GP are counted?". Or how many are not counted?

A key factor is (of course) to determine the "replacement" level limit. I suppose one would like to experiment with different ways of doing it.
Then you also sometimes compare with the 126th best scorer, and sometimes with the 36th best (O6 era), if I understood you right. It's easier for a player to assemble "above replacement" seasons if he needs to be 126th best instead of 36th best.

International hockey (best-on-best) is very interesting, because we get to see most of the best players spread out on 6 (or more) teams, sort of similar to how the O6 era worked.

Interesting to see Mats Sundin as high as 19th. It seems he did contribute to TOR, despite seemingly having the reputation here as being way below guys like Lafleur (33rd), Malkin (28th), etc.
On the other hand, if we set the replacement level at 3rd/4th "N" scorers, I guess Sundin would drop.
So it's a bit of a philosophical question... "What's best..??".

The replacement way of determining a player's contribution is often better than using the average. One reason is that we don't get minuses that aggregate, as in +/- where the best players (=most ice time) on the worst teams often gets the worst stats. Or when we punish players for being "below average" at killing penalties, when they're in fact contribute more to the penalty killing than those who doesn't kill penalties at all. (Using replacement player was my approach in 2003, when I got 11 out of 12 defensemen ranked "correctly" if comparing with Norris and AST voting, as well as getting Selke winner Lehtinen as the clearly best defensive forward, etc.)

 

[Czech Your Math]

I think this is an interesting approach. I've thought about it too, and was inspired by the "discounted career points" thread by @Hockey Outsider.

If it's easy to do, you could add columns for Seasons and GP. I mean, for example, "How many seasons are counted for each player?", and "How many GP are counted?". Or how many are not counted?

A key factor is (of course) to determine the "replacement" level limit. I suppose one would like to experiment with different ways of doing it.
Then you also sometimes compare with the 126th best scorer, and sometimes with the 36th best (O6 era), if I understood you right. It's easier for a player to assemble "above replacement" seasons if he needs to be 126th best instead of 36th best.

International hockey (best-on-best) is very interesting, because we get to see most of the best players spread out on 6 (or more) teams, sort of similar to how the O6 era worked.

Interesting to see Mats Sundin as high as 19th. It seems he did contribute to TOR, despite seemingly having the reputation here as being way below guys like Lafleur (33rd), Malkin (28th), etc.
On the other hand, if we set the replacement level at 3rd/4th "N" scorers, I guess Sundin would drop.
So it's a bit of a philosophical question... "What's best..??".

The replacement way of determining a player's contribution is often better than using the average. One reason is that we don't get minuses that aggregate, as in +/- where the best players (=most ice time) on the worst teams often gets the worst stats. Or when we punish players for being "below average" at killing penalties, when they're in fact contribute more to the penalty killing than those who doesn't kill penalties at all. (Using replacement player was my approach in 2003, when I got 11 out of 12 defensemen ranked "correctly" if comparing with Norris and AST voting, as well as getting Selke winner Lehtinen as the clearly best defensive forward, etc.)

It may be easier as you say in a larger league in terms of the absolute talent level and abilities of the 126th scorer vs. the 36th scorer, but we're not focused on talent/ability. We're focused on production, and when given more opportunity, most players will increase their production. Using a fixed number of players (unless perhaps you are using only Canadian players) won't yield a fair comparison either IMO. I believe using a number proportional to opportunity (so to the number of teams) rather than a fixed number is much truer to reality, but opinions may (and seem to) vary.

Sundin didn't actually move up that much in comparison to his career adjusted points or VsX rankings (one and seven spots, respectively). He's the type of consistently good (above replacement level) player whose not affected that much by this metric (similar to Dionne, Francis, etc.). He didn't hang on for a long time past his prime, so he didn't have many seasons discarded as below RL. It's players like Orr, Lafleur, Bure, Lindros, Forsberg, etc. that are most helped by this metric, since they were way above replacement level for much of their careers, so are losing a smaller % of their actual production than players who were typically closer to RL each season.

As far as determining a better method of calculating RL, I was thinking along these lines: We are typically analyzing players that are top 3 scorers on their team, so "first liners" that receive max ES ice time and max PP time. Replacing them means a "second liner" (4th-6th N) receives increased (first line) opportunity, that a "third liner" (7th-9th N) receives increased (second line) opportunity, and that a "fourth liner" (10th-12th N) receives increased (third line) opportunity.

So we could calculate, say, the difference between the production of: A) median 2nd N vs. median 5th N, B) median 5th N vs. median 8th N, and C) median 8th N vs. median 11th N. Those mostly cancel out, leaving median 2nd N vs. median 11th N. We are also adding a RL level forward, so bottom of 12th N scorer. The end result would be something like (in a 21 team league): Scorer #252 + Scorer #32 - Scorer #221. I didn't want to calculate that type of RL standard until I had some to solidify the best approach.

 

[Czech Your Math]

I calculated a new version of this metric using a different standard for replacement level. Replacement Level = Average of A) half of VsX standard & B) median 5N

Basically it's the average of A) half of the best non-outlier (VsX), and B) the median "second liner" for that season. This helps smooth out any random variance for each metric, as well as that of any flaw in the metric itself (bias for/against era, etc.). It's also a slightly higher standard than I used initially, which I wanted after seeing the results of the first run.

PAR = [ (Raw Points - RL) / RL ]

Some other changes:

* As suggested, I included the number of season for each player with PAR > zero
* I went back as far as 1930 season, instead of 1943
* I estimated missing seasons for the following cases: 2005 lockout, WWII, and KHL seasons if player played in NHL both before and after those years. I tried to be conservative with these estimates, while using the average of multiple surrounding seasons (before and/or after) as the basis of the estimates. If the first season before or after had a PAR score of zero, then I used zero. I also used equivalency ratios that I developed to estimate WHA seasons as NHL seasons. These were converted into NHL seasons using the equivalency ratio for that season, then to PAR using formula above.

So there are two PAR scores and rankings: The first using only NHL seasons and the second using NHL and all estimated seasons.

PLAYER	PAR	Rank	Years	X	PAR	Rank	Years
Gretzky	2,959	1	19		3,015	1	20
HoweG	2,236	2	24		2,323	2	28
Jagr	1,777	3	23		1,957	3	27
Esposito	1,609	4	16		1,609	4	16
Lemieux	1,539	5	12		1,539	5	12
Sakic	1,385	6	17		1,472	6	18
Crosby	1,370	7	15		1,370	9	15
Dionne	1,363	8	17		1,363	10	17
Ovechkin	1,319	9	16		1,412	7	17
Thornton	1,247	10	17		1,325	11	18
Mikita	1,243	11	17		1,243	12	17
Yzerman	1,203	12	18		1,203	13	18
HullBo	1,196	13	15		1,385	8	20
Beliveau	1,194	14	16		1,194	14	16
Francis	1,102	15	22		1,102	15	22
Kane	1,088	16	14		1,088	16	14
Selanne	1,075	17	15		1,075	17	15
Messier	1,072	18	19		1,072	18	19
RichardM	1,047	19	14		1,047	20	14
HullBr	1,022	20	17		1,022	22	17
Sundin	1,006	21	17		1,068	19	18
Oates	1,000	22	14		1,000	23	14
Recchi	996	23	20		1,027	21	21
Malkin	968	24	13		968	26	13
Bucyk	943	25	18		943	27	18
Orr	939	26	7		939	28	7
Ullman	931	27	18		931	29	18
Lafleur	927	28	13		927	30	13
Bathgate	923	29	13		923	31	13
Iginla	912	30	18		978	24	19
Delvecchio	912	31	21		912	32	21
Trottier	898	32	12		898	33	12
St. Louis	892	33	12		971	25	13
Coffey	879	34	15		879	34	15
Ratelle	877	35	14		877	35	14
Bossy	876	36	10		876	36	10
Lindsay	873	37	13		873	37	13
Robitaille	869	38	15		869	38	15
Hawerchuk	866	39	14		866	39	14
BackstromN	840	40	13		840	40	13
MahovlichF	821	41	15		822	41	16
Turgeon	817	42	14		817	44	14
Modano	797	43	16		816	45	17
Kurri	775	44	13		775	48	13
Forsberg	774	45	11		813	46	12
Kariya	774	46	10		774	49	10
Perreault	763	47	15		763	50	15
Alfredsson	753	48	16		821	42	17
Fleury	752	49	13		752	51	13
Kopitar	751	50	15		751	52	15
Shanahan	751	51	17		789	47	18
Hossa	750	52	16		817	43	17
Lindros	750	53	10		750	53	10
Clarke	743	54	14		743	54	14
Stamkos	743	55	10		743	55	10
StastnyPe	734	56	12		734	57	12
Fedorov	733	57	14		733	58	14
SedinH	727	58	13		727	61	13
Giroux	725	59	11		725	62	11
Gilmour	721	60	14		721	63	14
McDavid	720	61	6		720	64	6
Gilbert	712	62	13		712	65	13
Spezza	710	63	12		710	66	12
Tavares	699	64	12		699	67	12
Roenick	697	65	15		697	68	15
Staal	687	66	14		687	70	14
SavardD	679	67	12		679	71	12
SedinD	678	68	13		678	72	13
Cowley	677	69	10		677	73	10
Getzlaf	676	70	12		676	75	12
Bourque	672	71	19		672	76	19
Sittler	667	72	12		667	77	12
Datsyuk	666	73	12		732	60	13
Kovalchuk	664	74	11		735	56	12
ConacherC	664	75	8		664	78	8
Geoffrion	657	76	12		657	79	12
StewartN	646	77	10		646	81	10
Kessel	641	78	12		641	82	12
Barry	639	79	10		639	83	10
Zetterberg	630	80	14		631	84	15
Tkachuk	617	81	12		628	85	13
RichardH	612	82	16		612	89	16
RichardsB	602	83	12		654	80	13
Apps Sr.	596	84	10		693	69	12
Wheeler	590	85	10		590	91	10
Elias	589	86	13		589	92	13
JacksonB	588	87	10		588	93	10
Bure	587	88	9		587	94	9
BlakeT	585	89	10		585	95	10
Marchand	584	90	9		584	96	9
Damphousse	583	91	14		583	97	14
Nicholls	581	92	10		581	99	10
Heatley	581	93	9		581	100	9
BoucherF	577	94	7		577	102	7
Mogilny	576	95	11		576	103	11
Weight	568	96	12		582	98	13
Naslund	558	97	9		620	86	10
Federko	557	98	11		557	105	11
Lach	554	99	9		554	106	9
LeClair	552	100	8		552	107	8
LaFontaine	550	101	9		550	108	9
Lecavalier	549	102	12		613	88	13
Kucherov	543	103	6		543	109	6
Draisaitl	540	104	6		540	111	6
CookBill	537	105	5		537	112	5
Schriner	536	106	8		536	113	8
BentleyM	534	107	9		676	74	11
HoweS	533	108	12		533	114	12
ConacherR	533	109	9		733	59	13
Toews	530	110	13		530	115	13
Yashin	525	111	9		541	110	10
Marleau	521	112	15		562	104	16
BentleyD	519	113	7		593	90	8
Brind’Amour	519	114	15		519	116	15
Goulet	516	115	11		516	117	11
Whitney	508	116	14		513	118	15
Seguin	501	117	9		501	119	9
Hodge	501	118	10		501	120	10
Palffy	500	119	8		500	121	8
Benn	498	120	10		498	122	10
Schmidt	496	121	12		618	87	15
Leetch	488	122	12		488	125	12
MacKinnon	487	123	7		487	126	7
Morenz	481	124	6		481	127	6
Moore	479	125	8		479	128	8
Gartner	471	126	16		471	130	16
Kovalev	470	127	12		493	124	13
Bergeron	468	128	14		468	131	14
Perry	466	129	11		466	132	11
Lemaire	463	130	9		463	134	9
Ciccarelli	461	131	13		461	136	13
Nieuwendyk	456	132	14		466	133	15
Amonte	454	133	12		454	137	12
Lidstrom	454	134	14		454	138	14
Larmer	452	135	12		452	139	12
Cournoyer	452	136	10		452	140	10
Drillon	451	137	7		580	101	9
Demitra	451	138	10		479	129	11
Pavelski	450	139	11		450	141	11
MacInnis	449	140	15		449	142	15
Ribeiro	446	141	11		446	144	11
Andreychuk	445	142	13		445	145	13
Voracek	440	143	11		440	147	11
Kennedy	435	144	11		435	149	11
Tanguay	435	145	11		495	123	12
Keon	434	146	15		448	143	16
Bondra	433	147	10		433	150	10
Nolan	427	148	9		427	151	9
PariseZ	422	149	11		422	152	11
Mullen	420	150	11		420	153	11
Hejduk	420	151	9		440	148	10
Middleton	416	152	9		416	155	9
Potvin	415	153	10		415	156	10
Gaudreau	413	154	7		413	157	7
Clapper	412	155	10		412	158	10
Thompson	411	156	6		411	159	6
Kelly	404	157	12		404	160	12
Abel	404	158	8		462	135	11
SmithB	400	159	10		400	161	10
PrimeauJP	400	160	5		400	162	5
Hextall	399	161	6		418	154	7
MahovlichP	393	162	9		393	164	9
Dillon	391	163	8		391	165	8
SmithH	388	164	7		388	166	7
Anderson	386	165	10		386	167	10

[TBODY] [/TBODY]