Discounted career point totals

[Hockey Outsider]

I'm not sure if I've stumbled upon a new, interesting way of looking at career value, or if this is all nonsense. Feedback is welcome.

The obvious challenge in ranking players based on their career totals is it doesn't differentiate between a player with a dominant peak and then a bunch of weaker years, and a player who was steady from season to season. For example, Guy LaFleur and Mats Sundin have almost the same number of goals, assists and points. LaFleur was nearly unstoppable for six years but never placed in the top 25 in scoring after that. Sundin only placed in the top ten in scoring twice, but had ten years where he placed between 11th and 30th. They got their career totals in very different ways - and anybody who follows hockey would rank LaFleur well ahead.

Some people think that once you adjust for the scoring environment, the problem goes away. It doesn't. If you use VsX, Ron Francis ranks 7th in career scoring, Johnny Bucyk is 13th, and Mark Recchi is 14th. If you use hockey-reference.com's adjusted points, the results are similar - Francis is 5th, Recchi is 9th, and Bucyk is 23rd. Even if we adjust for league-wide scoring levels, it doesn't change the fact that these players had very long careers and put up huge totals despite never having a prominent peak.

My idea is to introduce a concept widely used in finance - discounting. In finance, future cash flows get discounted (reduced) to reflect the fact that a dollar earned in the future is worth less than a dollar earned today. If we apply that concept here, we'd take the player's point total from their best season, and leave it as is. Their point totals from their 2nd-best season would be discounted by 10%; point totals from their 3rd-best season would be discounted by a further 10% (so 21% overall), etc. By the time you get down to their 10th-best season, a point is only worth about 42% as much as a point from their best season. In a player's 20th-best season, a point is only worth 16% as much.

Click to read more...

 

[Hockey Outsider]

Why does this make sense?

This statistic places more value on a player's peak. What a player does in his 8th- or 13th- or 19th-best season is far less important than what he achieves in his best few years. A statistic that treats a player's best year and 13th best season equally - which is what career point totals do - fails to recognize that a player's legacy is largely defined by their peaks.

I think this is appropriate. Let's go back to the LaFleur/Sundin example. LaFleur was able to help his team win four Stanley Cups when he was at his peak, because he was nearly unstoppable. (Of course, he played on a strong, deep team - but they almost certainly don't win four Stanley Cups, and possibly not any, if he was merely an above-average first-line scoring winger).

He has all six of the best seasons (when using VsX) when comparing these two players. Sundin has all 16(!) of the next best between the two of them. If we compare, say, their 10th best season, Sundin has 74 points (again, using VsX) and LaFleur has 58. Neither of them was a superstar forward in their 10th best year. Good for Sundin for outscoring LaFleur by 16 VsX points - but I'm pretty sure the Leafs would have preferred, without hesitation, that Sundin scored those 16 extra points in 2002, when the Leafs were semi-legitimate Stanley Cup contenders. 16 extra points in Sundin's 10th best season didn't mean much; 16 extra points in his best year could have been enough to get the Leafs into the Stanley Cup finals.

At the same time, there's no artificial cut-off. I often present VsX (an adjusted scoring system) based on a player's best seven (or ten) years. The obvious challenge with that is anything beyond a player's seventh (or tenth) best season gets discarded entirely. Here, a player still gets credit for having a long, productive career. No data is cut-off or hidden. As we'll see from the results, "compiler" players can still get high scores.

Why doesn't this make sense?

The 10% discount rate is arbitrary. The results would surely look different if I used 5% or 15%, and I don't have a strong justification for 10%, other than that's the number of fingers I have.

Garbage in, garbage out - if you do this calculation using unadjusted points, the results would be heavily biased in favour of players who peaked in the late seventies to early nineties (just like most unadjusted stats are). If you use hockey-reference.com's flawed adjusted points, you might as well ignore everything prior to 1968 expansion (except for a few seasons in the late 1920's to early 1930's). I've used VsX - but as I've said elsewhere, it was never intended to capture the precise value of a single season.

 

[Hockey Outsider]

The results

Here are the top 100 players based on Discounted Career Points, and where they rank in VsX career points:

Player	Discounted	Original	Change
Wayne Gretzky	1	2	1
Gordie Howe	2	1	-1
Phil Esposito	3	6	3
Jaromir Jagr	4	3	-1
Mario Lemieux	5	18	13
Stan Mikita	6	5	-1
Jean Beliveau	7	12	5
Marcel Dionne	8	14	6
Bobby Hull	9	21	12
Joe Sakic	10	10	0
Sidney Crosby	11	20	9
Joe Thornton	12	8	-4
Maurice Richard	13	19	6
Steve Yzerman	14	11	-3
Alex Ovechkin	15	22	7
Mark Messier	16	4	-12
Ted Lindsay	17	32	15
John Bucyk	18	13	-5
Ron Francis	19	7	-12
Teemu Selanne	20	17	-3
Alex Delvecchio	21	9	-12
Norm Ullman	22	16	-6
Andy Bathgate	23	38	15
Guy Lafleur	24	45	21
Mark Recchi	25	15	-10
Patrick Kane	26	41	15
Adam Oates	27	27	0
Jarome Iginla	28	23	-5
Brett Hull	29	28	-1
Jean Ratelle	30	34	4
Bobby Orr	31	102	71
Bryan Trottier	32	44	12
Frank Mahovlich	33	29	-4
Evgeni Malkin	34	47	13
Paul Coffey	35	30	-5
Mats Sundin	36	26	-10
Henri Richard	37	33	-4
Luc Robitaille	38	35	-3
Nels Stewart	39	55	16
Martin St. Louis	40	63	23
Mike Modano	41	25	-16
Bernie Geoffrion	42	60	18
Bobby Clarke	43	61	18
Gilbert Perreault	44	46	2
Howie Morenz	45	104	59
Jari Kurri	46	53	7
Bill Cowley	47	88	41
Dale Hawerchuk	48	50	2
Doug Gilmour	49	37	-12
Pierre Turgeon	50	39	-11
Marian Hossa	51	40	-11
Brendan Shanahan	52	31	-21
Daniel Alfredsson	53	43	-10
Henrik Sedin	54	51	-3
Raymond Bourque	55	24	-31
Nicklas Backstrom	56	72	16
Milt Schmidt	57	77	20
Frank Boucher	58	101	43
Rod Gilbert	59	66	7
Sergei Fedorov	60	54	-6
Jeremy Roenick	61	48	-13
Denis Savard	62	71	9
Eric Staal	63	58	-5
Daniel Sedin	64	62	-2
Busher Jackson	65	89	24
Ryan Getzlaf	66	75	9
Anze Kopitar	67	70	3
Charlie Conacher	68	126	58
Syd Howe	69	81	12
Peter Stastny	70	97	27
Mike Bossy	71	118	47
Darryl Sittler	72	91	19
Patrick Marleau	73	36	-37
Patrik Elias	74	67	-7
Theoren Fleury	75	79	4
Claude Giroux	76	103	27
Steven Stamkos	77	105	28
Paul Kariya	78	93	15
Bill Cook	79	137	58
Elmer Lach	80	106	26
Phil Kessel	81	90	9
Red Kelly	82	49	-33
Max Bentley	83	127	44
Peter Forsberg	84	121	37
Keith Tkachuk	85	74	-11
Henrik Zetterberg	86	83	-3
Toe Blake	87	111	24
Bernie Nicholls	88	86	-2
Vincent Damphousse	89	59	-30
Pavel Datsyuk	90	99	9
Syl Apps Sr	91	147	56
Jason Spezza	92	85	-7
Dave Keon	93	69	-24
Ken Hodge	94	116	22
Doug Weight	95	84	-11
Rod Brind'Amour	96	57	-39
John Tavares	97	113	16
Marty Barry	98	138	40
Brad Richards	99	95	-4
Sweeney Schriner	100	161	61

[TBODY] [/TBODY]

Players with high peaks fare much better under this method, as expected. Lemieux jumps from 18th to 5th; Guy LaFleur leaps from 45th to 24th; Bobby Orr soars from 102nd to 31st.

Several older skaters make significant gains as well - Howie Morenz jumps 59 spots. Bill Cowley, Frank Boucher, Charlie Conacher and Bill Cook all move up at least 40 spots. Players had significantly shorter careers prior to WWII, and this method (indirectly) accounts for that, by lowering the value of points added in the 2nd half of a player's career.

Amongst the players with the largest drops are Patrick Marleau (37 spots), Dave Andreychuk (59), Mike Gartner (49), Joe Nieuwendyk (42), Dino Ciccarelli (38) and Shane Doan (59). It's like a who's who of HOH's least favourite players. Many of the players with large drops are defensemen (Bourque, MacInnis, Housley and Murphy all drop 30+ spots) - which makes sense since their offensive peaks are generally much lower than forwards.

 

[frisco]

General comments:

--If you truly believe peak is truly way more important this seems like an excellent method. I might use 7.5% as a required rate of return. Ten seems high.

--Another concept might be replacement level points. Since almost exclusively, analysis revolves top end forwards or high scoring d-men you could set a first-line replacement level of 52 points or something in that range (adjusted for era and such) and only count points over that threshold. I'd guess you would get you the same kind of list.

----Probably merits another thread but, although it is pretty much accepted as a given around here, is peak truly more valuable than consistent excellence? For example, let's say we take players like LaFleur and Sundin's best season and their 8th best seasons and adjust them accordingly the best we can. Let's say LaFleur comes in at 121 (best) and 62 (8th) and Sundin is 101 (best) and 82 (8th). Which combination of seasons is better? Peak would say LaFleur but the argument that Sundin makes up for his lower ceiling by having the higher floor overall can be made.

I'd like to see a baseball-style JAWS where 7-year peak and career is melded in tandem. Anyway, a lot of ink spilled going over this ground many times before.

My Best-Carey

 

[OppositeLocK]

Sounds like nonsense to me. Applying TVM and Rates of Return to hockey stats... lol.

 

[Bear of Bad News]

Sounds like nonsense to me. Applying TVM and Rates of Return to hockey stats... lol.

There's nothing weird about focusing on a player's peak years by discounting the impact of non-peak years. This is exactly what you do in your head when you're comparing players' peak years to one another.

You know which sub-forum you're currently posting in, yes?

 

[OppositeLocK]

There's nothing weird about focusing on a player's peak years by discounting the impact of non-peak years. This is exactly what you do in your head when you're comparing players' peak years to one another.

You know which sub-forum you're currently posting in, yes?

There's everything wrong because why would weak seasons carry less weight than good seasons? You're essentially cherry picking.

 

[Bear of Bad News]

There's everything wrong because why would weak seasons carry less weight than good seasons? You're essentially cherry picking.

That's what people do when they talk about a player's peak years.

What do you do when you talk about a player's peak years?

 

[OppositeLocK]

That's what people do when they talk about a player's peak years.

What do you do when you talk about a player's peak years?

Not, not pretend the bad ones didn't happen lol.

 

[Bear of Bad News]

I mean, if you don't understand what a player's peak is, then I don't see the point discussing why you don't understand that.

Especially as amusing as you apparently seem to find it. "I DON'T KNOW WHAT'S GOING ON LOL". Not something I'd be laughing out loud about.

 

[Hockey Outsider]

--If you truly believe peak is truly way more important this seems like an excellent method. I might use 7.5% as a required rate of return. Ten seems high.

Thanks for the feedback. I agree - the percentage is arbitrary. I don't know if there's a way to determine it more concretely.

--Another concept might be replacement level points. Since almost exclusively, analysis revolves top end forwards or high scoring d-men you could set a first-line replacement level of 52 points or something in that range (adjusted for era and such) and only count points over that threshold. I'd guess you would get you the same kind of list.

I like this idea. There probably would need to be a cap - for example, I don't think Bryan Trottier should be penalized for scoring a sub-replacement level towards the end of his career. I suspect the results would be very similar but conceptually your approach probably makes more sense.

----Probably merits another thread but, although it is pretty much accepted as a given around here, is peak truly more valuable than consistent excellence? For example, let's say we take players like LaFleur and Sundin's best season and their 8th best seasons and adjust them accordingly the best we can. Let's say LaFleur comes in at 121 (best) and 62 (8th) and Sundin is 101 (best) and 82 (8th). Which combination of seasons is better? Peak would say LaFleur but the argument that Sundin makes up for his lower ceiling by having the higher floor overall can be made.

Agreed, maybe better for another thread (and not necessarily one in the By The Numbers section). The higher the point totals climb, the harder it is to replace a player. If you assume the threshold for a first-line forward is 60 points, someone like Sundin who produces (say) 85, 80, 75, 75, and 70 points would be much easier to replace than someone who scores 110, 105, 70, 50, 50. (This is kind of a simplified comparison of Lafleur and Sundin). It's far more difficult to find a 105/110 point player than an 85/80 point player (looking at the scoring race in any year would confirm this). This is because talent in the NHL is generally at the tail of the distribution (and doesn't follow a normal distribution).

Sure, Sundin makes up for some of the difference in the later years, but nobody is saying the 2nd player, when he's producing 50 points, would be given a spot on the first line. If 60 points really is replacement level, simply demote him to the second line, and put another player into that position. This way, a team gets the player's actual production (if it exceeds replacement level), and if it falls below, they just put another player in that spot instead.

Speaking of the discount rate - that surely varies by team. For example, the mid-1990's Dallas Stars saw a small window and presumably had a much higher required rate of return - maybe 30%. They surely knew they were trading away hundreds of points in the future in the form of Jarome Iginla, to get Joe Nieuwendyk in order to have a much stronger #2 centre. The offense Nieuwendyk could provide over the next five years would almost certainly be less than what Iginla would provide over ten years until he became a UFA (under the old rules). But Nieuwendyk's offense over five years could be enough to win them a Stanley Cup, and Iginla scoring 80 points in years five through ten (when Nieuwendyk would be retired) wouldn't necessarily help them win a future Cup. (Not to mention Nieuwendyk was nice and consistent and, although Iginla was promising, there was significant uncertainty about how he'd do - which further supports why discounting his future performance makes sense). I'm sure nobody took out a financial calculator to do an NPV calculation, but implicitly, management was considering the time value of money (or offense, in this case) when making the trade. I'm almost certain that if you told the Dallas Stars that they were trading away a player who would score 500 goals and 1,000 points for them (with a Pearson trophy and three years as a Hart finalist) before they'd lose him to UFA status - but Nieuwendyk would win the Conn Smythe for them in 1999 when they won the Cup - they'd make that trade every time.

All of this, of course, is easy to write about. Actually identifying the performance while it's happening (and determining if it's an unsustainable hot or cold streak) is far more difficult. But I still think there's some value in having a framework.

I'd like to see a baseball-style JAWS where 7-year peak and career is melded in tandem. Anyway, a lot of ink spilled going over this ground many times before.

Yes, a JAWS-type system would be the holy grail of hockey stats. Given that hockey is much more complex and fluid than baseball, I'm skeptical that we'll get there, but the fun is in trying to see if you move things a bit further along.

 

[frisco]

Agreed, maybe better for another thread (and not necessarily one in the By The Numbers section). The higher the point totals climb, the harder it is to replace a player. If you assume the threshold for a first-line forward is 60 points, someone like Sundin who produces (say) 85, 80, 75, 75, and 70 points would be much easier to replace than someone who scores 110, 105, 70, 50, 50. (This is kind of a simplified comparison of Lafleur and Sundin). It's far more difficult to find a 105/110 point player than an 85/80 point player (looking at the scoring race in any year would confirm this). This is because talent in the NHL is generally at the tail of the distribution (and doesn't follow a normal distribution).

I've wrestled the peak vs. consistent excellence a lot over the years. A key point is the hindsight factor. With the Nieuwendyk/Iginla thing the discussion goes to a whole different place if Dallas fails to win the Cup with Joe and/or Iginla turns into the second coming of Dave Chyzowski.

In a similar vein, the needs of the team comes into play. A team might be in the position where they might need a career/peak year out of a star to push over the top or just to get to the playoffs. On the other hand, there's a certain amount of value in a Sundin-type where you "know" he's gonna get you 90 points and you can make plans based on that, rather than gambling on a boom or bust guy like Pavel Bure where he might be lights out one year, then disinterested/hurt/holding out or whatever the next.

That's the thing about consistent players. They are by definition reliable. You can plug and play a Ron Francis and not worry. The higher peak/low valley guys not as much. Now if you could plan ahead and knew when and what years Peter Forsberg would miss the bulk of the season beforehand, then you could make the adjustments for this proactively and replace him to a degree. However, when said player goes down with an injury or has a really bad year it is usually too late to scramble and compensate.

My Best-Carey

 

[Hockey Outsider]

Sounds like nonsense to me. Applying TVM and Rates of Return to hockey stats... lol.

See my example above where I talk about Iginla vs Nieuwendyk. It's obvious that teams don't treat a point today as equal to a point tomorrow (as evidenced by numerous teams trading draft picks and prospects for aging veterans). So it's not a question of if this happens - it's a question of can we figure out a way to talk about it intelligently.

 

[Hockey Outsider]

I've wrestled the peak vs. consistent excellence a lot over the years. A key point is the hindsight factor. With the Nieuwendyk/Iginla thing the discussion goes to a whole different place if Dallas fails to win the Cup with Joe and/or Iginla turns into the second coming of Dave Chyzowski.

In a similar vein, the needs of the team comes into play. A team might be in the position where they might need a career/peak year out of a star to push over the top or just to get to the playoffs. On the other hand, there's a certain amount of value in a Sundin-type where you "know" he's gonna get you 90 points and you can make plans based on that, rather than gambling on a boom or bust guy like Pavel Bure where he might be lights out one year, then disinterested/hurt/holding out or whatever the next.

That's the thing about consistent players. They are by definition reliable. You can plug and play a Ron Francis and not worry. The higher peak/low valley guys not as much. Now if you could plan ahead and knew when and what years Peter Forsberg would miss the bulk of the season beforehand, then you could make the adjustments for this proactively and replace him to a degree. However, when said player goes down with an injury or has a really bad year it is usually too late to scramble and compensate.

My Best-Carey

As I get older, I appreciate the steady types more and more. It's one thing to do something great a couple of times in your early/mid twenties - much harder to keep it up into your mid-thirties and beyond.

You're right - maybe the Nieuwendyk/Iginla example is too obvious. But even if it didn't work out, it was still the right call. Or look at the Leafs a few years later (say 2002-2004). They traded countless prospects and draft picks for aging veterans (Nieuwendyk himself, plus Nolan, Francis, Leetch etc). I'd argue that they still made the right call - going all-in when they had a window. With hindsight you can say it didn't work out, but I think they made the right decision at the time. From what I recall, if anything, fans complained that they didn't mortgage even more of their future to go after some really big names (Blake, Lindros, etc).

When it comes to playoff success, I wonder if a boom-or-bust player might be better (if your ultimate goal is winning the Stanley Cup - as opposed to trying to winning as many series as possible - ie consciously trading a few years of 1st round series wins for a better chance at the Stanley Cup). If we stick with Sundin (and none of my posts are intended to be negative towards him - just that he was remarkably consistent) - you know exactly what you're getting from him each year. Put him on a good but flawed team (with Joseph, Roberts, Mogilny, but weak defense) and he'll get you to the second round most years (with an occasional first round stumble, and an occasional trip to the conference finals). Maybe someone like Bure, who's boom or bust, might have been better for the Leafs. If Bure is injured or has a down year, maybe they go down in the first round, but maybe if he's healthy and motivated and scores at a 60-goal pace, Bure would push the Leafs to the SC finals. And maybe Sundin's Leafs and Bure's Leafs would have won the same number of playoff series in total - just that Bure's may have been distributed across the years in a way that's more conducive to the ultimate goal of winning the Stanley Cup.

It's hard to say. I have some ideas on how to go about testing this (is a boom-or-bust star more valuable than someone who's very consistent) but I don't have anything empirical to back it up - just some theories and anecdotes.

 

[frisco]

You're right - maybe the Nieuwendyk/Iginla example is too obvious. But even if it didn't work out, it was still the right call. Or look at the Leafs a few years later (say 2002-2004). They traded countless prospects and draft picks for aging veterans (Nieuwendyk himself, plus Nolan, Francis, Leetch etc). I'd argue that they still made the right call - going all-in when they had a window. With hindsight you can say it didn't work out, but I think they made the right decision at the time. From what I recall, if anything, fans complained that they didn't mortgage even more of their future to go after some really big names (Blake, Lindros, etc).

Agree. Maybe one point to be clarified. If you're trading Nieuwendyk for Iginla you are not only getting present value now vs. future value but pretty much guaranteed value. You know what Joe N. is going to give you. Prospects and picks are more high risk/high reward things with a much higher variance of outcomes (might be a complete bust or a star or anywhere in-between).

Also, there is that hindsight thing. If Dallas just must misses the Cup then it really is hard to justify dealing Iginla but "flags fly forever" and the Cup win is the ultimate validation. Calgary trading Brett Hull for Wamsley, Ramage or whatever is lauded because well because the Flames won a Cup out of that sequence so that sort of trumps everything.

My Best-Carey

 

[plusandminus]

The results

HPlayers with high peaks fare much better under this method, as expected. Lemieux jumps from 18th to 5th; Guy LaFleur leaps from 45th to 24th; Bobby Orr soars from 102nd to 31st.

Several older skaters make significant gains as well - Howie Morenz jumps 59 spots. Bill Cowley, Frank Boucher, Charlie Conacher and Bill Cook all move up at least 40 spots. Players had significantly shorter careers prior to WWII, and this method (indirectly) accounts for that, by lowering the value of points added in the 2nd half of a player's career.

Amongst the players with the largest drops are Patrick Marleau (37 spots), Dave Andreychuk (59), Mike Gartner (49), Joe Nieuwendyk (42), Dino Ciccarelli (38) and Shane Doan (59). It's like a who's who of HOH's least favourite players. Many of the players with large drops are defensemen (Bourque, MacInnis, Housley and Murphy all drop 30+ spots) - which makes sense since their offensive peaks are generally much lower than forwards.

Interesting idea and list. The new results at first glance makes more sense with how we tend to think of players.

Very impressive by Sundin to finish as high as 36th when basically portraying him in the "worst possible way". (The lack of NHL regular season peak is his main "weakness" scoring wise.)

If we stick to scoring, I think that help from teammates should be considered.
If I had more time, I would focus on study that. We could get somewhere by looking at how different players' scoring per game changed depending on environment. However, it's a quite difficult study to do properly.

Point scoring also has a lot to do with how much a player focus on it (often at the cost of defense).
A favorite example of mine is the 1975 BUF, where Ramsay-Luce-Gare scored as much at ES as Martin-Perreault-Robert, while allowing basically half as many goals. Ramsay and Luce then played PK, while the other played PP, thus making the overall difference in scoring huge. Some players simply don't get the same chance of boosting their scoring numbers. Ramsay and Luce, however, help keeping GA down by constantly giving BUF excellent PK stats.

We also know how empty net points affect scoring, benefitting players on winning teams while punishing players on losing teams. And so on...

--

Spoiler

These next paragraphs are not against you. Your topic is simply about scoring, which is perfectly OK to focus on in itself. So the text below is partly off-topic...

There are so many things to consider. And even if we would be able to produce "perfect" adjusted scoring lists (which we won't), it leaves out so much about the players' overall contribution.

Really, the regular season is being treated as some kind of scoring race. Really, many treat it as if the aim of the regular season is for teams to score as many goals as possible, so that its players can get as many points as possible.
But in reality, it's about winning games, where preventing goals against is as important as scoring goals for.

I wish the "best players" projects here had focused more on learning about what the players contributed (or did not contribute) apart from scoring. We know about the scoring, we just have to look at their scoring finishes, or the all-time scoring lists, or the adjusted ones, or VsX. I don't think we'll add our knowledge about a player's overall contribution by creating a formula that makes his scoring appear slightly better or worse. I think the real weaknesses in knowledge about players is what they contributed apart from scoring.

 

[Czech Your Math]

I think it might work better if you used a lower discount rate and/or kept the first X seasons at 100% (e.g. first 3, 5 or 7 seasons). Otherwise, it would seem to overly favor one or two season wonders (think Bernie Nicholls) compared to players with relatively consistent but high peaks/primes.

 

[decma]

Great thread.

The concept of discounting future production certainly makes sense, especially if examining things from the perspective of a GM whose job security is tied to short-term performance. And, in a salary cap world, even from a more global perspective if the best opportunity to win is narrowing rapidly.

But I don't see the application of discounting to the concept outlined in the original post. That is, assume that player A's best seasons, ranked from highest to lowest rather than chronologically, are 120, 100, and 80, and that player B's are 100, 100, and 100.

Under the methodology in the first post, any discount rate above 0 would rate player A higher, but there is no temporal variable here, as there is in the first example.

I agree with Frisco (and have tried to explain in other threads) that value over replacement might be a better way to deal with this. Producing season after season of 60 points (when getting top 6 time and opportunities) is of little value. Producing 90 points is of value, and prodcuing 120 points is of much greater value. Value over replacement, in this simplified 60-pt benchmark example, is twice as a high for the 120 pt season than the 90 pt season, rather than just 1/3 higher, as it is for raw points, which is consistent with what you are trying to capture.