By The NumbersHockey Analytics... the Final Frontier. Explore strange new worlds, to seek out new algorithms, to boldly go where no one has gone before.

I average by adding up all the gs in a season and dividing by the number of games played. What is my error?

Your error is in believing that this process results in normalization. It does not.

You seem to think that by using any kind of average in a calculation, you are normalizing the results. This is simply not true. Applying a flat multiplier, as adjusted scoring does, does not change the essential shape of the curve.

Last edited by Iain Fyffe: 11-13-2012 at 11:17 AM.

Have you even read it? You don't seem to understand it at all. Its as obvous as a sunset that AS is wrong. Averaging seasons is just avergaing players collectively. The study addresses that when it points out that its resutls (hockey players included) hold true whether talking about a team, a season or across seasons. I think you should actually read it before commenting further.

Take your own advice. The study to which you continue to refer makes two essential points:

1. That outliers should not be automatically be dimissed when analyzing human performance.

2. That human performance generally does not follow a bell curve, but instead a power law curve.

Neither of these points are relevant to adjusted scoring, because adjusted scoring neither ignores outliers nor assumes a bell curve. But of course, I've said this over and over and over again. Perhaps this time you'll take note of it?

If you want to show that this study is relevant to the discussion, you have to demonstrate that adjusted scoring ignores outliers (it doesn't, players are adjusted based on their actual stats regardless of whether they might appear to be outliers or not) and that it assumes a bell curve (it doesn't, since the same essentially flat multiplier is applied to all players in a season). Until you demonstrate these two things (which you cannot, since they are not true), this study is utterly irrelevant to this discussion, and you should stop trying to use it to support your position.

How about you explain what averaging actually means then. Further the debate.

I average by adding up all the gs in a season and dividing by the number of games played. What is my error?

Your error was not realizing the other definiton of "means".

Quote:

Originally Posted by Dalton

Slam dunk.

Nicely done!

The idea Czech has behind using AS for direct comparison of seasons played by multiple players is predicated on the fact that average scoring fluctuates on a yearly basis.

Example:

Joe Smith scores 20 goals every year in three consecutive years.
Bob Jones scores 25, 25, and 10 in those same years.

They have the same overall totals, and we'll assume they had the same GP.

Adjusted stats provide us insight into whether it was harder to score goals in a given season, and might highlight one or the other a truly achieving more. In this example, if the third season has a higher league GPG than the first two, there's a good chance Bob Jones ends up with more AG.

And before you begin with the "See, I told you it was flawed!" this is no different than taking three random seasons out of Gretzky's career and comparing them to three random seasons out of Jagr's.

The idea Czech has behind using AS for direct comparison of seasons played by multiple players is predicated on the fact that average scoring fluctuates on a yearly basis.

Example:

Joe Smith scores 20 goals every year in three consecutive years.
Bob Jones scores 25, 25, and 10 in those same years.

They have the same overall totals, and we'll assume they had the same GP.

Adjusted stats provide us insight into whether it was harder to score goals in a given season, and might highlight one or the other a truly achieving more. In this example, if the third season has a higher league GPG than the first two, there's a good chance Bob Jones ends up with more AG.

And before you begin with the "See, I told you it was flawed!" this is no different than taking three random seasons out of Gretzky's career and comparing them to three random seasons out of Jagr's.

No man, it's very different.
The only reason you use AS's is to bring 2 different seasons to a common place so they can be compared as equally and accurately as possible.
If you were comparing what Jagr did in 1998 with what Gretzky did in 1988, THEN you need to break those seasons down.
We're not!
We're comparing '91 with '91 + '92 with '92 + '93 with '93 ect ect You can't get more common ground or be any more accurate there. It's already 100% accurate!
They faced the same systems, the same goalies, the same opposition, the same fluctuations in league scoring, the same rules and same level of competition. Two different players at two different times of their careers playing at the exact same time under the exact same conditions.
All you're doing by bringing adjusted stats to the mix is distorting the information.
Trying to fix what doesn't need to be fixed.

I mean seriously, it's just plain stupid.

In your example there, if the question is simply who scored more goals in those 3 years? The answer is they both scored the same but that Bob was a little better goal scorer for 2 of those 3 seasons.
That's it! Whether it was harder to score from year to year doesn't matter one little bit because BOTH players had to deal with it equally.

No man, it's very different.
The only reason you use AS's is to bring 2 different seasons to a common place so they can be compared as equally and accurately as possible.
If you were comparing what Jagr did in 1998 with what Gretzky did in 1988, THEN you need to break those seasons down.
We're not!
We're comparing '91 with '91 + '92 with '92 + '93 with '93 ect ect You can't get more common ground or be any more accurate there. It's already 100% accurate!
They faced the same systems, the same goalies, the same opposition, the same fluctuations in league scoring, the same rules and same level of competition. Two different players at two different times of their careers playing at the exact same time under the exact same conditions.
All you're doing by bringing adjusted stats to the mix is distorting the information.
Trying to fix what doesn't need to be fixed.

I mean seriously, it's just plain stupid.

In your example there, if the question is simply who scored more goals in those 3 years? The answer is they both scored the same but that Bob was a little better goal scorer for 2 of those 3 seasons.
That's it! Whether it was harder to score from year to year doesn't matter one little bit because BOTH players had to deal with it equally.

Have to agree there. My position is that adjusted stats are needed when comparing across eras. Using it to compare players within an era, or worse, in the same season seems pointless. I'm at a loss as to why AS would be used to compare two players from the same season.

Have to agree there. My position is that adjusted stats are needed when comparing across eras. Using it to compare players within an era, or worse, in the same season seems pointless. I'm at a loss as to why AS would be used to compare two players from the same season.

Because some people are so enthralled (maybe enslaved is a better word) by the numbers that they can't see the Forrest for the trees.
Classic case of making something extremely more complicated than it needs to be.

As far as proving that AS's pulls everyone to the average, that's easy in principal, hard in the data you need.

Overpass did a measurement of scoring by tier in the 80's.
You would need his info and list of players broken down by tier from a year in the 80's.
Keep the tier groupings the same but run all players through Adjusted Stats. Then recalculate what % each tier contributed to league scoring.
See what happens.
If the %'s change, if the top 2 tiers drop in % while the bottom 2 tiers increase in %, you have your answer.

You can't get more common ground or be any more accurate there. It's already 100% accurate!

Of course, since adjusted scoring applies a flat multiplier to each player's stats in the same season, then they're also 100% accurate in that sense. It's an unnecessary step, but it doesn't make it any less accurate. A player 10% ahead of another player in raw stats will remain 10% ahead in adjusted stats, barring blips from rounding etc.

Quote:

Originally Posted by Rhiessan71

As far as proving that AS's pulls everyone to the average, that's easy in principal, hard in the data you need.

Overpass did a measurement of scoring by tier in the 80's.
You would need his info and list of players broken down by tier from a year in the 80's.
Keep the tier groupings the same but run all players through Adjusted Stats. Then recalculate what % each tier contributed to league scoring.
See what happens.
If the %'s change, if the top 2 tiers drop in % while the bottom 2 tiers increase in %, you have your answer.

It won't happen, because adjusted scoring only applies a coefficient (essentially the same coefficient) to every player in the same season, at least in modern seasons. So other than small blips caused by rounding etc, the % by tier will be the same, mathematically speaking.

In a league with 1000 goals, say you have the following:

Strictly speaking, this isn't entirely true, because players with zero goals will always remain at zero goals. So in seasons with relatively low goals per game, the bottom tier % will decrease a little, while in seasons with relatively high goals per game, the bottom tier % will increase a little. You don't need to run data for this one, it's simply based on an understanding of what adjusted scoring does, mathematically.

Of course, since adjusted scoring applies a flat multiplier to each player's stats in the same season, then they're also 100% accurate in that sense. It's an unnecessary step, but it doesn't make it any less accurate. A player 10% ahead of another player in raw stats will remain 10% ahead in adjusted stats, barring blips from rounding etc.

Oh, is that so???
Hmmmm...then how come in raw stats from 90/91-98/99 we get the following results...
Gretzky 878 points
Jagr 862 points

But with Adjusted stats from the website we get...
(I had to redo the '95 season for each to the actual number of games they played and not the pro-rated full seasons it was listing)
Gretzky 843 points
Jagr 856 points

What were you saying again? 10% should stay at 10%
Funny, cause it looks like it went 2% Gretzky to 2% Jagr
You should have just stopped after saying "It's an unnecessary step".

Quote:

It won't happen, because adjusted scoring only applies a coefficient (essentially the same coefficient) to every player in the same season, at least in modern seasons. So other than small blips caused by rounding etc, the % by tier will be the same, mathematically speaking.

In a league with 1000 goals, say you have the following:

Strictly speaking, this isn't entirely true, because players with zero goals will always remain at zero goals. So in seasons with relatively low goals per game, the bottom tier % will decrease a little, while in seasons with relatively high goals per game, the bottom tier % will increase a little. You don't need to run data for this one, it's simply based on an understanding of what adjusted scoring does, mathematically.

Oh, is that so???
Hmmmm...then how come in raw stats from 90/91-98/99 we get the following results...
Gretzky 878 points
Jagr 862 points

But with Adjusted stats from the website we get...
(I had to redo the '95 season for each to the actual number of games they played and not the pro-rated full seasons it was listing)
Gretzky 843 points
Jagr 856 points

What were you saying again? 10% should stay at 10%
Funny, cause it looks like it went 2% Gretzky to 2% Jagr
You should have just stopped after saying "It's an unnecessary step".

Did you intentionally miss the words "in the same season"?

Since you and I were talking about the same season in this case, it is so. Directly contemporaneous player-seasons are adjusted by the same amount. I made sure to specify that in my post. Did you not read it?

Quote:

Originally Posted by Rhiessan71

Try it and see what happens

As I said, what happens is entirely predictable, if you understand the math (which is really quite simple). No normalization will occur. Everyone's shifted up or down by essentially the same percentage, except for the players at zero, who will always remain at zero.

Since both the player's stats and the total stats of all players are being adjusted by the same percentage, each player's stats will remain at the same percentage of the total. That's simple math, and only rounding and the zero cases will make an apparent difference.

If you try it and find otherwise, I'd be interested to see the results.

Since you and I were talking about the same season in this case, it is so. Directly contemporaneous player-seasons are adjusted by the same amount. I made sure to specify that in my post. Did you not read it?

As I said, what happens is entirely predictable, if you understand the math (which is really quite simple). No normalization will occur. Everyone's shifted up or down by essentially the same percentage, except for the players at zero, who will always remain at zero.

Since both the player's stats and the total stats of all players are being adjusted by the same percentage, each player's stats will remain at the same percentage of the total. That's simple math, and only rounding and the zero cases will make an apparent difference.

If you try it and find otherwise, I'd be interested to see the results.

Take a step back and listen to yourselves. If that were indeed true then it shouldn't make a difference if I use 1 year or 5 years or 9 years as long as they are the same years for each.
That is clearly not the case.
There is 0.4-1.3% discrepancy in every year which adds up to account for the roughly 4% difference I cited earlier.

What is the point of introducing that discrepancy in the first place?
We already have it EXACTLY as it happened but no, that's not good enough? You want to run it through a system that reduces the 100% accuracy it already had and use those numbers instead?

Yeah, lets use the system that is only about 99% accurate in the short term and only 96% accurate in the longer term as opposed to the original that is 100% accurate from start to finish, no matter the term...sounds like a good idea to me

Seriously...time to give yer heads a shake.

Last edited by Rhiessan71: 11-13-2012 at 06:22 PM.

Take a step back and listen to yourselves. If that were indeed true then it shouldn't make a difference if I use 1 year or 5 years or 9 years as long as they are the same years for each.
That is clearly not the case.
There is 0.4-1.3% discrepancy in every year which adds up to account for the roughly 4% difference I cited earlier.

It's true, regardless of the number of times you rebut people with large fonts and emoticons.

What you're failing to consider (or rather, what you're mis-considering) are mix issues.

I had $20 in 1975, and I've got $20 now. That's the same amount of money, and that fact is 100% accurate!

Why would you want to introduce the concept of inflation, when it's a fact that I have the same amount of money now as I did in 1975?

Good analogy actually...if we were comparing Gretzky's $20 in 1975 to Jagr's $20 today.
Too bad we're talking about Gretzky's $20 from '91-'99 vs Jagr's $20 from '91-99 eh?

Last edited by Rhiessan71: 11-13-2012 at 06:40 PM.

Good analogy actually...if we were comparing Gretzky's $20 in 1975 to Jagr's $20 today.
Too bad we're talking about Gretzky's $20 from '91-'99 vs Jagr's $20 from '91-99 eh?

You're evidently still missing it. I really can't make this much simpler; however, you're derailing the thread, so I'll try one more example. Hopefully you'll be able to find a snappy LOLCat for your rebuttal.

Suppose that Millionaire A has $10 million in 1975, and has $500 today.

Millionaire B has $500 in 1975, and $10 million today.

Are you suggesting that these are equivalent? And that Millionaire A and Millionaire B has/had equal purchasing power?

But they're the same two years, right? Surely they could have bought the same amount of goods in total, right?

It's mathematically clear that year to year, AS's is only about 99% as accurate as the original and only 96% as accurate over the 9 years compiled.

Again I ask, why introduce these inaccuracies when you don't have to and you absolutely don't have to in this case!

Where did you get 99% and 96%? Making up numbers doesn't help.

Also, please define "accurate" in this case. If you're going to define how "accurate" something is, then doesn't it also make sense to define what you're trying to measure?

(I'll give you a head start. Non-adjusted goal totals measure how many times the puck went into the opposing net in official National Hockey League games. No one's disputing that - so if you think that we are, then I'd suggest going back to the start of the thread and reading from there. )

Good analogy actually...if we were comparing Gretzky's $20 in 1975 to Jagr's $20 today.
Too bad we're talking about Gretzky's $20 from '91-'99 vs Jagr's $20 from '91-99 eh?

It's more like Gretzky "earning" $20 when there was goal inflation, while Jagr earned $15 during that period. Then in a period of goal deflation, Jagr earned $20 and Gretzky earned $15.25.

So Gretzky earned a quarter more, but Jagr's extra five bucks would have bought more during that period than Gretzkys extra five and a quarter would have in the previous period.

If you asked them each to buy loaves of bread or gallons of gas with the money they earned each year, Jagr would have ended up with slightly more. Yet, Gretkzy actually made slightly more in "nominal dollar" terms.

Quote:

Originally Posted by Taco MacArthur

You're evidently still missing it. I really can't make this much simpler; however, you're derailing the thread, so I'll try one more example. Hopefully you'll be able to find a snappy LOLCat for your rebuttal.

Suppose that Millionaire A has $10 million in 1975, and has $500 today.

Millionaire B has $500 in 1975, and $10 million today.

Are you suggesting that these are equivalent? And that Millionaire A and Millionaire B has/had equal purchasing power?

Hmmmm...then how come in raw stats from 90/91-98/99 we get the following results...
Gretzky 878 points
Jagr 862 points

But with Adjusted stats from the website we get...
(I had to redo the '95 season for each to the actual number of games they played and not the pro-rated full seasons it was listing)
Gretzky 843 points
Jagr 856 points

I'm not going to bother looking into the math, but I'd imagine that a large part of the discrepancy is do to the fact that the lockout shortended 1994-95 (when Jagr won the Art Ross outscoring Gretzky 70-48) is adjusted to 82 games by the adjusted stats.

Take a step back and listen to yourselves. If that were indeed true then it shouldn't make a difference if I use 1 year or 5 years or 9 years as long as they are the same years for each.

No, that's not accurate. If you're talking about an amalgam of different seasons then the math changes. If you assume that a player is ahead by 10% over 9 particular seasons in raw stats should necessarily be 10% ahead in adjusted stats, that means you assume that the scoring in each particular season is the exact same value, which is in fact what adjusted scoring is intended to account for.

A player could build big "leads" by having his best years in high-scoring times, while the other player has his best years in low-scoring times. If they have an equal numbers of best years versus each other, of the same average betterness, then the first player will remain ahead in raw total because it's easier to have big seasons in a high scoring environment. Adjusted stats attempt to account for this.

To break this down to a very simple example:

Player A scores 60 goals in a 8.00 GPG environment. Player B scores 50 goals that same season. Player A is 20% better.

The next season, there's a shift in the scoring dynamics and the league now features 4.00 GPG. Player B scores 30 goals, and player A scores 25. Player B is 20% better.

By raw totals, player A has 85 total goals, and player B has 80. Player A seems to be 6% better, despite the fact that each player had one season of being 20% better in direct competition, and the players in total scored the same percentage of league goals. If each player had one season of being the same amount ahead of the other, surely in total they should be considered equal.

Adjusting to 6.00 GPG would give 45 (A) and 37.5 (B) in the first season, and 37.5 (A) and 45 (B) in the second. Totals 82.5 each, which in this hypothetical case seems the more fair result.

Quote:

Originally Posted by Rhiessan71

Seriously...time to give yer heads a shake.

And this sort of crap doesn't help your case. If you have points make them.

Good analogy actually...if we were comparing Gretzky's $20 in 1975 to Jagr's $20 today.
Too bad we're talking about Gretzky's $20 from '91-'99 vs Jagr's $20 from '91-99 eh?

$20 in 1991 is not the same as $20 in 1999, which is the point you're missing. According to the bank of Canada, a 1991 Canadian dollar is $1.12 in 1999 money.

Even if two players played against each other in the seasons in question, that doesn't mean that their totals over the span of the seasons can be directly compared, as I illustrated in my last post.

If Gretzky made his $20 in 1991 and Jagr made his in 1999 (zeroes for each in all other years), then they seem to have made the same amount. But Jagr's 1999 $20 is equivalent to $17.86 in 1991 dollars. $20 in 1999 buys less than it did in 1991.

Last edited by Iain Fyffe: 11-13-2012 at 07:21 PM.
Reason: Had calc backwards

I'm not going to bother looking into the math, but I'd imagine that a large part of the discrepancy is do to the fact that the lockout shortended 1994-95 (when Jagr won the Art Ross outscoring Gretzky 70-48) is adjusted to 82 games by the adjusted stats.

That's a very important difference. However, he's disputing the entire principle of using adjusted stats to compare players over the same range of seasons. So if '91-94 were all 48 game seasons, that would reduce Gretzky's actual points from '91-99 to less than Jagr's actual points. Therefore, if that had been the case, we can assume Rhiessan would say that Jagr was the better point producer over that time, even though the actual point production per scheduled game of each player in each season would not have been changed at all.

You're evidently still missing it. I really can't make this much simpler; however, you're derailing the thread, so I'll try one more example. Hopefully you'll be able to find a snappy LOLCat for your rebuttal.

Suppose that Millionaire A has $10 million in 1975, and has $500 today.

Millionaire B has $500 in 1975, and $10 million today.

Are you suggesting that these are equivalent? And that Millionaire A and Millionaire B has/had equal purchasing power?

But they're the same two years, right? Surely they could have bought the same amount of goods in total, right?

C'mon, that was at least a little funny

And it's not about what they have, it's about what they earned and that they each had exactly the same earning opportunities year to year.
The way it actually happened when both players were facing the exact same circumstances, opposition and factors, was like this...
163 vs 57
121 vs 69
65 vs 94
130 vs 99
48 vs 70
102 vs 149
97 vs 95
90 vs 102
62 vs 127

What you want to do is bring Adjusted stats in so you can do this...
146 vs 145
119 vs 144
108 vs 117
103 vs 99
101 vs 90
97 vs 76
70 vs 73
52 vs 61
47 vs 51

Not funny in the slightest - magic tricks and distractions don't work well in this forum. Come with facts, or don't come at all.

Why are you making up columns of numbers and then telling us what we "want to do with them"? Are you so frustrated with arguing what we're saying that you're going to resort to making up our half of the conversation?

Since you once again ignored it: please define "accurate" in this case. If you're going to define how "accurate" something is, then doesn't it also make sense to define what you're trying to measure?

(I'll give you a head start. Non-adjusted goal totals measure how many times the puck went into the opposing net in official National Hockey League games. No one's disputing that - so if you think that we are, then I'd suggest going back to the start of the thread and reading from there. )