Marvin

I consulted for someone who was working on the goal determination and had the patent for doing this. I think his kids sold it to the NHL when he died a few years ago. It would not surprise me if this is an outgrowth of that work. You can, in theory, work out precisely where the puck is if it completely crosses over the goal-line -- even if it is on-edge, angled, etc. However, the metal in the goal is ferromagnetic, so unless you have very good proximate sensors, they distort the data slightly, so you have the grey area you mentioned. Also, the machinery in the ice has electricity which generates magnetic fields when it varies in current, so that also affects the sensors in the puck. Thus, if the puck crosses the line at a funny angle for a fraction of a second, you probably can't do anything. Where it would be useful would be when the puck clearly crosses the goal line, but is not visible. That information could be transmitted within the televised signal to Toronto and to both teams' representatives at the game.

I love the Bee Gees. As I now have twice had a mod complain about my posts' length while I am trying to be thorough and clear with posts on statistics. I am just trying to be helpful, but it appears The Powers That Be would prefer that I not post anything that detailed. Far more importantly, as I was branded a terrorist in 1984 for reporting a threat on my person by an Indian national to the INS (precursor of ICE) and almost had him thrown out of the country, these posts were used as part of the basis of the claim that I am a trouble-maker (read: terrorist) by the Indian government to disallow me from going to my Dad's Alma Mater to donate the money he willed them (at the invitation of the Dean and my Dad's former roommate, former Prime Minister Manmohan Singh). I am very PISSED OFF that the Mods' comments against my posts were used to deny me that visit. As a Sikh, I want to go to Anmritsar and visit the 5 Takhats once more before I die. Your behaviour may have denied me that opportunity permanently. As I hope to do so in future, I shall do what The Man wants and excuse myself permanently. Before leaving, I will let you know what I bought when I was pulled over for DWB in Columbus, Ohio. Goodbye, everyone. It has largely been good.

I actually think that the only time I trusted the way the Sabres were run under the Pegulas was when Lindy and Darcy were still here.

As long as he passes the audition. https://www.youtube.com/watch?v=wboz-_KKVg4

Actually, statistical analysis and such is part of why I find sports fun. And the analysis thereto made playing it and talking about it much simpler for me. So, believe it or not, this made it more fun and simpler for me. I will get to that when I finish working. I have been doing this as a stuff to do for a break.

I put 4 stats in there. I avoided stats where I know we have far greater expertise on this board, such as TRpm and RApm. I will let the experts put them in. I added some evaluations of those statistics, because they are very old, and therefore have a long track record which we can evaluate. I would other people to chip in and let me know what they think and what adjustments to make. ASIDE: One assertion that gets a lot of support is @pi2000 claiming that because you can't rehearse set plays, only those that use concrete measures, such as TRpm, are worthwhile. I agree in principle that hockey is controlled chaos. So is the stock market. That does not make it impossible to derive figures based on seemingly ephemeral situations. It just means that you have to take them in context and with a bit of a jaded eye. For instance, I am a huge believe in quality of competition (Q of C) from a tactical evaluation; however as a long-term statistic, it is not worth nearly as much because almost all changes on the fly tend to flatten out the QofC. If we just ignored these numbers in other walks of life, virtually all applied mathematics that involves statistics and operations research would vanish. (You ever tried quantifying and modelling luck and trust?) Because of this uncertainty (kind of like a Hockey Heisenberg Uncertainty Principle), I don't use any single number to evaluate a player. For instance, I start with Adjusted Plus-Minus, incorporate Defencive Zone Starts, situational adjustments, and such to get as complete and nuanced an evaluation of a player who does not score a lot. (Or, for that matter determine if a big scorer should be moved because he scores a disproportionate amount of trivial goals in low-leverage situations and is completely defencively inept.)

These are the fun stats, where we can measure greatness and incompetence. Many of these have obvious variations which I will not bother to enumerate here. Team Devastation Rating (good teams): Team Goal Differential / League Average Goal Differential Team Devastated Rating (bad teams): League Average Goal Differential / Team Goal Differential Individual Player Presence (think of this as "lone wolf" situations): rate of stat when player is on the ice / team's rate of stat without that player on the ice. So when you see that the Sabres' numbers all congregate in a tiny area near "BAD" on a chart with either Vladimir Sobotka or Tage Thompson, but they players' performance away from those two go all over the bloody map, you know they suck. Conversely, you get a very good idea of how much better the team has been with the addition of Jeff Skinner. You also find out how disastrous the Scandella-Ristolainen defence pair was. Without each-other on the ice, Scandella was at least a #6-8 D-man and Risto was in the #3-5 range. Put them together and you have, um, magic, I guess. Prorated Scoring seasons: Adjust goals and assists in all seasons to put all of the individual and team stats onto a uniform scale against the NHL historical average. Until the DPE, this was 1972-3. Now the historical average is 2006-7.

Crucial Situations Originally Created: Early 1980s Creators: Roger Nielson, Al Arbour, Emile Francis, Jeff Z. Klein, Karl Eric-Reif, writers for the old hockey annuals Inspiration: Find out who the Joe Schlabotniks are who score goals in borderline irrelevant situations, make spectacular saves when the game is out of hand, etc. Logic: Track who is making key plays that preserve leads or tie games How to Measure It: What you measure and how you use it varied wildly from statistician to statistician. I will concentrate on tying or go-ahead goals, although you can do a lot more than this Examples: Cruicial scoring Goals and assists scored when tying the game or gaining the lead. Crucial +/- A player's plus-minus stats during crucial situations. Crucial Perseverance rating Which goaltenders are not allowing "the next goal." Adjustments and other examples: Who is put on the ice defencively in crucial situations Who is put on the ice offencively in crucial situations Who gets the puck out of the defencive zone after a crucial defencive zone start Who gets into the offencive zone when down 1 or tied. Who makes these plays in the 3rd period At the time of the creation of this stat, 70% of 3rd period leads were "safe". Performance in this part of the game was often called "critical" Defencive players who start a shift against a top offencive line. Goaltenders who replace injured goaltenders and do not have a back-up.

Adjusted Plus-Minus Originally Created: Late 1970's Original Creators: Lou Nanne, Emile Francis, and others Inspiration: Try to get players on good teams and bad to be measured on the same relative two-way scale. Logic: How do we determine players on bad teams who are actually performing well, but are dragged down by lousy team-mates? Conversely, who on good teams is actually performing poorly because his team-mates inflate his raw numbers? How to compute it: There were actually 3 versions of this stat. Original Background: Easiest Used by Emile Francis and Lou Nanne to help evaluate player assignments, roles, etc. Allegedly pioneered in the 1950's (!) by Anatoli Tarasov, Arkady Chemyshev, Vsevolod Bobrov, Boris Kulagin, and Viktor Tikhonov -- even before the NHL adopted +/-. Computation Add up the raw +/- stats for a given team. Call that PM_total Divide PM_total by the number of skaters required to dress for a game. Call that PM_ave In the 1970's, when this was developed, that number was 16. Now, it is 18. For each player on the team who have played a "statistically significant" number of games, take his raw +/- and subtract the PM_ave. That is his original adjusted +/- Depending on whom you ask, this could be anywhere from 30 to 60. I personally say "half a season". First Revision Background: Some extra complexity Appeared in The Hockey News about 1980; introduced by Jeff Z. Klein and Karl-Eric Reif Was apparently used as far back as 1973 by Fred Shero and Joe Crozier Computation Each time a goal is scored on the ice, if the situation is one where you count a plus or minus, take the reciprocal of the number of players on the ice and multiply it by +1 (GF) or -1 (GA). This is PM_per_player for each player on the ice. Normal Simplification: Just assume 5 players on the ice, which is typical. Note that without this simplification, goals in 3-on-3 OT are over-valued somewhat. Add PM_per_player over the entire season for the entire team. This is the PM_ave. Also, for each goal where plus-minus applies, add the PM_per_player for each applicable player's adjusted plus-minus. This is PM_player_raw. For each player, subtract the PM_ave from PM_player_raw. This is his adjusted plus-minus. Second Revision Background: Add more situational understanding Pioneered by Viktor Tikhonov. Computation: Use any of those above. Adjustments: Do not include empty net goals. At the time, ENG outnumbered goals scored by the team that pulled the goaltender something like 30-1, so it inflated plus figures for defencive forwards and deflated plus figures for scoring players. Weight complete gaffes against specific players who screwed up, such as a defenceman coughing the puck up to an opposing forward in the slot and "crucial goals". Advantages: Fairly easy to derive from the raw data at the end of the year; easy to see when a player has played enough games to warrant this extra scrutiny; allows for underrated players to shine (e.g., Bill Hajt) and finds over-rated players relative to their peers (e.g., Ramsay-Luce-Gare were a better checking line than anything involving Bob Gainey!). Disadvantages: Still kind of crude; does not do as good a job finding good players on bad teams as it should (e.g., Ron Stackhouse); allows really good players to buoy the statistics of team-mates (e.g., Dallas Smith had the good fortune to be partnered with Bobby Orr and then Brad Park).

Goaltender Perseverance ratings: (Save pct *6 + average shots against / game) / 0.6 Created: 1981 Creators: Hockey News Writers Jeff Z. Klein and Karl-Eric Reif Inspiration: Avoid using GAA for comparing goaltenders because good goaltenders on bad teams look worse than bad goaltenders on good teams. Logic: Save Percentage is generally a more predictable long-term, team-independent statistic than GAA. Add in the shots against per game to measure workload; thus the same save percentage for a goaltender on a weaker team that surrenders more shots will show a higher perseverance rating and therefore better performance. Advantages: First goaltender stat to try to rate goaltenders by combining personal performance and workload; found goaltenders who were over-rated by GAA who were terrible but played on very defencive teams. (Prototype: Pete Peeters later in his career) Disadvantages: Rated all shots equally; proportions were derived to rescale goaltenders to the THN staff's perceptions and evaluations. (Prototype: Tom Barrasso early in his career) Common Adjustments: Varying the dependence on the shot rates; incorporating shot difficulty; incorporating situational issues, such as a two-man advantage.

Pending Admin approval, I created a new club so that we can have a repository for statistics references and discussion of the methodology, quality, etc. When I add a stat to the discussions, I will always give the simplest way to arrive at a variant of the stat, some more complex adjustments, etc. I will also try to add evaluation to the discussions. I have access to the very earliest of hockey data analysis, even pre-dating my own from 1992. I have the original computations used in The Hockey News for the columns, "For Argument's Sake." These are very primitive and date back to when a $2500 Atari 400 was close to top-of-the-line. For example Goaltender Perseverance ratings: (Save pct *6 + average shots against / game) / 0.6 Created: 1981 Inspiration: Avoid using GAA for comparing goaltenders because good goaltenders on bad teams look worse than bad goaltenders on good teams. Logic: Save Percentage is generally a more predictable long-term, team-independent statistic than GAA. Add in the shots against per game to measure workload; thus the same save percentage for a goaltender on a weaker team that surrenders more shots will show a higher perseverance rating and therefore better performance. Advantages: First goaltender stat to try to rate goaltenders by combining personal performance and workload; found goaltenders who were over-rated by GAA who were terrible but played on very defencive teams. (Prototype: Pete Peeters later in his career) Disadvantages: Rated all shots equally; proportions were derived to rescale goaltenders to the THN staff's perceptions and evaluations. (Prototype: Tom Barrasso early in his career) Common Adjustments: Varying the dependence on the shot rates; incorporating shot difficulty; incorporating situational issues, such as a two-man advantage. I did a pile of stuff when I got access to our old Sun machine at the MSU Math Department (the Solaris beta OS). I did a lot of work on what we call analytics back on my old Amiga in the 1990s. Most of this stuff has been largely superseded by modern analytics, but they are still pretty accurate, simple enough to compute, and easy enough to understand that I like to use them for basic analysis just to get a rough idea whenever I run into a claim that looks either counter-intuitive or completely out of whack.

I can tell there are several posters with technical degrees. What I am saying is that I am the only one dumb enough to almost put the Riemann Mapping Theorem into an analytics post. As the living embodiment of someone with less common sense than the intersection of 4 main characters in "The Big Bang Theory", I can safely assert that what is "common sense" to everyone else on this board often requires somewhere between immense and inordinate reflection on my part.

Once I get my laptop out, I will do something to make a reference for these graphs, stats, etc. IMHO, as the one most likely to come up with number crunching that requires a graduate math degree to interpret, I should do this. After watching the responses to some of the the analyses here, I think that explaining what I can see is like me trying to understand how Rashid Nezhmetdinov could think chess the way he did.

One first line, two fourth lines, and a sixth. <sarcasm>See, we we had 4 top-6 lines.</sarcasm>

This is so demonstrably false that I have to ask if you are like my wife, who never misses a second of action, but almost never watches the games critically. We had this discussion in early November, so we watched games in analysis mode until the All-Star Break so that she could see what I did. To disabuse you of your perception, I recommend that you start with the player on-ice charts which are available for each game of the season at nhl.com. Aggregates can be found at numerous raw and fancy stats sites. Thank you.

Oh, heck. My point of logging in. I like the signing. Of course, anything that makes it more likely that Vladimir Putin^H^H^H^H^H Sobotka is not in the line-up was going to make me happy. Try this line-up out: Skinner-Eichel-Vesey Rodrigues-Mittlestadt-Reinhart Olofsson-Johansson-Asplund Girgensons-Larsson-Okposo Ruotsalainen-Smith-Nylander I protected Mittlestadt with a pair of 2-way players who can also play some Centre. I put a couple of young guys with Johansson to learn and allow both wingers to transition to Centre. I think the Eichel line will have great chemistry. I kept the 4th line together. I demoted Sheary based upon his play at the end of the season. The idea is to get 4 functioning lines and to clear out dead weight. I suddenly feel badly for Housley.

Should we create a fancy stats reference thread? It should have the stat name and a reference to click on. (Among other things, it would have made @pi2000's TRpm easier to find.) IMHO, nothing more should be required of the poster: we are all "extra effort" fans; let us learn together what these stats are and develop our own evaluation of their quality. We can even nominate what we think are the really good stats for an official @Randall Flagg seal of approval. If I were the first person to use a stat, I personally would take my initial use and work through it for people to follow what it is. It's the Math Professor in me. (Sorry, no Math Ginger or Math Mary Ann.)

Adjusted +/- = player's +/- minus team average +/-. I used the estimate of the aggregate +/- of -259 and divided it by 18 skaters per game to get an estimate of -14. That makes Reinhart +4, Eichel +3, Larsson +6, Girgensons +3, and Dahlin +1. I start from here. You and I have everyone hovering around 0, so we seem to be talking the same language family, albeit maybe not the same language and certainly not the same dialect. As such, I suspect that TRpm is probably a solid overall measure of 2-way play. I should mention that I agree with you that Larsson and Girgensons don't cash in enough on glorious chances. They are pretty typical, but definitely a bit more frustrating than the rest of the Mike Ryans and Jiri Novotnys of the league. But I see enough of other 3rd and 4th liners to say that they do more than well enough. IMHO, If Okposo is with them all year, I can see the line hitting 30 ES goals, even with 80+% DZS. I found that the zone face-off stat is a decent, but non-linear proxy for zone starts. The biggest thing that these 5 have that is much tougher than the rest of the team is that the other lines were often terrible. The must get the puck from the opposition, clear the zone, get to the offensive zone, and have possession there. The 4th line usually has to deal with the top line of the opposition while the top line has to deal with the best checkers and top D pair. The hardest part is determining their defencive worth concretely. I have a calculation where I measured the opposition players' seconds between goal against the defenders versus their norms and then correcting for zone starts, game situations, etc. Girgensons-Larsson-Okposo very well here. The one thing you probably won't like is that I adjust for go-ahead and tying goals more heavily (depending on game situation, up to 10%) and I slightly devalue empty-netters. This gives a huge extra plus for the protectors of the lead and those who tie or win games late. There are other weights to game situations that I won't trouble you with. I also like using a lot of different measure to tease out the nuances of a player's effectiveness. Oh, I should mention that, like math contests, chess tournament analyses, and music structure, I do this for fun and have put an inordinate amount of thought and time into it since I first saw the column, "For Arguments' Sake" in _The Hockey News_ back in the 1980s.

@pi2000 Among other things, I have been using adjust plus-minus since 1989 as a start for analysing skaters. I have been doing adjustments to its output with zone starts, game situation, situational quality of opponents and teammates, crucial situations, and the like. I used this along with some operations research and what we now call predictive analytics to derive raw statistics and adjustments based on my initial data mining and revision in 1992. These are easily quantifiable and have rigourous definitions that allow us to verify their accuracy. I did this enough from 1992-2002 that I largely trust the typical numbers. Example: in 2001, the Buffalo Sabres were the only non-Cup winner to correlate strongly positively against every statistic that is predictive of a Cup winner for collection of statistically similar years over the entire history of the franchise. However, in each era, they had a glaring defect that would correlate to being a disappointment. (1970's - goaltending; early 1990's - injuries; late 1990's - scoring balance.) As you noted, from a raw statistical perspective, Dahlin,Girgensons, Larsson, Eichel, and Reinhart all had raw adjusted plus-minus in the neighbourhood of 0. In theory, if we had exchanged their total ice time with better raw performers, such as Bogosian, Pominville, and Elie, the team would have improved. (I am looking at the raw stats. This is 100% accurate.) The problem is that these 5 players were used to perform one of the highest leverage, highest difficulty tasks: flipping the ice at even strength; i.e., getting the puck away from the opposition in the defencive zone and transitioning to have possession in the offensive zone. After we adjust for this factor, all 5 player shoot from about team-average raw to about 0.5 to 1.0 standard deviations above average adjusted. (As a contrast, Skinner starts at the top and these guys close the gap a LOT.) Hands down, they also tended to face the toughest opposition because Housley rightly did not trust the middle 6. (Of course, he was the lunatic who gave hours of ice time to Vladimir Sobotka.) This is balanced out by their quality of teammate for this task. As such, I am quite confident in the usage adjustments and my evaluations of them as maybe the best 4th-liners in the NHL. Aside: because of my background, I strongly disagree that only measurements based upon or derived from adjusted plus-minus mean anything. Other numbers can be and are both well-defined (in a mathematical sense) and properly posed; they then make a very good raw stat like adjusted plus-minus even better for both past analysis and future performance. These kinds of adjustments are used all the time in situations of controlled chaos; they allow the number cruncher to be able to perform useful analyses and make statistically accurate predictions.

Would they have that low scoring if they didn't have 85% DZS? Let's see what others in this exact role with other teams have: https://www.hockey-reference.com/play-index/ppbp_finder.cgi?request=1&match=single&year_min=2008&year_max=2019&season_start=1&season_end=-1&rookie=N&age_min=0&age_max=99&pos=F&situation_id=ev&c1stat=zs_defense_pct&c1comp=gt&c1val=75&c2stat=games_played&c2comp=gt&c2val=40&order_by=zs_defense_pct Here is the complete list of people who scored more than Zemgus or Larry in this role with comparable defence: Marcel Kruger (Chi 2013-4 [8 + 19 = 27, 79.1% DZS]) Brandon Sutter (Van 2017-8 [11 + 11 = 22, 77.4% DZS]) Manny Malhotra (Van 2010-1 [7 + 15 = 22, 75.7% DZS]) Maxim Lapierre (Van 2011-2 [9 + 10 = 19, 77.7% DZS]) Zemgus Girgensons (Buf 2018-9 [5 + 14 = 19, 84.9% DZS]) Manny Malhotra (Van 2011-2 [7 + 11 = 18, 87.1% DZS]) Marcus Kruger (Chi 2014-5 [6 + 10 = 16, 75.9% DZS]) Matt Cullen (Pit 2018-9 [5 + 11 = 16, 80.7% DZS]) Scottie Upshall (StL 2016-7 [7 + 8 = 15, 76.7% DZS]) Boyd Gordon (Edm 2013-4 [6 + 9 = 15, 80.4% DZS]) Dominic Moore (NYR 2013-4 [5 + 10 = 15, 75.5% DZS]) Matt Hendricks (Edm 2013-4 [7 + 7 = 14, 76.0% DZS]) Brandon Bollig (Chi 2013-4 [7 + 7 = 14, 81.8% DZS]) Brian Boyle (NYR 2013-4 [5 + 9 = 14, 77.0% DZS]) Paul Gaustad (Nsh 2014-5 [4 + 10 = 14, 88.3% DZS]) Johan Larsson (Buf 2018-9 [5 + 8 = 13, 84.4% DZS]) I have arranged the players in decreasing order of points to maximally be unfair to Zemgus and Larry. Almost all of the top scorers were from playoff teams; the only exceptions are Matt Hendricks and Boyd Gordon in 2013-4 for Edmonton and Brandon Sutter for Vancouver in 2017-8. Most of these guys are no longer in the NHL. Only two editions of Paul Gaustad and one of Manny Malhotra had a higher DZS percentage than Zemgus and Larry. NONE of them had better Corsi or Fenwick, raw or relative. Now, I am sure there are better scoring 4th liners, and I do wish they could score more. But how many of their peers are even in this ballpark of defencive zone play? The total number of players in this ballpark from 2007-present (12 seasons) is 37. That is not a typo - thirty-seven. You need guys like this to kill penalties, turn momentum, finish checks, and defend leads. Conclusion: based on these numbers and numerous other metrics (like, how horrible Sobotka, Thompson, and Mittlestadt were for much of the year), Zemgus and Larry may be the best 4th liners in the NHL. Indeed, if I were GM and they asked me for 5 years @ $2M AAV, I would give them a contract so fast it would make your head spin.

A debate about the sabres #2C potentially not being up to the task and the GM does not seem to have a back-up plan? Let me check my command history. $ cd /opt/sabres/ $ vim sabres_centre_debates.2009 :%s/Owner B. Thomas Golisano/Owner Terry and Kim Pegula/g :1 :%s/GM Darcy Regier/GM Jason Botterill/g :1 :%s/2C 19 Tim Connolly/2C 37 Casey Mittlestadt/g :wq $ diff -w sabres_centre_debates.2009 sabres_centre_debates.2019 $

If we were going to be picking 20+, I would agree with you. I think "20+" has an extra digit for where I think we pick even with Marner. Not a #1/2 Centre => Not right now. Point, on the other hand, would be perfect.