Adjusted Playoff Scoring
Adjusted playoff goals, calculated by season as follows:
GPG: goals per game
RSG: regular season goals/game
EPG: expected playoff goals/game
APG: actual playoff goals/game
A/E: ratio of APG/EPG
ADJ: adjusted playoff goals/game
P/RS: ratio of PO GPG to RS GPG
EPG = Sum (RSG * PO gms) / Sum (PO gms) for all playoff teams
ADJ = RSG * (APG/EPG)
This looke like it could be quite useful... but can you better explain it?
I am attempting to derive a number to use to calculate adjusted playoff goals per game, by using the regular season GPG and adjusting it based on actual playoff results. The point of adjusting statistics is to give them the proper contextual value. When goals are more easily scored, the value of each goal is diminished. When goals are scarcer, the value of each goal is increased.
To account for the difference in scoring level between the playoffs, I calculated expected playoff goals by team. For each team, the equation would be:
(EPG) Expected Playoff Goals = poGM * [ (rsGF + rsGA) / rsGM]
GF=Goals For; GA=Goals Against; GM=Games; po=playoffs; rs=regular season; GPG=total goals per game
The EPG for all teams would then be summed to get a total EPG for that season.
Actual Playoff Goals (APG) is then summed by team and then totalled for the season.
If a team scored at the same level as the regular season (and likewise the league did overall during the playoffs), then APG=EPG. The teams in the playoffs scored at the level you would expect based on regular season statistics.
If there was a four team league, where each plays 50 games:
team A: 200 GF, 150 GA
team B: 150 GF, 100 GA
team C: 250 GF, 250 GA
team D: 200 GF, 300 GA
The regular season scoring level is (800 GF + 800 GA)/200 GM = 8.0 GPG
Two teams play for the trophy, A and B. They play a 6 game series, during which A outscores B 24-21.
So what number should be used to adjust playoff statistics? Could use regular season GPG of 8.0 or calculate actual playoff GPG:
APG = (24+21)/6 = 45/6 = 7.5 GPG
However, I took this approach:
in regular season team A averaged (200+150)/50 = 350/50 = 7.0 GPG, while team B averaged (150+100)/50 = 250/50 = 5.0 GPG
So, in the playoffs, EPG = [(7.0*6) + (5.0*6)]/(6+6) = (42+30)/12 = 72/12 = 6.0 GPG
Since actual APG was 7.5 GPG, the ratio of actual to expected GPG is (7.5)/(6.0) = 1.25. This means the teams scored 25% more goals than expected by their regular season performance.
To get a number for adjusted playoff goals that corresponds to the regular season number, it is adjusted as follows:
Adjusted Playoff GPG = rsGPG * (APG/EPG) = 8.0 * 1.25 = 10.0
This happens in some playoff seasons, but it's more common that adjusted playoff GPG is less than regular season GPG.
I hope this helped to clarify my approach to this project.
So the expected palyoff goals per game is based on which teams made the playoffs, and the GF/GA totals of those teams?
As for the adjused playoff goals per game, I am still not clear on what that represents.
Adjusted playoff scoring would be similar to "regular" adjusted scoring. The importance is that, due to the methodology, one could not only compare playoff seasons to one another, but also playoffs from any year to regular seasons from any year. It basically tries to level the playing field for all such comparisons.
I know it may be flawed, due to different teams playing different numbers of games, differences between conferences, etc., but I still don't see a superior methodology, although their may be one.
Would it be more appropriate to do it per 60 minutes to account for lengthy playoff overtimes?
An alternative would be to deduct all the OT goals during the regular season and all of the OT goals during the playoffs. However, those OT goals are still being scored. The purpose of adjusting playoff GPG is to better (not perfectly or completely fairly) compare playoff scoring of individual players. Deducting the goals from the totals and still crediting players for those goals/points doesn't seem like a good solution either.
Game 1: Ottawa wins 5-4
Game 2: Pittsburg wins 2-1
Game 3: Pittsburg wins 4-2
Game 4: Pittsburg wins 7-4
Game 5: Ottawa wins 4-3 - 3 OT - 47:06 of OT played
Game 6: Pittsburgh wins 4-3 OT - 13:24 of OT played
There is a pretty big difference here of an entire goal. While both totals are a bit high, 6.83 is clearly quite a bit higher.
I think it would be important to take time into consideration, but maybe in the end it won't matter?
I don't think it matters to this type of study, because only one goal can be scored in OT. Once OT starts, the fact that one more and exactly one more goal will be scored is a certainty. Therefore, the time it takes to score that goal is basically irrelevant IMO.
Using per-minute data is not only much more time-consuming, but I think it would cause playoffs with a high % of OT games to appear lower scoring than they really are (assuming goals in OT are less frequent than in regulation). It's comparing gpg scored under regular season conditions to gpg scored under playoff conditions, weighted by games played for each PO team. I don't think using per-minute data helps, because the same condition (unlimited OT) was not present during regular season games.
This is meant as a guideline to compare groups of seasons for players in different eras, not as an exact adjustment factor for single seasons (although it's likely better than comparing raw data).
I think Pnep has worked on adjusting playoff scoring also. I'm not sure his methodology. He may just use regular season gpg to adjust the data.
My 2 cents on whether to count per 60 minutes:
It seems to be a truism that the longer an overtime lasts, the harder it is to score. Playing conditions erode in countless little ways -- players get fatigued, refs swallow their whistles, TV timeouts disappear, in some cases the ice degrades, coaches are no longer on their game plan, sticks break down... so on and so on. It's usually not very good hockey in the third or fourth overtime.
Comparing 60 minutes of overtime to 60 minutes of regular play is guaranteed to produce faulty results, IMO.
It just occurred to me that this could be quantified by calculating the G/60 of overtime play for a season or two as a sample. My money says it's a lot lower than regulation.
Tarheel - I could get you that info in a couple days if no one else does.
As far as whether to use 60 minutes, or games, it depends whether you are doing adjusted stats for goalies or skaters.
For goalies it does matter how long it takes and how many shots it takes before an ot goal is allowed. For a skater when it comes to doing adjusted scoring, a game is a game. OT has one goal in it, no more, no less.
Ok, it was a little painful on an iPhone but I crunched the G/60 numbers for the 2012 playoffs. The results surprised me.
GP/60 in regulation - 4.55
GP/60 in overtime - 6.18
The reason it went against my gut was simple -- I underestimated how many OTs end within a few minutes.
That triggered my curiosity, so I took it another step and calculated G/60 for each five-minute increment of an overtime period.
First 5 minutes - 7.53
Second 5 minutes - 3.08
Third 5 minutes - 8.28
Fourth 5 minutes - 4.79
That's closer than it looks to a linear decline. If a goal scored at 10:36 had been scored at 9:59, we would see a nice graceful downward curve. A larger sample size should smooth it out.
So... here's what really got me:
Fifth 5 minutes, AKA the beginning of double OT - 17.51 :amazed:
Of the four games which went to double-OT, three were decided within the first five minutes of that period (the other one went to 3OT). I'm sure this is a sample size issue, since I glanced over the past few years and the pattern doesn't extend to those seasons. However, it triggers a new hypothesis that during the playoffs, GAA is highest at the beginning of each OT period and makes a linear decline till the end, then resets at the start of a new period... possibly even increasing with each period. There are some common-sense explanations for that phenomenon, but I'd love to see the data confirm it first.
- In 2012, G/60 went up substantially when playoff games entered OT.
- G/60 appeared to make a linear decline as time passed in each OT period.
- It may be the case that G/60 spikes substantially at the beginning of each progressive OT period.
That's all I can bear on a phone at this ungodly hour :)
Also, I wouldn't compare any one playoff season with much confidence, but for groups of seasons, it's more useful.
5.48/60 in regulation
4.84/60 in OT
4.46/60 in 1OT
6.38/60 in 2OT
Someone should verify these numbers.
It would be worthwhile to use per 60 min. data for goalies, since that is how their GAA is calculated during the season.
For skaters, one would have to back out their regular season OT goals to compare properly. That would be rather complicated and time-consuming, but the effect should be minimal.
Here's what I have for the 7 years since the lockout. I may have made some mistakes, feel free to double check any playoff season.
First, just the OT data:
Here's the actual GPG, total G/60, G/60 in regulation and G/60 in OT:
To properly compare it to the regular season, one would have to deduct the OT goals or add the extra OT minutes in the regular season. What I liked about my methodology was that it allowed fairer comparison to regular season benchmarks to give a better frame of reference. We must realize that comparing playoff data from one season to the next and/or one player to the next is never close to fair, due to the large differences in team/opponent quality and other such factors.
The median time of an OT goal during this period was 7:19. The first 1/3 of the first OT period is highest scoring, less so in the second 1/3. After that, it further decreases until about halfway through the second OT period. Once it gets to that stage, it could go on for a while.
Goals vs. Time in OT:
Same but only for first ~30 minutes of OT:
But it's an interesting thing to think about :) It could have some practical application in terms of playoff OT strategy -- it might be advantageous to double-shift your top lines early in OT, increasing your chances of scoring a goal within the most favorable timeframe.
Throwing this out there - adjusted playoff stats
This is just a bit of an idea dump since we now have a place that qualifies as a wall for me to throw stuff at to see if it sticks.
For years I’ve been intrigued by the idea of an “adjusted playoff scoring” metric. I think pnep did one but I have no idea about the methodology behind it. Plus, like many adjusted systems, it still appears to result in a disproportionately high number of modern players in the career leaders.
The obvious thing that needs to be accounted for in adjusted playoff scoring is the league scoring level. That much is not debatable. But from there, there are many other issues:
- Other issues that are accounted for in regular season adjustments, like roster size and assists per goal,
- Competition level issues (strong teams always get to pile in the goals on weak teams for the first round or even two, the opposite for bubble teams)
- Team issues (being on a strong team for a long time will inflate one’s totals to an even more amplified degree than in the regular season, due to the above point)
- The number of series it takes to win the cup,
- The number of games you need to win, to win those series,
- The percentage of teams that make the playoffs
To create a season-by-season adjusted playoff point total for each player would be a complete mess, and I don’t even know how you account for the last point properly (using a downward adjustment for 80s teams and an upward adjustment for modern teams, yes, but how?) – so that concept is being thrown out, at least by me.
However, I think it’s possible to develop a reasonably reliable shorthand for career playoff points that can treat all eras equally and account for most of the above. The first thing that comes to mind is, all the above factors apply equally to all players whose careers occurred at the same time as eachother. So simply create a standard for adjustment based on the career playoff point totals of all players with birthdates within a certain range. The standard could be something as simple as the career total of the “xth” highest scorer in that range, with x being the average number of teams in the NHL when the players in the range were 20-35.
Example: Player A, born in 1930, had 100 playoff points. His “range” of years, then, is 1928-1932. He was 20-35 in the 1950-1965 seasons. The average number of teams in the NHL from 1950-1965 seasons was, of course, 6. So x = 6. The 6th-highest playoff scorer from the 1928-1932 range of birthdates had 80 career playoff points. Therefore, player A had 1.25 times as many points as the xth player.
From there we’d just need a constant to normalize from – perhaps 100? – and could say “player A has 125 adjusted playoff points.”
One flaw I thought of right away was that you’re bound to find a couple of weak spots in the birthdate ranges, particularly in earlier years when there were just not as many NHL players to smooth out the yearly ebbs and flows. For example, from 1920 – 1930 birthdates, you might find that the five year ranges have an “xth” highest playoff scorer of 80, 82, 68, 78, 79, 81, 83, 85, 84, 80. That 68 really stands out as a low number, indisating that for whatever reason that 1920-1924 range of birthdates in particular didn’t produce a player with a lot of playoff points (1922 itself could probably be blamed) and there is no reason why it shouldn’t be “smoothed out” to fit what appears to be a slow upward rise that could be substantiated with decades more data.
Anyway, I’ve had this thought in my brain for like 6 years now, and I’m just dusting it off now. What do you think? It basically takes something very complex and makes it simple, but does it make it TOO simple?
You bring up a number of important factors that influence playoff scoring. I'm not sure whether it would be better to separate the "adjusted PO scoring" part from the "team success" part. For at least the last ~30 years, PO adjusted plus-minus could be estimated as well. Strictly dealing with adjusted PO scoring, I favor a more direct approach:
Adjusted Playoff Scoring
I used actual regular season GPG for each team, weighted by number of PO games played that year, to calculate an Expected PO GPG for that PO season. I used the ratio of Actual PO GPG to Expected PO GPG, and multiplied that by regular season league avg. GPG to calculate a PO equivalent of league GPG, which can then be used to adjust PO data. I have used regular season Assist/Goal ratio, although it would be better to have the actual A/G ratio during each PO season.
What you are talking about is further adjusting for strength of team and strength of opposition. The other factors mostly affect totals rather than per-game metrics (number of games to win series, number of series to win Cup) or may be captured in other variables (% teams that make playoffs affects relative quality of avg. playoff team, but this can be measured by strength of opposition). If we stick to per-game metrics, it allows elimination of these extra variables which mostly/only affect the totals.
Another way of calculating a useful metric is to use regular season PPG to calculate expected playoff PPG, then compare it to actual playoff PPG. One could use raw PPG or adjusted PPG (using adjusted PO points as described above in link), as long as one is consistent in each case. The formula for each season is then (RS PPG) * (PO GP) = Expected PO Points. The Exp. PO Pts. and actual PO points are each summed and Actual/Expected yields a useful ratio. I've calculated such number for ~30 of the best post-expansion players, and the numbers ranged from Gilmour's 102-112% (raw and adjusted, respectively) to the lows of Dionne (65% raw) and Selanne (69% adjusted). I also ran a regression, using % of expected as dependent variable, and estimated team ESGF/GA ratio w/o player (weighted by PO games) for team strength and expected PO PPG for expected performance level as independent variables. I used ESGF/GA "Off" ratio, since it was less dependent on differences in player usage (TOI for special teams) and I had the data readily available for most of the players included. The results for this limited sample were (these are all based on career numbers):
- For each .10 increase in ESGF/GA "Off" ratio, there was a .56% increase in outperformance (actual/expected)
- For each .10 increase in expected PO PPG, there was a 1.2% decrease in outperformance.
The other big factor, which you mentioned, is strength of opposition (strength of PO schedule). This could be measured using a weighted overall metric, such as GF/GA ratio, ESGF/GA ratio or team points of opponents... and/or a weighted defensive metric of opponents (GA/game).
I would like to do/see a separate study based on team strength and opposition strengths, measuring how well a player's teams played in the playoffs. The dependent variable(s) could be PO games won, PO series won, or PO GF/GA ratio. The independent variables could be weighted variables such as team points, opposition points, team GF/GA ratio, opposition GF/GA ratio, etc. Using games won would require use of some version of Pythagorean win formula, while series won would require Pythagorean and some additional probability calculations based on maximum length of series.
These were the weighted average (by PO games) of the player's teams' ESGF/GA "Off" (without player on ice) ratios of some of the players in the study:
Br. Hull 1.14
One can see the prevalence of strong teams for many of the stars during the 70s and/or those we associate with dynasties of sorts. The increased difficulty of making the playoffs over the past ~20 years should mean that the more modern players towards the bottom often were at a disadvantage in the playoffs. This may help explain the lack of dynasties, as the best players are not always on the best teams and the playoffs, and dynasties have mostly disappeared with ever-increasing parity in the league.
The three most underperforming (in adjusted terms, out of 29 calculated) were Selanne, Dionne and Thornton (weaker teams). Lindros was hurt by a high expected PPG, while Lemieux by both weak teams and high expectations.
Players on strong teams (Kurri, Forsberg), with relatively lower expectations (Gilmour, Hawerchuk, Stastny), or both (Anderson, Messier, Fedorov) tended to overperform.
The expected GPG in the playoffs is a bit of a problem for me as the style of play and indeed the rules are sometimes different for the regular season and the playoffs.
A simple extension of the Hockey Reference adjusted method for regular season scoring using a baseline over time seems to be a good starting point to me.
Of course it would be less reliable for a number of reasons including exclusively different opponents for different players as not all teams play consistent schedules as they do in the regular season.
Like it was mentioned PNEP did soemthign like this and it's a good baseline but there are alos alot of differences over time which can cause problems if one reads too much into any "adjusted playoff stat" IMO.
An example of this is number of games and series.
Today the SC winner needs 16 wins but could play up to 28 games and in the past it was much lower and required 2 series and less games.
I think that the more that we try to account for these differences in any formula it would also take away from it's accuracy and subjectivity as well.
Playoff performance is uneven as it's largely team driven as well and for this reason I'm not sure on how much to value "playoff performance" except to say that it should not be weighted more than 25% of any players resume IMO and perhaps less.
25% would apply only to the absolute best of the best like Wayne, Richard ect and would only be for their best seasons.
I'm always struggling on how much weight to give playoffs and 25% is the max and maybe it should be more like 15%.
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