Bigger gap between 1 and 10 or 10 and 20?

[An Unbiased Fan]

My tiers get substantially larger the further I go out.

The Top 4 or 5 players for me are in a tier. The next 5 or 6 are in a tier. Then the next 6 or 7 are in a similar tier. Once I get to around #75 or #80, my tiers are probably 40 to 50 players large.

That's fair, you have your tiers, and everyone else has their rankings too. The Top 10 players is very close, and switch around a lot on various lists, even here on Real GM. Why? because they all were greats in their eras. But at you move form 10 to 20, the gaps get bigger, obvious flaws in resumes get more numerous.

In the last RGM Top 100 list, Lebron was #1, Bird was #10, Moses was #20. Where's the bigger gap? Clearly it's Bird to Moses to me. #20 Moses to #30 Walt is even bigger. #30 Walt to #40 Artis even more.

Yeah, I gotta disagree with this premise haha

You argue the gap is smallest between 1 and 10, bigger from 10 to 20, bigger from 20 to 30, and so on. Well, let's take this to the extreme.
-Let's look at the Athletic's Top 75 All time list. Do we really think the gap between Chris Webber (#65) and Lenny Wilkins (#75) is bigger than the gaps at the top?
-What about SLAM's 500 Greatest Players of all time: Do we really think the gap between Šarūnas Marčiulionis (#490) and Pervis Ellison (#500) is bigger than the gaps at the top, between 1 and 10 or 10 and 20? I gotta be honest... I have no idea who those players are
-What about AinsworthSports Top 1000 NBA players. IS the gap between Walt Williams (#990) and Floyd Volker (#1000) bigger than the gap at the top?

I have trouble thinking so. Once we get to a certain point (e.g. the bottom of the Top 75, and any certainly further down) most lists basically have no agreement whatsoever on who's #65 vs #75, who's #490 vs #500, or who's number #990 vs #1000. So if there's so much uncertainty, why should the gap be bigger?

For those discussing how much Top 10 Lists change vs top 10-20 lists... I wonder how much that just comes from how much more people debate the #1–#10 spots, as opposed to debating #10-#20. I mean, just look at this website... my guess would be the first 10 threads in a Greatest Peaks or Greatest Players project is wayyy more active than the next 10 threads. After the top ~10, people stop caring about exact ordering and just go with inertia. If we debated 10-20 as fiercely, I wonder whether we'd find there's more uncertainty there.

...

Let me introduce some math (if you're intimidated, just stick with me here... ). There's a concept in math called a "Normal Distribution" (https://en.wikipedia.org/wiki/File:Standard_deviation_diagram.svg). It looks like a big bump in the middle, with small arms at either end. It was called a "Normal Distribution" because people noticed this is how Normal things tend to be Distributed. For example, take height: there's lots of people who are close to average height in the middle... very few people who are super tall and super short. Take IQ: there's lots of people who have average intelligence (even if IQ is a stupid measure of intelligence), while there's much fewer people at the extremes (e.g. there are not many true geniuses), and these extremes are much more spread out from the masses.

This is how things normally tend to be distributed. Why should basketball be any different? We should expect lots of people to be average, and very few All-Time-Great outliers. Since there's very few all-time greats, we should expect the biggest outliers, the true all-time-greats, to have a bigger separation from the masses than the masses have from each other (otherwise we wouldn't agree on who the all-time great players were, which is certainly not true... nobody has MJ or LeBron or Kareem outside of their top 10... plenty of people have Šarūnas Marčiulionis outside of their top 490).

Even if this exact case happens to be an exception to this rule (if by random chance the gap is bigger between 10 and 20 than between 1 and 10), we should expect this to be pretty unlikely unlikely, and we should expect this pattern to absolutely not hold once we get lower down the GOAT list. There's just no way the gap between #490 and #500 is bigger than the gap between #1 and #10.

Problem with your math is that distribution is more like a bell curve when it comes to ability.

So the gap is smaller at the top and bottom, biggest towards the center. Middle of the curve is the average NBA player

[DraymondGold]

That's fair, you have your tiers, and everyone else has their rankings too. The Top 10 players is very close, and switch around a lot on various lists, even here on Real GM. Why? because they all were greats in their eras. But at you move form 10 to 20, the gaps get bigger, obvious flaws in resumes get more numerous.

In the last RGM Top 100 list, Lebron was #1, Bird was #10, Moses was #20. Where's the bigger gap? Clearly it's Bird to Moses to me. #20 Moses to #30 Walt is even bigger. #30 Walt to #40 Artis even more.

Yeah, I gotta disagree with this premise haha

You argue the gap is smallest between 1 and 10, bigger from 10 to 20, bigger from 20 to 30, and so on. Well, let's take this to the extreme.
-Let's look at the Athletic's Top 75 All time list. Do we really think the gap between Chris Webber (#65) and Lenny Wilkins (#75) is bigger than the gaps at the top?
-What about SLAM's 500 Greatest Players of all time: Do we really think the gap between Šarūnas Marčiulionis (#490) and Pervis Ellison (#500) is bigger than the gaps at the top, between 1 and 10 or 10 and 20? I gotta be honest... I have no idea who those players are
-What about AinsworthSports Top 1000 NBA players. IS the gap between Walt Williams (#990) and Floyd Volker (#1000) bigger than the gap at the top?

I have trouble thinking so. Once we get to a certain point (e.g. the bottom of the Top 75, and any certainly further down) most lists basically have no agreement whatsoever on who's #65 vs #75, who's #490 vs #500, or who's number #990 vs #1000. So if there's so much uncertainty, why should the gap be bigger?

For those discussing how much Top 10 Lists change vs top 10-20 lists... I wonder how much that just comes from how much more people debate the #1–#10 spots, as opposed to debating #10-#20. I mean, just look at this website... my guess would be the first 10 threads in a Greatest Peaks or Greatest Players project is wayyy more active than the next 10 threads. After the top ~10, people stop caring about exact ordering and just go with inertia. If we debated 10-20 as fiercely, I wonder whether we'd find there's more uncertainty there.

...

Let me introduce some math (if you're intimidated, just stick with me here... ). There's a concept in math called a "Normal Distribution" (https://en.wikipedia.org/wiki/File:Standard_deviation_diagram.svg). It looks like a big bump in the middle, with small arms at either end. It was called a "Normal Distribution" because people noticed this is how Normal things tend to be Distributed. For example, take height: there's lots of people who are close to average height in the middle... very few people who are super tall and super short. Take IQ: there's lots of people who have average intelligence (even if IQ is a stupid measure of intelligence), while there's much fewer people at the extremes (e.g. there are not many true geniuses), and these extremes are much more spread out from the masses.

This is how things normally tend to be distributed. Why should basketball be any different? We should expect lots of people to be average, and very few All-Time-Great outliers. Since there's very few all-time greats, we should expect the biggest outliers, the true all-time-greats, to have a bigger separation from the masses than the masses have from each other (otherwise we wouldn't agree on who the all-time great players were, which is certainly not true... nobody has MJ or LeBron or Kareem outside of their top 10... plenty of people have Šarūnas Marčiulionis outside of their top 490).

Even if this exact case happens to be an exception to this rule (if by random chance the gap is bigger between 10 and 20 than between 1 and 10), we should expect this to be pretty unlikely unlikely, and we should expect this pattern to absolutely not hold once we get lower down the GOAT list. There's just no way the gap between #490 and #500 is bigger than the gap between #1 and #10.

Problem with your math is that distribution is more like a bell curve when it comes to ability.

So the gap is smaller at the top and bottom, biggest towards the center. Middle of the curve is the average NBA player

Hiya UnbiasedFan!

Sorry to be blunt, but that's not how to interpret bell curves or normal distributions at all.

y axis = number of players
x axis = skill.

The average player is in the middle, so you're correct about that! But since there's more players closer together in the middle, that means the horizontal gaps between players in the middle are smaller. Since there's fewer players at the edges, that means the horizontal gaps (i.e. the "skill" gaps) are farther apart.

Here's an example normal distribution (which isn't that different qualitatively from a bell curve) with data points: https://i.stack.imgur.com/FdU3r.png
Look at the middle... look at how close together the middle points are horizontally.
Look at the edges... look at how much further apart the extreme cases are.
This example is made of random data points unrelated to basketball, but this is exactly the same trend I'm trying to explain. And remember, it's called a "normal distribution" because it's normal for things to be distributed like that. If basketball weren't normal (unlike the majority of other human traits, skills, and even other sports)... we'd have to have pretty strong explanation for why this were the case.

This is what it means to be an outlier. all-time players wouldn't be outliers if they were close together... being an outlier means you're further apart from the pack!

If the graph is confusing, look at what SickMother said:

What information is that? All the statistical information is informative but incomplete or flawed. I am curious what you think of as an objective rating system here.

Any statistical information is incomplete or flawed, sure, but it's still far more objective than subjectively assigning point ratings like in NBA2K.

I already provided one example (while admitting its imperfection above) with Win Shares, but look at just about any leaderboard for anything at all & the difference from 1-10 will almost always be greater than the difference between 10-20.

VORP 1-10: LeBron (142.6) to Admiral (81.9). Diff: 60.7
VORP 10-20: Admiral (81.9) to Harden (72.0). Diff: 9.9

MVP Shares 1-10: LeBron (8.8) to Kobe (4.2). Diff 4.6
MVP Shares 10-20: Kobe (4.2) to Pettit (2.7): Diff 1.5

Points 1-10: Kareem (38,387) to Shaq (28,596). Diff: 9,791
Points 10-20: Shaq (28,596) to Havlicek (26,395). Diff: 2,201

Rebounds 1-10: Wilt (23,924) to Garnett (14,662). Diff: 9,262
Rebounds 10-20: Garnett (14,662) to Barkley (12,546). Diff: 2,116

Assists 1-10: Stockton (15,806) to Payton (8,966). Diff: 6,840
Assists 10-20: Payton (8,966) to Cousy (6,955). Diff: 2,011

NBA Owner Net Worth 1-10: Ballmer (75.6 billion) to DeVos (5.4 billion). Diff: 70.2 billion
NBA Owner Net Worth 10-20: DeVos (5.4 billion) to Lasry (1.8 billion). Diff: 3.6 billion

These are 7 cases that are exactly showing what the normal distribution / bell curve distribution is trying to say. The gaps at the edges are bigger than the gaps in the middle.

[DraymondGold]

This might be a more fun way to convey my point.

Let's take a look at Basketball Reference's all time Records page: https://www.basketball-reference.com/leaders/.
I'd reckon there's almost 1000 different records listed here, with all the different stats for regular season/postseason/career/year-by-year, etc.

In this group of almost 1000 NBA statistical record lists, how many stats can you find that have a bigger gap from #10-20 and a smaller gap from #1-#10? Can you find any?

If you're noticing that the gap from 1-10 seems bigger than the gap from 10-20 in so many of these stats, why should we expect career impact / the Greatness gap to be any different?

[An Unbiased Fan]

Yeah, I gotta disagree with this premise haha

You argue the gap is smallest between 1 and 10, bigger from 10 to 20, bigger from 20 to 30, and so on. Well, let's take this to the extreme.
-Let's look at the Athletic's Top 75 All time list. Do we really think the gap between Chris Webber (#65) and Lenny Wilkins (#75) is bigger than the gaps at the top?
-What about SLAM's 500 Greatest Players of all time: Do we really think the gap between Šarūnas Marčiulionis (#490) and Pervis Ellison (#500) is bigger than the gaps at the top, between 1 and 10 or 10 and 20? I gotta be honest... I have no idea who those players are
-What about AinsworthSports Top 1000 NBA players. IS the gap between Walt Williams (#990) and Floyd Volker (#1000) bigger than the gap at the top?

I have trouble thinking so. Once we get to a certain point (e.g. the bottom of the Top 75, and any certainly further down) most lists basically have no agreement whatsoever on who's #65 vs #75, who's #490 vs #500, or who's number #990 vs #1000. So if there's so much uncertainty, why should the gap be bigger?

For those discussing how much Top 10 Lists change vs top 10-20 lists... I wonder how much that just comes from how much more people debate the #1–#10 spots, as opposed to debating #10-#20. I mean, just look at this website... my guess would be the first 10 threads in a Greatest Peaks or Greatest Players project is wayyy more active than the next 10 threads. After the top ~10, people stop caring about exact ordering and just go with inertia. If we debated 10-20 as fiercely, I wonder whether we'd find there's more uncertainty there.

...

Let me introduce some math (if you're intimidated, just stick with me here... ). There's a concept in math called a "Normal Distribution" (https://en.wikipedia.org/wiki/File:Standard_deviation_diagram.svg). It looks like a big bump in the middle, with small arms at either end. It was called a "Normal Distribution" because people noticed this is how Normal things tend to be Distributed. For example, take height: there's lots of people who are close to average height in the middle... very few people who are super tall and super short. Take IQ: there's lots of people who have average intelligence (even if IQ is a stupid measure of intelligence), while there's much fewer people at the extremes (e.g. there are not many true geniuses), and these extremes are much more spread out from the masses.

This is how things normally tend to be distributed. Why should basketball be any different? We should expect lots of people to be average, and very few All-Time-Great outliers. Since there's very few all-time greats, we should expect the biggest outliers, the true all-time-greats, to have a bigger separation from the masses than the masses have from each other (otherwise we wouldn't agree on who the all-time great players were, which is certainly not true... nobody has MJ or LeBron or Kareem outside of their top 10... plenty of people have Šarūnas Marčiulionis outside of their top 490).

Even if this exact case happens to be an exception to this rule (if by random chance the gap is bigger between 10 and 20 than between 1 and 10), we should expect this to be pretty unlikely unlikely, and we should expect this pattern to absolutely not hold once we get lower down the GOAT list. There's just no way the gap between #490 and #500 is bigger than the gap between #1 and #10.

Problem with your math is that distribution is more like a bell curve when it comes to ability.

So the gap is smaller at the top and bottom, biggest towards the center. Middle of the curve is the average NBA player

Hiya UnbiasedFan!

Sorry to be blunt, but that's not how to interpret bell curves or normal distributions at all.

y axis = number of players
x axis = skill.

The average player is in the middle, so you're correct about that! But since there's more players closer together in the middle, that means the horizontal gaps between players in the middle are smaller. Since there's fewer players at the edges, that means the horizontal gaps (i.e. the "skill" gaps) are farther apart.

Here's an example normal distribution (which isn't that different qualitatively from a bell curve) with data points: https://i.stack.imgur.com/FdU3r.png
Look at the middle... look at how close together the middle points are horizontally.
Look at the edges... look at how much further apart the extreme cases are.
This example is made of random data points unrelated to basketball, but this is exactly the same trend I'm trying to explain. And remember, it's called a "normal distribution" because it's normal for things to be distributed like that. If basketball weren't normal (unlike the majority of other human traits, skills, and even other sports)... we'd have to have pretty strong explanation for why this were the case.

This is what it means to be an outlier. all-time players wouldn't be outliers if they were close together... being an outlier means you're further apart from the pack!

If the graph is confusing, look at what SickMother said:

What information is that? All the statistical information is informative but incomplete or flawed. I am curious what you think of as an objective rating system here.

Any statistical information is incomplete or flawed, sure, but it's still far more objective than subjectively assigning point ratings like in NBA2K.

I already provided one example (while admitting its imperfection above) with Win Shares, but look at just about any leaderboard for anything at all & the difference from 1-10 will almost always be greater than the difference between 10-20.

VORP 1-10: LeBron (142.6) to Admiral (81.9). Diff: 60.7
VORP 10-20: Admiral (81.9) to Harden (72.0). Diff: 9.9

MVP Shares 1-10: LeBron (8.8) to Kobe (4.2). Diff 4.6
MVP Shares 10-20: Kobe (4.2) to Pettit (2.7): Diff 1.5

Points 1-10: Kareem (38,387) to Shaq (28,596). Diff: 9,791
Points 10-20: Shaq (28,596) to Havlicek (26,395). Diff: 2,201

Rebounds 1-10: Wilt (23,924) to Garnett (14,662). Diff: 9,262
Rebounds 10-20: Garnett (14,662) to Barkley (12,546). Diff: 2,116

Assists 1-10: Stockton (15,806) to Payton (8,966). Diff: 6,840
Assists 10-20: Payton (8,966) to Cousy (6,955). Diff: 2,011

NBA Owner Net Worth 1-10: Ballmer (75.6 billion) to DeVos (5.4 billion). Diff: 70.2 billion
NBA Owner Net Worth 10-20: DeVos (5.4 billion) to Lasry (1.8 billion). Diff: 3.6 billion

These are 7 cases that are exactly showing what the normal distribution / bell curve distribution is trying to say. The gaps at the edges are bigger than the gaps in the middle.

I should have said "inverted" bell curve, weighted heavily to the front. I feel the gap on the high end is less than what people think. But I was speaking abstractly. I feel talent is top heavy, and big gaps follow as you go down to the median. I generally don't think there's much gap between the Top 15 players. Like Curry is #15 for me, and many would have him much higher. Wilt is outside of many Top 10s and Top 2-3 in some also. Clearly things level off as you go away from the elite players, the median would be starter level, and grow more and more as you go on after that

[An Unbiased Fan]

This might be a more fun way to convey my point.

Let's take a look at Basketball Reference's all time Records page: https://www.basketball-reference.com/leaders/.
I'd reckon there's almost 1000 different records listed here, with all the different stats for regular season/postseason/career/year-by-year, etc.

In this group of almost 1000 NBA statistical record lists, how many stats can you find that have a bigger gap from #10-20 and a smaller gap from #1-#10? Can you find any?

If you're noticing that the gap from 1-10 seems bigger than the gap from 10-20 in so many of these stats, why should we expect career impact / the Greatness gap to be any different?

What are you measuring career impact by? Because again, Lebron's career impact is not that much bigger than Bird's, in comparison to Bird's vs Moses.

HOF probability is more how I view the gaps with players: https://www.basketball-reference.com/leaders/hof_prob.html

Obviously I would make the stat a bit more precise(not so many at 1.00 and change the criteria), but generally that's how I view gaps

[Cavsfansince84]

This might be a more fun way to convey my point.

Let's take a look at Basketball Reference's all time Records page: https://www.basketball-reference.com/leaders/.
I'd reckon there's almost 1000 different records listed here, with all the different stats for regular season/postseason/career/year-by-year, etc.

In this group of almost 1000 NBA statistical record lists, how many stats can you find that have a bigger gap from #10-20 and a smaller gap from #1-#10? Can you find any?

If you're noticing that the gap from 1-10 seems bigger than the gap from 10-20 in so many of these stats, why should we expect career impact / the Greatness gap to be any different?

While I get the logic you are using the answer would be two fold:

1. The 20 player sample being used being small enough that it wouldn't necessarily conform to a mathematical model.
2. The differences between them going well beyond just a box score numbers sort of approach which is where the nuance lies.

[DraymondGold]

This might be a more fun way to convey my point.

Let's take a look at Basketball Reference's all time Records page: https://www.basketball-reference.com/leaders/.
I'd reckon there's almost 1000 different records listed here, with all the different stats for regular season/postseason/career/year-by-year, etc.

In this group of almost 1000 NBA statistical record lists, how many stats can you find that have a bigger gap from #10-20 and a smaller gap from #1-#10? Can you find any?

If you're noticing that the gap from 1-10 seems bigger than the gap from 10-20 in so many of these stats, why should we expect career impact / the Greatness gap to be any different?

What are you measuring career impact by? Because again, Lebron's career impact is not that much bigger than Bird's, in comparison to Bird's vs Moses.

HOF probability is more how I view the gaps with players: https://www.basketball-reference.com/leaders/hof_prob.html

Obviously I would make the stat a bit more precise(not so many at 1.00 and change the criteria), but generally that's how I view gaps

Ah, now I understand what your reasoning is better.

Comment: the hall of fame purposefully doesn't differentiate from any players at the top. If we're just looking at who got into the hall of fame, there's no gap between Michael Jordan and Mo Cheeks/Bill Bradley. Meanwhile, there's a massive gap between the greatness of Mo Cheeks/Bill Bradley and Paul Pierce/Rasheed Wallace.
Question: Does this seem right to you? If not, are we sure hall of fame probability is better measure than the general trend seen in... any of the ~1000 stats I pointed to?

Question: You mention that this stat is flawed, because it has a bunch of people at 1.00. Another player said 10/20 players is too small. So let's look at a larger sample size. Using Your suggested stat (Hall of Fame probability), which gap is bigger... the gap between #1 and #25 or the gap between #25 and #50?
What about the gap between #1 and #50 vs the gap between #50 and #100?
What about the gap between #1 and #100 vs the gap between #100 and #200?

This might be a more fun way to convey my point.

Let's take a look at Basketball Reference's all time Records page: https://www.basketball-reference.com/leaders/.
I'd reckon there's almost 1000 different records listed here, with all the different stats for regular season/postseason/career/year-by-year, etc.

In this group of almost 1000 NBA statistical record lists, how many stats can you find that have a bigger gap from #10-20 and a smaller gap from #1-#10? Can you find any?

If you're noticing that the gap from 1-10 seems bigger than the gap from 10-20 in so many of these stats, why should we expect career impact / the Greatness gap to be any different?

While I get the logic you are using the answer would be two fold:

1. The 20 player sample being used being small enough that it wouldn't necessarily conform to a mathematical model.
2. The differences between them going well beyond just a box score numbers sort of approach which is where the nuance lies.

Thanks for the comment!

1a, if it doesn't conform to any mathematical model, we'd expect it to be random, right? So we'd expect it to be ~50-50%, whether the gap is bigger between 1 and 10 vs 10 and 20 in all these stats? Take a look at them and see if they're close to 50-50. Seriously!
1b, re: small sample -- good point! Then let's increase the sample size. In any of these stats, check the gap between 1 and 25 vs 25 and 50. Or check the gap between 1 and 50 vs 50 and 100.

2. If you're looking for more wholistic measures, that should be more closely captured in advanced stats like plus minus, right? Do any of the advanced stats on that list show a different trend?
And if there's so many of these stats support my favor... and you're saying the only difference is in nuance... what good are any stats at all? I literally can't find one stat that supports the opposing claim when we use the bigger sample size you suggest. Not one. It would take a heck of a lot of nuance to explain that away!

[Cavsfansince84]

Thanks for the comment!

1a, if it doesn't conform to any mathematical model, we'd expect it to be random, right? So we'd expect it to be ~50-50%, whether the gap is bigger between 1 and 10 vs 10 and 20 in all these stats? Take a look at them and see if they're close to 50-50. Seriously!
1b, re: small sample -- good point! Then let's increase the sample size. In any of these stats, check the gap between 1 and 25 vs 25 and 50. Or check the gap between 1 and 50 vs 50 and 100.

2. If you're looking for more wholistic measures, that should be more closely captured in advanced stats like plus minus, right? Do any of the advanced stats on that list show a different trend?
And if there's so many of these stats support my favor... and you're saying the only difference is in nuance... what good are any stats at all? I literally can't find one stat that supports the opposing claim when we use the bigger sample size you suggest. Not one. It would take a heck of a lot of nuance to explain that away!

I think you might get a better idea of the nuance I mean by looking at some of the arguments/debates that went on in the last top 100 project. It goes beyond just numbers and in this case also depends on which players you have ranked where. Not everyone uses a cumulative stats sort of approach based mostly on the rs either. That would be rare tbh. So you need to look at things from a lot of angles which includes what gets left out of many metrics and things like intangibles. That would be where the nuance comes into play as well as things like how you might adjust for era and teammates. As well as whether someone focuses more on just prime years or top 3-5 years.

[DraymondGold]

Thanks for the comment!

1a, if it doesn't conform to any mathematical model, we'd expect it to be random, right? So we'd expect it to be ~50-50%, whether the gap is bigger between 1 and 10 vs 10 and 20 in all these stats? Take a look at them and see if they're close to 50-50. Seriously!
1b, re: small sample -- good point! Then let's increase the sample size. In any of these stats, check the gap between 1 and 25 vs 25 and 50. Or check the gap between 1 and 50 vs 50 and 100.

2. If you're looking for more wholistic measures, that should be more closely captured in advanced stats like plus minus, right? Do any of the advanced stats on that list show a different trend?
And if there's so many of these stats support my favor... and you're saying the only difference is in nuance... what good are any stats at all? I literally can't find one stat that supports the opposing claim when we use the bigger sample size you suggest. Not one. It would take a heck of a lot of nuance to explain that away!

I think you might get a better idea of the nuance I mean by looking at some of the arguments/debates that went on in the last top 100 project. It goes beyond just numbers and in this case also depends on which players you have ranked where. Not everyone uses a cumulative stats sort of approach based mostly on the rs either. That would be rare tbh. So you need to look at things from a lot of angles which includes what gets left out of many metrics and things like intangibles. That would be where the nuance comes into play as well as things like how you might adjust for era and teammates. As well as whether someone focuses more on just prime years or top 3-5 years.

Sounds like you haven't checked any of the stats pages I recommended, which I'm a bit sad to hear Because on that page isn't just a list of regular season stats cumulative/career stats, it includes playoffs, and single year leaders as well.

To reiterate: basically every single stat on Basketball Reference, says the gap between #1 and #25 is bigger than the gap between #25 and #50, and that applies whether we look at regular season or playoffs, full career or single year or a several year span. Can you find any stat on basketball reference where this isn't the case? Literally just one?

Since the stats are so universally in agreement that the gap between 1 and 25 is bigger than between 25 and 50, you'd have to have the "nuance"/intangibles advantage of #25 to be massively ahead of the nuance and intangibles of #1, in order for #25 to close the gap. Do you really have the intangibles of Stockton / Isaiah Thomas / Rick Barry (~25th Greatest players all time) >>> the intangibles of Jordan or Kareem or LeBron (~top 3ish players of all time)?

Now, with the nuance advantage, you suggest the ~25th Greatest player of all time catches up so much ground to get close to #1... that way the gap between 1 and 25 is smaller than the gap between 25 and 50. We compared 1 vs 25 vs 50 because you said the sample size to compare 1 vs 10 vs 20 is too small. What if we increase the sample size again? What if we compare 1 vs 50 vs 100.

Well, the statistical gap remains (i.e. according to all the stats we have, the gap between 1 and 50 is smaller than the gap between 50 and 100). So to make up for it, you'd also have to have the nuance advantage of 50 >> the nuance of 1, that way #50 can close the distance between him and 1. So the process repeats.... do you also have the intangibles of Kevin McHale, Paul Pierce, or Dominique Wilkins (~50th greatest players) >> the intangibles and nuance of Jordan, LeBron, or Kareem (~greatest players)? Because that's what you'd need to argue for the 50th GOAT player to close the gap to get closer to 1, when all the statistics have 50 closer to 100...

we could keep repeating this process. IN the end, to make up for the statistical gap that increases as we get towards the top, you're going to have to argue that all the worse and average players have better nuance and intangibles than the players at the top. Is that really what you want to do?

[Cavsfansince84]

Sounds like you haven't checked any of the stats pages I recommended, which I'm a bit sad to hear Because on that page isn't just a list of regular season stats cumulative/career stats, it includes playoffs, and single year leaders as well.

To reiterate: basically every single stat on Basketball Reference, says the gap between #1 and #25 is bigger than the gap between #25 and #50, and that applies whether we look at regular season or playoffs, full career or single year or a several year span. Can you find any stat on basketball reference where this isn't the case? Literally just one?

Since the stats are so universally in agreement that the gap between 1 and 25 is bigger than between 25 and 50, you'd have to have the "nuance"/intangibles advantage of #25 to be massively ahead of the nuance and intangibles of #1, in order for #25 to close the gap. Do you really have the intangibles of Stockton / Isaiah Thomas / Rick Barry (~25th Greatest players all time) >>> the intangibles of Jordan or Kareem or LeBron (~top 3ish players of all time)?

Now, with the nuance advantage, you suggest the ~25th Greatest player of all time catches up so much ground to get close to #1... that way the gap between 1 and 25 is smaller than the gap between 25 and 50. We compared 1 vs 25 vs 50 because you said the sample size to compare 1 vs 10 vs 20 is too small. What if we increase the sample size again? What if we compare 1 vs 50 vs 100.

Well, since the statistical gap remains (i.e. according to all the stats we have, the gap between 1 and 50 is smaller than the gap between 50 and 100). So to make up for it, you'd also have to have the nuance advantage of 50 >> the nuance of 1, that way #50 can close the distance between him and 1. So the process repeats.... do you also have the intangibles of Kevin McHale, Paul Pierce, or Dominique Wilkins (~50th greatest players) >> the intangibles and nuance of Jordan, LeBron, or Kareem (~greatest players)? Because that's what you'd need to argue for the 50th GOAT player to close the gap to get closer to 1, when all the statistics have 50 closer to 100...

I didn't check those stats because I am already extremely familiar with them. I've actually been really into the whole stats aspect of bb since the late 80's and into metrics quite a bit for the last 10 years. So I know about the differences in those stats from 1 to 10 or 20 to 100 or 100 to 500. Shifting the debate from the op to a 1-50 comparison also invalidates the whole point of it. I'm well aware that as you go further out its going to make things more and more in line with the numbers aspect you are bringing up. This is more than just a strict numbers comparison though you are welcome to make it about that if that's the way you judge players when making an all time list. It's completely up to whatever criteria you use to make such a list but you can't say that you're way is necessarily the best method because that's not a good basis for debate.

[DraymondGold]

Sounds like you haven't checked any of the stats pages I recommended, which I'm a bit sad to hear Because on that page isn't just a list of regular season stats cumulative/career stats, it includes playoffs, and single year leaders as well.

To reiterate: basically every single stat on Basketball Reference, says the gap between #1 and #25 is bigger than the gap between #25 and #50, and that applies whether we look at regular season or playoffs, full career or single year or a several year span. Can you find any stat on basketball reference where this isn't the case? Literally just one?

Since the stats are so universally in agreement that the gap between 1 and 25 is bigger than between 25 and 50, you'd have to have the "nuance"/intangibles advantage of #25 to be massively ahead of the nuance and intangibles of #1, in order for #25 to close the gap. Do you really have the intangibles of Stockton / Isaiah Thomas / Rick Barry (~25th Greatest players all time) >>> the intangibles of Jordan or Kareem or LeBron (~top 3ish players of all time)?

Now, with the nuance advantage, you suggest the ~25th Greatest player of all time catches up so much ground to get close to #1... that way the gap between 1 and 25 is smaller than the gap between 25 and 50. We compared 1 vs 25 vs 50 because you said the sample size to compare 1 vs 10 vs 20 is too small. What if we increase the sample size again? What if we compare 1 vs 50 vs 100.

Well, since the statistical gap remains (i.e. according to all the stats we have, the gap between 1 and 50 is smaller than the gap between 50 and 100). So to make up for it, you'd also have to have the nuance advantage of 50 >> the nuance of 1, that way #50 can close the distance between him and 1. So the process repeats.... do you also have the intangibles of Kevin McHale, Paul Pierce, or Dominique Wilkins (~50th greatest players) >> the intangibles and nuance of Jordan, LeBron, or Kareem (~greatest players)? Because that's what you'd need to argue for the 50th GOAT player to close the gap to get closer to 1, when all the statistics have 50 closer to 100...

I didn't check those stats because I am already extremely familiar with them. I've actually been really into the whole stats aspect of bb since the late 80's and into metrics quite a bit for the last 10 years.

. Oh sweet, that's really cool to hear!

So I know about the differences in those stats from 1 to 10 or 20 to 100 or 100 to 500. Shifting the debate from the op to a 1-50 comparison also invalidates the whole point of it. I'm well aware that as you go further out its going to make things more and more in line with the numbers aspect you are bringing up.

The only reason I started talking about 1-50 wasn't to invalidate the whole point of op. I did it because both you and An Unbiased Fan suggested doing so in your argument. At least that's what it sounded like...?

Here's your quote where you said 1-20 isn't a big enough sample size: " The 20 player sample being used being small enough that it wouldn't necessarily conform to a mathematical model." So I responded by taking a a bigger sample size. I did 1-50 and 1-100. Now it's too big a sample size? I'm a bit confused by what you want...

Here's An Unbiased Fan's quote that I was responding to: "But at you move form 10 to 20, the gaps get bigger, obvious flaws in resumes get more numerous. In the last RGM Top 100 list, Lebron was #1, Bird was #10, Moses was #20. Where's the bigger gap? Clearly it's Bird to Moses to me. #20 Moses to #30 Walt is even bigger. #30 Walt to #40 Artis even more." I brought brought up 1-50 because that's where the conversation was headed... no?

This is more than just a strict numbers comparison though you are welcome to make it about that if that's the way you judge players when making an all time list. It's completely up to whatever criteria you use to make such a list but you can't say that you're way is necessarily the best method because that's not a good basis for debate.

I certainly didn't mean to suggest that there's only one way to do it. But if one set of criteria pretty universally points towards one answer, without any ambiguity at all, is that not relevant?

Moreover, if other types of criteria lead to cases that seem obviously wrong to me... for example:
1) just looking at whether players make the hall of fame to measure a player's greatness, which would make us think the gap between Jordan and Mo Cheeks is smaller than the gap between Mo Cheeks and Rasheed Wallace.
2) just looking at hall of fame probability to argue that the separation between players gets bigger and bigger the further down the GOAT list you go, despite the fact that once you get out of the "100% Probability of making HoF" range, that very metric shows the opposite
3) arguing that nuance/intangibles shrink the statistical gap that's larger between 1-10 and smaller between 10-20, which requires having the nuance/intangibles of GOAT #10 >> the nuance/intangibles of GOAT #1
... when some criteria lead us to conclusions that seem obviously inconsistent with common sense, like in these examples, is it really wrong to bring it up?

See, I ain't tryin to win some internet debate. I'm just trying to learn about basketball and enjoy discussing it with some pretty smart people. And sure, plenty of these smart people have different criteria. But if some people's criteria lead us to conclusions that seem somewhat silly to me, should I not bring it up and question if that's the best criteria?

[Cavsfansince84]

The only reason I started talking about 1-50 wasn't to invalidate the whole point of op. I did it because both you and An Unbiased Fan suggested doing so in your argument. At least that's what it sounded like...?

Here's your quote where you said 1-20 isn't a big enough sample size: " The 20 player sample being used being small enough that it wouldn't necessarily conform to a mathematical model." So I responded by taking a a bigger sample size. I did 1-50 and 1-100. Now it's too big a sample size? I'm a bit confused by what you want...

Here's An Unbiased Fan's quote that I was responding to: "But at you move form 10 to 20, the gaps get bigger, obvious flaws in resumes get more numerous. In the last RGM Top 100 list, Lebron was #1, Bird was #10, Moses was #20. Where's the bigger gap? Clearly it's Bird to Moses to me. #20 Moses to #30 Walt is even bigger. #30 Walt to #40 Artis even more." I brought brought up 1-50 because that's where the conversation was headed... no?

I did bring up the sample being small enough to not conform to a purely mathematical form of analysis but not to suggest any need to change the question I was asking because its not meant to conform to just that way of looking at it. It's just meant to be a question posters can answer using whatever method they prefer. I agree though that the hof based way doesn't carry much weight either.

[Jaivl]

This might be a more fun way to convey my point.

Let's take a look at Basketball Reference's all time Records page: https://www.basketball-reference.com/leaders/.
I'd reckon there's almost 1000 different records listed here, with all the different stats for regular season/postseason/career/year-by-year, etc.

In this group of almost 1000 NBA statistical record lists, how many stats can you find that have a bigger gap from #10-20 and a smaller gap from #1-#10? Can you find any?

If you're noticing that the gap from 1-10 seems bigger than the gap from 10-20 in so many of these stats, why should we expect career impact / the Greatness gap to be any different?

What are you measuring career impact by? Because again, Lebron's career impact is not that much bigger than Bird's, in comparison to Bird's vs Moses.

It absolutely is.

[falcolombardi]

This might be a more fun way to convey my point.

Let's take a look at Basketball Reference's all time Records page: https://www.basketball-reference.com/leaders/.
I'd reckon there's almost 1000 different records listed here, with all the different stats for regular season/postseason/career/year-by-year, etc.

In this group of almost 1000 NBA statistical record lists, how many stats can you find that have a bigger gap from #10-20 and a smaller gap from #1-#10? Can you find any?

If you're noticing that the gap from 1-10 seems bigger than the gap from 10-20 in so many of these stats, why should we expect career impact / the Greatness gap to be any different?

What are you measuring career impact by? Because again, Lebron's career impact is not that much bigger than Bird's, in comparison to Bird's vs Moses.

HOF probability is more how I view the gaps with players: https://www.basketball-reference.com/leaders/hof_prob.html

Obviously I would make the stat a bit more precise(not so many at 1.00 and change the criteria), but generally that's how I view gaps

Mmm, lebron 2006-2014 is already as long and impactfuk as bird prime (80-88) and where bird declinrd to a lower level of play post injuries lebron added another monster 5 years (15-18,20)