Improving Adjusted Scoring and Comparing Scoring of Top Tier Players Across Eras

[seventieslord]

Ice time data is not available until more recently in NHL history, so this did not seem a real option.

estimated icetime is available going back to 1967. the results pass the smell test, and when the formula is used to generate results for seasons in which the true ice times are known, there is a correlation of something like 96% between the actual and calculated times.

 

[overpass]

I'm certain improvements could be made in different parts of the methodology, such as the means of selecting which players and which of their seasons to include. Realize also that any assumptions are going to influence the results. If you use a standard such as "any player who finished in the top X in at least Y seasons", then you'll probably end up with more weaker players from eras where the competition was less intense, while excluding some stronger players who didn't fit the criteria due to competition. Basically, it's a lot more difficult than it sounds to come up with strictly objective criteria free of bias.

Thanks for the explanation. I realize it's very difficult to come up with objective criteria.

OK, I forgot you were using the median third for each season. It's a good system for the short run year-to-year changes, I'm just trying to wrap my head around the effect of the methodology on the long-term trend. Not sure what effect taking the median would have...I guess I'll have to think about it some more.

 

[Czech Your Math]

I think Esposito's career may help shed some light on the uses and limits of analyzing and adjusting data, and how there is still room for different perspectives of evaluation.

Looking at the actual (raw) data, Espo's best PPG in Chicago was .88, while an average of his best 3 PPG's in Boston is 1.85. So one might conclude that some combination of Espo improving and being at his peak, a larger role in his new team's offense, and playing with a powerhouse Bruin team including Bobby Orr increased his PPG by about 110%. Since it's difficult to separate these factors, we'll combine them into what we'll call the "Bruin factors"

Looking at adjusted data from HR.com, Espo's best adjusted PPG in Chicago was about .94, while an average of his best 3 PPG's in Boston is about 1.75 (my simple adjustment using gpg & assists per goal would yield 1.80). So the adjusted data would suggest that the "Bruin factors" accounted for 85-90% of Espo's increased production, while another 20-25% was an illusion due to increased scoring league-wide.

The doubly adjusted data I presented would suggest that the "Bruin factors" accounted for about 75% of his increased PPG, while another 35% was due to increased scoring league-wide, as well as another factor that isn't fully reflected in league scoring data. I would guess this extra 10-15% has to do with the lack of parity between the O6 and expansion teams, as well as depletion of talent to the WHA during Espo's prime.

Now I'm not saying any of those numbers is exact or 100% accurate. However, I believe the adjusted data is a lot more accurate than the raw data, and that the doubly adjusted data is very likely quite a bit more accurate than the simple adjusted data. That still leaves a lot of room for interpretation and discussion, such as my guess as to how the extra 10-15% arose, as well as how much of the "Bruins factor" could be attributed to his new team and his increased role there and how much should be attributed to Espo himself.

 

[Czech Your Math]

estimated icetime is available going back to 1967. the results pass the smell test, and when the formula is used to generate results for seasons in which the true ice times are known, there is a correlation of something like 96% between the actual and calculated times.

I was unaware of that, thanks. What is the source of such data?

That would certainly help with defining objective criteria for which of each player's seasons to include and exclude.

IDK what the best way to define objective criteria for which players to include. If you use total points or career PPG, it's biased towards players in high-scoring eras. If you use total adjusted points or adjusted PPG, it's biased towards players who played during eras when adjusted points were easier to attain, which is basically the effect we're measuring. If you use X seasons in the top Y, it's biased towards eras when there was less depth of top competition. If you use total games, you end up with many less elite players whose roles tend to change more, and with players who aren't primarily scorers (so whose data will vary much more due to random factors).

 

[Czech Your Math]

Thanks for the explanation. I realize it's very difficult to come up with objective criteria.

OK, I forgot you were using the median third for each season. It's a good system for the short run year-to-year changes, I'm just trying to wrap my head around the effect of the methodology on the long-term trend. Not sure what effect taking the median would have...I guess I'll have to think about it some more.

I would guess you know that as well as anyone here.

I believe that in this case, using the median third or half possibly sacrifices a small bit of potential accuracy (OTOH is it possible there would be less or the same accuracy?) for a very large reduction in error of uncertainty. That's just my intuition, I'm not an advanced statistician.

 

[seventieslord]

I was unaware of that, thanks. What is the source of such data?

I forget who put it together but Iain Fyffe knows them. I got the file from the yahoogroup HAG_List. (hockey analysis group)

I can send it to you if you message me an email address.

 

[Czech Your Math]

But we still need more context to truly capture this. I feel we are in a Ptolemeic age just using numbers and a flawed belief (that past seasons must be adjusted downward). What would these calculations look like if the belief was that the 90's were a golden age and everything revolved around them? Of course this would be unacceptable to most fans of the day to see Ovie and Crosby adjusted downwards.

If you think I'm a fan of Ovie and Crosby compared to the stars of the '90s... well, then we must not frequent the same threads. However, their peak point production is probably on par with anyone besides Gretzky, Lemieux, Jagr and Howe.

The methodology is transparent, as flawed as it may or may not be, so that anyone can replicate or improve on the methodology (and hopefully the results as well). I've also suggested an alternative way that might be even more accurate and which could not only capture more variable, but in the process measure more effects (how players' productivity changes with age e.g.).

Until then this type of data manipulation just serves the fan base that thinks the heroes of today are better than the heroes of yore. Giroux is better than Gretzky type arguments. This stuff needs an asterisk and a safe place to keep it until the modelling reflects that the Earth goes around the sun. Talent not numbers.

I've yet to see any serious adjusted data that even comes close to suggesting that Gretzky or Lemieux weren't the best peak/prime point producers.

The players who don't fare as well (in comparison to simple adjusted data) are those from WWII until the early 60's... and those from the late 60's until the late 70's. The reasons for that are clear to me: There were many less hockey players to choose from back in the 40's and 50's due to the war and less population, no overseas talent. The talent was more diluted than in the mid 60's. After expansion, there was an uneven distribution of the diluted talent, and continued expansion and defection of players to the WHA did not help matters.

This study involves the vast majority of the top 25-70 forwards at any one time and the best producing defensemen. The results do not necessarily directly suggest that the best 5 or average player was worse at a certain time, although that also may be the case.

We do not know which era was the most talented, Which era should be the center that all other numbers revolve around. Today it's just a moving target. The belief that talent is more prevalent per player than it was in any other era except next years. Eventually Gretzky reduces to a 30 goal season.

The goal of the study was to learn and quantify which seasons and eras it was easier or more difficult to score points. It doesn't surmise that the best hockey was played at a certain time, only when the best times to score (actual or adjusted) points were.

Maybe we just need a talent quotient. A numerical estimation based simply on how much better a player was than his peers. A player or profile that is 100. Maybe we need a set of numbers according to different talents.

That is like awards voting, it is simply quantifying opinion and while useful in some instances, is like trying to prove the best religion is that which has the most or most fervent followers.

Stats are just a reflection of the player's talent in a context not analyzed with similar methods. Many of these adjustments just don't pass the eyeball test.

The context is the scoring environment. It's the context that is effectively being studied, not the talents of those in the context.

The problem with the eyeball test is that we see or don't see what we expect to see or not see. One's preconception has been influenced by one's own preferences, those of one's peers, and those of alleged authorities on the matter.

 

[Czech Your Math]

For someone with the database, (software?), and know-how, this would be an interesting project:

Use regression to study the effect on scoring by season as well as by other factors such as age. I believe the criteria for selecting which players to include (as well as possibly which seasons for each player) would be less important in this format, so that would save some time and effort.

Dependent variable = points

Independent variables:

season
age- would use as discrete not continuous variable (if player is 25 and 3 months, e.g. could use .75 for "age 25" and .25 for "age 26")
player
injury?
????

all of these listed so far would be discrete variables (except for possibly age, Yes = 1 No = 0)

depending on how your database is formatted, if you limited it to player/age/season, you may be able to use if/then type formulas to automatically fill in the independent variables, although age would probably be a bit trickier (unless you had age or DOB already listed in your database).

The results should be not only a very unbiased metric of the past, but a possible predictive model of future production (although season would have to be fixed, e.g. assumed to be same environment as present). I tried a small-scale trial of this method in Excel many moons ago, but could not get the coefficients to generate consistently.

 

[Dalton]

If you think I'm a fan of Ovie and Crosby compared to the stars of the '90s... well, then we must not frequent the same threads. However, their peak point production is probably on par with anyone besides Gretzky, Lemieux, Jagr and Howe.

The methodology is transparent, as flawed as it may or may not be, so that anyone can replicate or improve on the methodology (and hopefully the results as well). I've also suggested an alternative way that might be even more accurate and which could not only capture more variable, but in the process measure more effects (how players' productivity changes with age e.g.).



I've yet to see any serious adjusted data that even comes close to suggesting that Gretzky or Lemieux weren't the best peak/prime point producers.

The players who don't fare as well (in comparison to simple adjusted data) are those from WWII until the early 60's... and those from the late 60's until the late 70's. The reasons for that are clear to me: There were many less hockey players to choose from back in the 40's and 50's due to the war and less population, no overseas talent. The talent was more diluted than in the mid 60's. After expansion, there was an uneven distribution of the diluted talent, and continued expansion and defection of players to the WHA did not help matters.

This study involves the vast majority of the top 25-70 forwards at any one time and the best producing defensemen. The results do not necessarily directly suggest that the best 5 or average player was worse at a certain time, although that also may be the case.



The goal of the study was to learn and quantify which seasons and eras it was easier or more difficult to score points. It doesn't surmise that the best hockey was played at a certain time, only when the best times to score (actual or adjusted) points were.



That is like awards voting, it is simply quantifying opinion and while useful in some instances, is like trying to prove the best religion is that which has the most or most fervent followers.



The context is the scoring environment. It's the context that is effectively being studied, not the talents of those in the context.

The problem with the eyeball test is that we see or don't see what we expect to see or not see. One's preconception has been influenced by one's own preferences, those of one's peers, and those of alleged authorities on the matter.

First let me make clear that anything in my post that suggests you personally are biased and on some mission is simply poor writing on my part. I have no reason whatsoever to believe that you are trying to support a personal agenda. My apologies if you perceived that.

I did say that others could do this better than me.

I never really studied stats. I should have perhaps because I believe it to be more lucrative than my interest and studies in mathematical modelling in Cosmology and it's history with respect to Cosmology and physical science to a lessor degree.

I also had some trouble with arbitrary assumptions but I didn't mention it since even math itself has arbitrary assumptions and I didn't feel up to that debate. Your assumptions may be reasonable in the context of what you are doing. Perhaps I'm wrong but it appeared that these assumptions were central to your presentation of your calculations as an improvement.

I simply feel that analysis of points, goals and assists however sophisticated is not enough to reach a conclusion that points achieved in a certain time are more or less than those achieved in a different time.

Thank you for the rundown on the historical basis for seeing some eras as easier to score than others. My memory is a bit rusty. It's been awhile since I've read good hockey history books. This kind of info initially attracted me to this thread and others as I attempt to add to this debate. But this a priori information carries too much weight IMHO.

Lafleur's Habs weren't known to run up the score. What if they did? How many more points would Lafleur have? Would their even be a Lafleur - Jagr debate if Bowman let the guy run wild and run up a score against opponents when the game was pretty much decided from the outset in so many cases.

Goals and points cannot be accurately adjusted simply because of a priori beliefs and linear regression analysis. No more than the motions of the planets without considering gravity and the sun at the center of the motions and eventually spacetime with discrete arithmetic.

Hence this stuff needs an asterisk to identify that it's a non-predictive modelling based on points alone with no other context.

I'm simply saying that we need an equivalent to the Drake equation. An estimation of what goes into a season. The coach or team playing style, team mates, competition in unbalanced schedules, competition for advancement or divisional makeup or playoff qualification criteria or number of games against same team, equipment and training and ice quality, rules and enforcement, health, age and probably more or less. Talent?

A defensive style team is inversely proportional to an offensive minded player. An offensive style is directly proportional. Having talented team mates is directly proportional, low talent is inversely proportional. Bowman as your coach? This stuff is pretty intertwined and too much complexity renders the outcome uncertain. Put in 1.

Until then comparing Espo with Orr to Stamkos with St Louis really has no definitive meaning. If it fails the eyeball test of those who actually saw both careers (if that's possible in my example) then who can argue the point? An excel spreadsheet with math the average fan couldn't possibly comprehend?

Tossing a metal sphere onto a deformed rubber sheet is an elegant way to reach children. Linear regression analysis? Where's the razor?

Again I wish to emphasize that the analysis is important and should go on. We're just missing the other parts of the equation.

Sometimes I think we're trying to quantify talent. A noble effort indeed. If that's the case then perhaps we should look at how IQ is quantified over Western history. But then hockey is a team sport. Does Espo get hockey dumb in Chicago because of the wind? Clearly more is needed. An asterisk would be a start. It might get some talented fans thinking in more than 1 dimension.

My ramblings. Feel free to ignore. Maybe that should be my sig? LOL

 

[plusandminus]

estimated icetime is available going back to 1967. the results pass the smell test, and when the formula is used to generate results for seasons in which the true ice times are known, there is a correlation of something like 96% between the actual and calculated times.

Yes, there is a high correlation according to Pearson's correlation coefficient.
http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient
But, that does not necessarily be taken as proof that the estimations are "96 %" correct, because when actually (for example) taking a table with estimated icetimes in one column, and factual ones in another, one can see that they are significantly less accurate than that. The correlation coefficient (for example +.96) needs to be viewed in context. And what I did, was to actually take the time to study how wrong (or right) the estimations actually were, rather than relying on a number.
If combining several seasons, we get more and more accurate results. Two seasons combined generally gives far more reliable results than one season alone. Yet, there are certain players and circumstances that needs to be accounted for (Kovalchuk for example being a typical "on ice for many goals per minute" player).

I forget who put it together but Iain Fyffe knows them. I got the file from the yahoogroup HAG_List. (hockey analysis group)

I have studied it, talked about it here on the board, and given examples. I actually would think I have studied it more carefully than anyone else I've seen here. But, as I think you're aware of, there is no interest for my studies, which I find strange and frustrating as finding out as much as possible about these things should be of interest for those here paying attention to adjusted icetimes.

Even if this is no pity party, I do feel frustrated about the lack of interest for my different research on some topics - topics that are being talked about all the time here (like adjusted stats, how much players help each other regarding point production, how much better/worse a player tends to make his team perform result wise, strength of different eras, etc.). You have a guy here on the board (I'm refering to myself) who actually spend lots of time in collecting and organizing data, and who spend almost as much time doing research on it, but who is constantly met with negative comments, or quietness or getting comments like "this is the history board, not the stats board" (despite most threads here contains talk about points, +/-, adjusted stats, etc.).

 

[BraveCanadian]

Yes, there is a high correlation according to Pearson's correlation coefficient.
http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient
But, that does not necessarily be taken as proof that the estimations are "96 %" correct, because when actually (for example) taking a table with estimated icetimes in one column, and factual ones in another, one can see that they are significantly less accurate than that. The correlation coefficient (for example +.96) needs to be viewed in context. And what I did, was to actually take the time to study how wrong (or right) the estimations actually were, rather than relying on a number.
If combining several seasons, we get more and more accurate results. Two seasons combined generally gives far more reliable results than one season alone. Yet, there are certain players and circumstances that needs to be accounted for (Kovalchuk for example being a typical "on ice for many goals per minute" player).

I don't recall seeing this but I'd be interested in what you found.

I have long suspected that the ice time estimates which were fudged to match up with player usage from the late 90s would get less accurate the farther we go back from the calibration seasons.

Particularly for seasons before the mid-80s when ice time management changed dramatically.

 

[plusandminus]

For someone with the database, (software?), and know-how, this would be an interesting project:

Use regression to study the effect on scoring by season as well as by other factors such as age. I believe the criteria for selecting which players to include (as well as possibly which seasons for each player) would be less important in this format, so that would save some time and effort.

Dependent variable = points

Independent variables:

season
age- would use as discrete not continuous variable (if player is 25 and 3 months, e.g. could use .75 for "age 25" and .25 for "age 26")
player
injury?
????

all of these listed so far would be discrete variables (except for possibly age, Yes = 1 No = 0)

depending on how your database is formatted, if you limited it to player/age/season, you may be able to use if/then type formulas to automatically fill in the independent variables, although age would probably be a bit trickier (unless you had age or DOB already listed in your database).

The results should be not only a very unbiased metric of the past, but a possible predictive model of future production (although season would have to be fixed, e.g. assumed to be same environment as present). I tried a small-scale trial of this method in Excel many moons ago, but could not get the coefficients to generate consistently.

I have lots of data organized in useful manners, and the know how to make advanced studies based on it.

Like you, I have looked at (my English is not good, which frustrates me very much) say the 1967-68 and the 1968-69 season to see how scoring changed. I actually made code that made it possible to compare any two seasons.

I also have the ability to do studies based on age, but only partly on injuries.
Overall, there are so many things I could do, and have done, but to my big frustration there simply seems to be no interest here.
I do things that the other "stat guys" can't easily do (due to lack of time or tools). But instead of feeling curiosity, and thinking positively about that, and looking at it like an opportunity, it is simply being disregarded as unimportant.
Maybe people prefer studies that they can perform themselves.

I don't know if you remember, but probably more than a half year ago I presented a fairly easy way to do schedule adjusted stats. It was a great way to adjust, and took care of so many things. I just get upset now that I was about to explain it again, because no one probably anyway would be interested whatsoever, and instead just more or less automatically just assume it's not useful.

I have studied scoring within teams also, for every team, during every season from whenever it was (1952 onwards?). Scoring distribution within a team matters.
Strength of eras matters too.

(Paragraph about adjusted stats deleted.)
Sorry, but it is probably no point trying to continue to write right now, as I'm not in a good mood. I also really detest that my English once again is not good enough to help me communicate the way I'd like to.

 

[Czech Your Math]

First let me make clear that anything in my post that suggests you personally are biased and on some mission is simply poor writing on my part. I have no reason whatsoever to believe that you are trying to support a personal agenda. My apologies if you perceived that.

I did say that others could do this better than me.

I never really studied stats. I should have perhaps because I believe it to be more lucrative than my interest and studies in mathematical modelling in Cosmology and it's history with respect to Cosmology and physical science to a lessor degree.

I also had some trouble with arbitrary assumptions but I didn't mention it since even math itself has arbitrary assumptions and I didn't feel up to that debate. Your assumptions may be reasonable in the context of what you are doing. Perhaps I'm wrong but it appeared that these assumptions were central to your presentation of your calculations as an improvement.

I simply feel that analysis of points, goals and assists however sophisticated is not enough to reach a conclusion that points achieved in a certain time are more or less than those achieved in a different time.

Thank you for the rundown on the historical basis for seeing some eras as easier to score than others. My memory is a bit rusty. It's been awhile since I've read good hockey history books. This kind of info initially attracted me to this thread and others as I attempt to add to this debate. But this a priori information carries too much weight IMHO.

Lafleur's Habs weren't known to run up the score. What if they did? How many more points would Lafleur have? Would their even be a Lafleur - Jagr debate if Bowman let the guy run wild and run up a score against opponents when the game was pretty much decided from the outset in so many cases.

Goals and points cannot be accurately adjusted simply because of a priori beliefs and linear regression analysis. No more than the motions of the planets without considering gravity and the sun at the center of the motions and eventually spacetime with discrete arithmetic.

Hence this stuff needs an asterisk to identify that it's a non-predictive modelling based on points alone with no other context.

I'm simply saying that we need an equivalent to the Drake equation. An estimation of what goes into a season. The coach or team playing style, team mates, competition in unbalanced schedules, competition for advancement or divisional makeup or playoff qualification criteria or number of games against same team, equipment and training and ice quality, rules and enforcement, health, age and probably more or less. Talent?

A defensive style team is inversely proportional to an offensive minded player. An offensive style is directly proportional. Having talented team mates is directly proportional, low talent is inversely proportional. Bowman as your coach? This stuff is pretty intertwined and too much complexity renders the outcome uncertain. Put in 1.

Until then comparing Espo with Orr to Stamkos with St Louis really has no definitive meaning. If it fails the eyeball test of those who actually saw both careers (if that's possible in my example) then who can argue the point? An excel spreadsheet with math the average fan couldn't possibly comprehend?

As you say, there's assumptions inherent in any such work. If I didn't list all of these assumptions, it's mainly because those who understand this study will understand most or all of the implicit assumptions contained within.

It seems that you are saying that there are so many elements of the game and the context which cannot be properly or fairly quantified. I do not disagree with you, but you must realize that the goal of this study was not to quantify what's essentially not quantifiable, but rather to examine what is already quantified and improve on it in some fashion.

I've tried to make it clear that whether you subscribed to "stats are all junk", "raw stats", "adjusted stats", or "doubly adjusted" stats, there is still room for interpretation and discussion, including the consideration of context. The data merely gives us a somewhat objective starting point. The less accurate the starting point, the more likely the eventual conclusion is to be inaccurate.

You ask whether there would even be a debate about a player's superiority if the context were different. It's very likely there would be, but both the data and the context would then be different.

Whether my results fail your "eyeball test" and whether most people can or wish to understand this or any other study, does not invalidate the study nor the results.

 

[Canadiens1958]

A Few Points

As you say, there's assumptions inherent in any such work. If I didn't list all of these assumptions, it's mainly because those who understand this study will understand most or all of the implicit assumptions contained within.

It seems that you are saying that there are so many elements of the game and the context which cannot be properly or fairly quantified. I do not disagree with you, but you must realize that the goal of this study was not to quantify what's essentially not quantifiable, but rather to examine what is already quantified and improve on it in some fashion.

I've tried to make it clear that whether you subscribed to "stats are all junk", "raw stats", "adjusted stats", or "doubly adjusted" stats, there is still room for interpretation and discussion, including the consideration of context. The data merely gives us a somewhat objective starting point. The less accurate the starting point, the more likely the eventual conclusion is to be inaccurate.

You ask whether there would even be a debate about a player's superiority if the context were different. It's very likely there would be, but both the data and the context would then be different.

Assumptions should be up front going in. Otherwise no one knows with 100% accuracy what is being studied.

Second bolded is the key element here. If the purpose is to explain what happened from game to game, season to season, era to era considering the various variables then I`ll at least have a look. If the purpose is to create some abstract notion of a player`s superiority or any type of superiority then you are drifting away from scientific method towards partisanship.

 

[Czech Your Math]

Assumptions should be up front going in. Otherwise no one knows with 100% accuracy what is being studied.

Second bolded is the key element here. If the purpose is to explain what happened from game to game, season to season, era to era considering the various variables then I`ll at least have a look. If the purpose is to create some abstract notion of a player`s superiority or any type of superiority then you are drifting away from scientific method towards partisanship.

I've tried to be as clear as possible about my methodology and calculations. If there's any confusion, it's due to the length of explanation and volume of data. I think it's clear what was being studied.

The purpose of the study was to examine year to year scoring changes among a fixed group of the top point producers since WWII. The issue of superiority was brought up by another poster, not by me, and was not the goal of the study.

However, that does not mean that the results can't be applied by those that believe the results are valid. For instance, I never said Steve Yzerman was superior to Phil Esposito. I demonstrated that from the results of the study, a reasonable conclusion would be that in terms of point production, Yzerman's '89 season was probably superior to 3 of Espo's 4 seasons from '71-74, given the differing scoring environments.

You are free to disagree with the results. I think whatever partisanships we have are clear: You more favor the players of the distant past based mostly on what you saw, I more favor the players of the more recent past based mostly on the data.

If you have any genuine questions about how I arrived at these results, I would be happy to attempt to answer them.

 

[Canadiens1958]

Methodology

I've done a study of a large, but fixed, group of players over several decades. I think it's worthy of presentation at this point, if only to satisfy the curiosity of a select few that have discussed or also studied this or similar topics. I know this is far from perfect, but I tried to be as fair and objective as possible in my methodology. I intend the results as a general guideline, not as anything close to gospel. Perhaps someone with a better database and ability to write code can further improve upon this, and I certainly welcome any and all attempts to do so.

GOAL: To adjust the "adjusted scoring" data, since it's been suspected for some time that certain eras are "under-adjusted" and others "over-adjusted".

METHODOLOGY: Use a large, fixed group of the higher end point producers and examine their PPG production from one year to the next. There were approximately 30-40 players in each pair of seasons from WWII until expansion, and approximately 50-75 players in each pair of seasons from expansion until the most recent lockout. The group of players never changes, hence the term "fixed group". It's not the top 50 (or X) players each season or something of that nature. It's players that I deemed to be consistently toward the top X players in terms of point production, along some of the top point producing defensemen.

Methodology. So WWII to expansion, assuming you mean the end of WWII which would be the 1945-46 season. You are looking at 30 to 40 players in an NHL where the game roster size was compact, peaking at 17 x 6 teams means TOI was split accordingly. Your sample size represents approximately 30-40% of the players. Conversely if you look at the 2003-04 season the game day roster was slightly larger with 30 teams. Yet you only look at the top 50-75 players.Your sample size represents roughly 10 -15% of the players. How will this not benefit results in favour of the modern player?

 

[Czech Your Math]

I have lots of data organized in useful manners, and the know how to make advanced studies based on it.

That's great. I don't believe my database, know-how, nor software are on par with many here, such as yourself.

If you ever wish any assistance while designing and structuring a study, please PM me.

Like you, I have looked at (my English is not good, which frustrates me very much) say the 1967-68 and the 1968-69 season to see how scoring changed. I actually made code that made it possible to compare any two seasons.

Would you like to briefly summarize your method and results here?

I am very interested in what you found out.

BTW, your English is very good, I doubt anyone has any trouble understanding you.

I also have the ability to do studies based on age, but only partly on injuries.
Overall, there are so many things I could do, and have done, but to my big frustration there simply seems to be no interest here.
I do things that the other "stat guys" can't easily do (due to lack of time or tools). But instead of feeling curiosity, and thinking positively about that, and looking at it like an opportunity, it is simply being disregarded as unimportant.
Maybe people prefer studies that they can perform themselves.

I understand your frustration. The first time I presented the preliminary data ITT, it was met with basically silence. I'd rather genuine criticism than no response at all.

Perhaps most either aren't able to fully understand your work (the math and logic side, not your English) or are not really that curious and prefer to hold onto their existing beliefs.

I didn't perform this study in the belief that it would be generally understood, nevermind accepted. I did it out of my own curiosity and hopes that, if successful, it might improve the existing knowledge of a few and possibly spur another to do a similar or complementary study of some kind to further our knowledge.

I don't know if you remember, but probably more than a half year ago I presented a fairly easy way to do schedule adjusted stats. It was a great way to adjust, and took care of so many things. I just get upset now that I was about to explain it again, because no one probably anyway would be interested whatsoever, and instead just more or less automatically just assume it's not useful.

I remember that study and believe it was a useful improvement in adjusting data. However, I think for the "common fan", it just doesn't resonate:

- the effects in most cases are relatively small, so it's easy to dismiss as unimportant (when in fact it is an improvement)

- it's not very user-friendly, in that one would presumably need a large matrix by season/team to calculate the effect, which is relatively small

- the general resistance to change and that which we don't understand (and many have very little knowledge of math/stats)

- most are results-oriented, in that if the results aren't what they're "looking for", they find it easy to dismiss or ignore them (which is why I don't find the "eyeball test" very important in most cases)

I have studied scoring within teams also, for every team, during every season from whenever it was (1952 onwards?). Scoring distribution within a team matters.
Strength of eras matters too.

How does scoring within a team matter? I mean in terms of an individual player's production. If you could briefly explain that, I would be interested in hearing it.

Strength of era certainly matters, but how to measure it? That was a primary purpose of this study, to determine which eras were stronger (tougher) and which were weaker (easier) for top tier players to score. While scoring is not the only aspect, it's a very important aspect.

A general note of encouragement: Don't give up if it genuinely intrigues you. You've demonstrated an interest and capability in this capacity. I would recommend you be selective and tend to choose studies with large effects and possibly broad implications. The smaller the effects and narrower the applications of the results, the fewer people will be interested.

I outlined a regression study that seems worthwhile. Do you think such a study makes sense and is feasible?

 

[Canadiens1958]

1961-62 Ralph Backstrom or Scoring within a Team

How does scoring within a team matter? I mean in terms of an individual player's production. If you could briefly explain that, I would be interested in hearing it.

Scoring within a team. 1961-62 Ralph Backstrom would be a prime example:

http://www.hockey-reference.com/players/b/backsra01.html

1961-62 Canadiens saw Jean Beliveau injured for 27 games and Henri Richard injured for 16 games resulting in a situation where Ralph Backstrom the third center played a significant amount of time with first and second line RWers and LWers producing a unique situation where he actually lead the team in scoring. Before and after the 1961-62 season his numbers were lower.

Parker MacDonald with the Detroit Red Wings in the early sixties playing with Howe and Delvecchio scored at a very interesting pace without and on other teams he was a borderline NHL/minor league player. This was a common phenomena on the Red Wings during the Howe /Delvecchio years after Lindsay was traded away.

The Leafs under Imlach. No defined PP so the scoring was more balanced.

Look at how scoring was distributed in Pitts burgh with/without Crosby or with/without Crosby and Malkin.

 

[Czech Your Math]

Methodology. So WWII to expansion, assuming you mean the end of WWII which would be the 1945-46 season. You are looking at 30 to 40 players in an NHL where the game roster size was compact, peaking at 17 x 6 teams means TOI was split accordingly. Your sample size represents approximately 30-40% of the players. Conversely if you look at the 2003-04 season the game day roster was slightly larger with 30 teams. Yet you only look at the top 50-75 players.Your sample size represents roughly 10 -15% of the players. How will this not benefit results in favour of the modern player?

1945-6 was the first season included in this study.

I'm not certain how the variation in the number of the players over time affected these results, but I don't see that it would necessarily benefit the modern player on balance. There are probably unintentional biases in both directions, but I don't know the net effect of these as a whole. Remember that what is being directly measured is not production (using PPG) but the % change in production from one year to the next. Any bias would be for/against players whose PPG is more likely to fluctuate in one direction. This is why Overpass brought up age as a potential source for bias.

It's difficult to decide how many and which players to include.

First, they had to be the better point producers, because:

- they are the ones most often compared, so the results of the study should have particular significance to this group

- they have higher point totals, so random errors will affect their % changes less

- they have longer careers, so provide more data per player, reducing error

- they tend to get more and more consistent ice time, again reducing error

So, ideally it seems best to include first liners, most of the second liners and top producing defensemen. The number of players for each pair of seasons is only that number for whom data was available for both seasons and not excluded due to excessive variance.

From the '47-8 pair of seasons to the '67-8 pair of seasons, it was 32-44 players and an average of ~37 players per pair of seasons. So it's the best 6-7 players on each team.

From '68-9 to 79-80 seasons, it was 50-62 players and an average of ~55 players per pair of seasons, except in '1978-79 pair there were only 40 players (probably related to WHA, as many players who played large portion of career in WHA were not included due to lack of NHL seasons).

From '80-81 to '03-4 seasons, it was 51-81 players and an average of 69 players per pair of seasons.

It would be much easier if the number of teams were constant over the period, but it wasn't. The reasons more players are included over time:

- Players tend to have longer careers in more recent years, so there are more seasons included for each player (more total player-seasons over the same number of seasons, per player included in the study).

- There are more teams, so more opportunities for players to play and receive quality time and post both higher and less erratic point totals.

It's generally better to have a larger sample, when possible, to reduce error. However, this was not really possible in the earlier portions of the period. If you keep constant the number of players' data in each season pair, you are actually reducing the number of players from the period which has longer careers, because these players have longer careers. I don't see that as beneficial to the results either. So I went with a group of players whose net number over time increased, but not as much as the number of teams increased. I don't see an easy solution to this dilemma, but would like to hear others' ideas.

Basically, over time, a lot of the second liners and defenseman are being removed, but the sample of data is growing larger, which decreases error in the result.

The important thing to remember is that the fundamental basis for the results is how individual players' PPG changes from one season to the next. The changes from season N to season N+1 (X > 1) will not directly affect any single pair of consecutive seasons. In addition, by using the middle (median) third or half of players, it removes most or all outliers arising from various potential biases. Can the results still be biased in some manner by effects we cannot account for? Yes, but the magnitude of any such bias should be substantially reduced by the methodology used.

 

[Rexor]

No seriously, I can nothing but admire the effort and knowledge behind your work. Just wish I had the intellectual capacity/tenacity to understand only a half of it.

 

[Czech Your Math]

Scoring within a team. 1961-62 Ralph Backstrom would be a prime example:

http://www.hockey-reference.com/players/b/backsra01.html

1961-62 Canadiens saw Jean Beliveau injured for 27 games and Henri Richard injured for 16 games resulting in a situation where Ralph Backstrom the third center played a significant amount of time with first and second line RWers and LWers producing a unique situation where he actually lead the team in scoring. Before and after the 1961-62 season his numbers were lower.

Parker MacDonald with the Detroit Red Wings in the early sixties playing with Howe and Delvecchio scored at a very interesting pace without and on other teams he was a borderline NHL/minor league player. This was a common phenomena on the Red Wings during the Howe /Delvecchio years after Lindsay was traded away.

The Leafs under Imlach. No defined PP so the scoring was more balanced.

Look at how scoring was distributed in Pitts burgh with/without Crosby or with/without Crosby and Malkin.

Sounds like the "linemate effect" and variation in opportunity to me.

One can quantify to some degree the effect of different linemates, if they indeed differ significantly over time. Overpass's adjusted plus-minus is a metric of overall even strength productivity and efficiency with the linemate effect removed.

Opportunity can be more closely studied when ice time data available, although I'm not much of a proponent of "per minute" data. Scoring .4 ppg with 8 minutes per game isn't the same as scoring 1.0 ppg with 20 mpg.

 

[Czech Your Math]

No seriously, I can nothing but admire the effort and knowledge behind your work. Just wish I had the intellectual capacity/tenacity to understand only a half of it.

Is that the the episode where he goes to college and gets the mascot drunk? That's classic.

Nerd... guilty as charged.

 

[plusandminus]

I don't recall seeing this but I'd be interested in what you found.

I have long suspected that the ice time estimates which were fudged to match up with player usage from the late 90s would get less accurate the farther we go back from the calibration seasons.

Particularly for seasons before the mid-80s when ice time management changed dramatically.

Thank you for showing interest.
I focused on the seasons where we have factual icetimes, and when available also looked at situational stats (ES, PP, SH) separated.
I actually found the error margins so large that I omitted using estimated icetime. I might use it later. I know estimated icetimes are used here on the board, for example a lot in the best defencemen project, but think a better name for the stat might be "share of goals (forward and against) the player was on ice for". I understand that different people think differently, and that it's up to each one to decide how to use stats and what to call it. I personally find it of importance to distinguish between what we do know and what we don't know.

Meeting eye-ball tests is important. But when I post, rather than just pointing out well-known and obvious things, I often write about things that may not be as obvious or well-known. One example was regarding New Jersey's penalty killing in 2002-03. It is very well-known that Scott Stevens is considered one of the best defensive defencemen ever. Yet, their 2nd penalty killing unit had far better "per minute" stats.
http://hfboards.mandatory.com/showthread.php?t=1116663&page=3
(posts 52 and especially 62)
Facts are that S.Stevens was on ice during 51.54 % of the penalty killing icetime. The "adjusted icetime" suggested he was on ice for 81.25 %.
Facts are that S.Niedermayer was on ice during 40.61 % of the penalty killing icetime. The "adjusted icetime" suggested he was on ice for 18.75 %.
The "adjusted stats" shows that "Wow!!! Stevens played an amazing 81 % during PK! Niedermayer played far, far less, just 19 %."
Facts says "Stevens played 51.54 % of the time, while Niedermayer played 40.61 %".
Why manipulate stats to say that a player had 4 times more icetime than another, when in reality he had just 1.3 times more icetime?
The reply I got was - when analyzed - that Stevens faced more than 3 times harder opposition than Niedermayer. (Someone is welcome to show me factual proof that supports that claim.) I think I even researched that, by looking at which opponents that was on the ice during the goals, and found that things were not as black and white as I was told here on the board. It should also be noted again that when New Jersey played on the road, they didn't have the benefit of choosing which opponents Stevens or Niedermayer played against.

The above case is admittedly definitely rather extreme, and it's about penalty killing ice time. But there are many cases where even strength adjusted icetimest turned out to be rather wrong. I ranked every defenceman within each team based on estimated versus factual icetimes, and looked at the top-5 ones to see if the estimations at least managed to tell if a defenceman was e.g. "2nd defenceman", and I think the estimations produced errors in about 50 % of the cases.
Estimations seem to have been used during newer seasons too, if players were changing team during the season, and seem to be relatively unreliable.

I currently can't find my study for all the players during say the last 13 or so seasons

I don't know about older seasons, as we don't have the factual icetimes. This may be a case where someone like Canadiens1958 or you yourself can make a better guess than myself.

When I wrote above that I omitted using estimated icetimes, I meant that I for now accept that I simply don't know the factual icetimes for older seasons and instead focus on what we do know.

Basically I just want it to be clear that estimated icetimes are estimations and not facts. They are fairly accurate, but are unreliable to use to "rank" players based on "who played most". I also find them unreliable as a parameter in larger formulas, like "best scorers per 60 minutes of icetime". I understand it's up to everyone to decide how to use estimated icetimes.

 

[plusandminus]

Would you like to briefly summarize your method and results here?

I am very interested in what you found out.

It's not so easy to explain. Basically I focus on the opponent's GA.

1. Take the GA per game for each team.
2. Go through the schedule for each team, and for each game summarize the GA per game of the opponent.
3. Compare the result (of step 2) with a standard of say 3.0 GA per game, to see how "favoured" or "unfavoured" a team was. If EDM played vs teams that surrendered on average 3.3 goals per game, they were favoured by 3.3/3.0 = 1.1.
4. Every team gets their own number. Those numbers are team and season specific. Think of a table with three columns; season, team, factor. For each season we get 30 rows, so for say 20 seasons we get 600 rows. 1.0 is average.

To be more specific... In step 2, I exclude the opponent's games vs own team. If looking at EDM vs LAK, I focus on LAK's GA per game against other teams (you may understand this intuitively, it's sort of standard procedure). I also separate home and away stats.

The table after step 4 tells us how "favoured" or "unfavoured" a certain team was during a certain season. If 1984 Edmonton has 0.75, we should multiplay their players' scoring stats by 0.75 (for example, 200 pts becomes 150 pts). If a "dead puck" era team has 1.2, their players' scoring stats should be multiplied by 1.2 (for example, 100 points would become 120 pts).

I think this is a fairly "easy" and effective method. The table one gets after step 4 is useful for other applications as well. We may for example use it to "schedule adjust" team stats as well. A team goal difference of 250-240 may in fact end up as 242-245 or so. One can use the GF and GA in pythagoran win formulas.
If we always use 3.0 GA per game as the standard, we get "era adjusted" stats automatically. If we want to instead look at single seasons without context, one may use league average for that season instead.

I have to admit it took me some while to arrive to the final results (the step 4 table), and there were some tricky steps to overcome. Being able to use tools like SQL Server helps a lot. (I wouldn't know how to do this in Excel.)
Once we have the table (after step 4), we can just use it.

I understand your frustration. The first time I presented the preliminary data ITT, it was met with basically silence. I'd rather genuine criticism than no response at all.

Yes, criticism is usually better than silence (although blunt and discouraging one-liners can be an exception). The end result is usually what I'm after, so suggestions on how to improve things are welcome.
What's ITT?

Perhaps most either aren't able to fully understand your work (the math and logic side, not your English) or are not really that curious and prefer to hold onto their existing beliefs.

I didn't perform this study in the belief that it would be generally understood, nevermind accepted. I did it out of my own curiosity and hopes that, if successful, it might improve the existing knowledge of a few and possibly spur another to do a similar or complementary study of some kind to further our knowledge.

This might (in many ways) be it.

I remember that study and believe it was a useful improvement in adjusting data. However, I think for the "common fan", it just doesn't resonate:

- the effects in most cases are relatively small, so it's easy to dismiss as unimportant (when in fact it is an improvement)

- it's not very user-friendly, in that one would presumably need a large matrix by season/team to calculate the effect, which is relatively small

- the general resistance to change and that which we don't understand (and many have very little knowledge of math/stats)

- most are results-oriented, in that if the results aren't what they're "looking for", they find it easy to dismiss or ignore them (which is why I don't find the "eyeball test" very important in most cases)

I agree.

Yet, as you acknowledge, schedule likely does matter and can sometimes alter scoring stats by say 5-8 % or so. It is common here to compare players. If a player scored 4 % more points than another. But there seem to be no attention being paid to things like schedule.
If I remember right, it was fairly common to see seasonal top-ten scoring lists being altered. In some case(s) I even think it affected the leading scorer (Art Ross winner) of the season.

How does scoring within a team matter? I mean in terms of an individual player's production. If you could briefly explain that, I would be interested in hearing it.

(This is not reserached yet. -->) For example, during seasons with a lot of powerplays, scoring within teams may look differently than seasons with little powerplays. Seasons with much powerplay may lead to power play specialist scoring points on a higher percentage of goals, than otherwise. Scoring during even strength appear to be much more balanced between players on a team.

I think I have posted table showing things like (made up):

Season|1st|2nd|3rd|...|15th
1984-85|40.2|36.3|33.0|...|12.5
1985-86|40.7|35.9|32.5|...|9.6

where 1st is the average for the leading scorer on each team. 2nd is the average for 2nd best scorer on each team. And so on...
I've also posted the above but with factual, as well as adjusted, stats.
If I remember right, some thought the schedule adjusted stats still didn't do the 1980s players total justice (based on "eye-test").

Then guys like Canadiens1958 seem able to tell us about how coaching and roster sizes has changed over the years. To take an extreme example, let's compare today's NHL with the NHL where some players played 60 minutes per game (if I remember right).

By the way, adjusted points hasn't really been on my mind during the last months.

Strength of era certainly matters, but how to measure it? That was a primary purpose of this study, to determine which eras were stronger (tougher) and which were weaker (easier) for top tier players to score. While scoring is not the only aspect, it's a very important aspect.

I think what you have done is one piece of the puzzle, but to get it the "whole picture" needs to be integrated with other pieces.
I started studying the year-to-year changes, but found that I wanted to include more things in the equation. Age is one of those things.
I think it was during the best defenceman project that I did a fairly advanced study on strength of different seasons. I don't remember the details right now, but I think the strongest season for defencemen appeared to be around 1981. I think I didn't post it, or possibly posted it but deleted it. (It probably was yet another of those cases where people on one hand were constantly doing more or less arbitrary adjustments within their heads, but on the other hand didn't find a study trying to determine it to be of much value.)

A general note of encouragement: Don't give up if it genuinely intrigues you. You've demonstrated an interest and capability in this capacity. I would recommend you be selective and tend to choose studies with large effects and possibly broad implications. The smaller the effects and narrower the applications of the results, the fewer people will be interested.

Thank you. I do enjoy studying stats and doing research to try to find out "how things really are (or may be)". Part of my problems may also be that I think that some things (like strength of eras, etc., etc.) ought to be "settled" and might require partly narrow studies to build upon.


I've been more interested in building upon your win % thinking that Overpass' thread on adjusted +/- developed into. I spent quite some time integrating SH and PP play into the study. I even "adjusted" for goaltending, which (goaltending) I think is among the most overlooked things when focusing on +/-. I was planning on posting a thread on it. I posted a small example, but got discouraging replies, got the impression that no matter how thorough and/or complete the study would be, it would just not affect the already made up minds on how things are.

During the last 1-2 months, I've studied how team performance is affected when a player is out of the team (for example being injured). To me very interesting. I posted a chosen example showing that Pavol Demitra actually significantly made his team perform far better with him playing than when his out injured. Not during one team during one season, but season after season on 4-5 different teams. No interest whatsoever, apart from one comment more or less automatically dismissing the study.
(In the "best defencemen" project, there sometimes were mentioning of how a team performed when a player (don't remember if Eddie Shore or Sprague Cleghorn) played or not. I have done that for every player on every team since 1987-88 to 2010-11. In the project, this stat was considered meaningful, even if there was no comparison at all made to other players. When I do it, it's considered uninteresting or meaningless.)
To me, it's amazing to see Lidstrom place very highly, with his team being nearly average with him not on the team (and this not even including 2011-12, and even not counting games during end of regular season where Detroit rested players).
I would have pointed out that Gretzky didn't seem to make LAK better during the regular seasons, something that meets my own eye-ball test. But how ridiculed would I be if posting something like that?

Both of the above studies have a holistic approach, which I find is a good way to go. Compare team with a player with team without player. In my opinion more useful than studying +/- when on ice, compared to +/- when on the bench.

I have also started studying how different players actually affect each others scoring stats. For example, how did Mario Lemieux benefit by playing with Kevin Stevens, and vice versa. I can find out by filtering out games where both played, or just one of them.

I outlined a regression study that seems worthwhile. Do you think such a study makes sense and is feasible?

See above (one piece of the puzzle, or rather several pieces).
I have to say I agree with some of the criticism you have received, but I suppose you basically do too. I basically agree with your replies to the replies you have gotten. You have started something good, that should be able to be improved and built upon.


Gosh, this takes time... I started on this post 2 1/2 hours ago...

Regarding adjusted points (or goals), I think one needs to understand and keep in mind how the most common methods work. We first normalize scoring to say 6 goals per game, to make different seasons comparable.
I can't find the words properly now, but I think it's valuable to understand what we're normally doing. We have a set number of "total goals" and what the common methods does is to tell how much different players stand out compared to some sort of league average. How much they stand out depends in things like:
* How many teams were there in the league? The more teams, the more spread out quality, and the more easy it may be for the top scorers to stand out compared to their average teammate.
* What was the strength of era? Again, the higher quality per team, the more hard to stand out.
I'm very tired now, and can't think very straight, but just wanted to point out that traditional adjusted scoring has a lot to do with percentages. It's "team GF divided by league average GF" multiplied by "player's pts divided by team's GF". Or just "player's pts" divided by "league average GF".

That's great. I don't believe my database, know-how, nor software are on par with many here, such as yourself.

I think you're among the better/best ones here.

If you ever wish any assistance while designing and structuring a study, please PM me.

Thank you.

BTW, your English is very good, I doubt anyone has any trouble understanding you.

Thanks. I think people understand me. It's rather that I need to express myself in simple, perhaps childlike, school English, and I suspect that may affect the way I'm being perceived(?) here by some.

 

[seventieslord]

Lafleur's Habs weren't known to run up the score. What if they did? How many more points would Lafleur have? Would their even be a Lafleur - Jagr debate if Bowman let the guy run wild and run up a score against opponents when the game was pretty much decided from the outset in so many cases.

Is there actually any data to support this notion? That Jagr was more likely to pick up extra points running up the score but Lafleur wasn't?