Leafs Players Sorted By Defence (The "Minus" Score) Version 2.0

[WordsOfWisdom]

Okay, after listening to feedback (I do occasionally listen lol) I took a second crack at this stat.... and here's what I came up with: 

 

 

To me, what was missing previously was a way to get defensive scores back UP again through continued playing time, so now it's here. It's like a "counter-balance" to allow defensive scores to rise. 

 

With this recent improvement, there was no longer a need to add 100 to try and pretty up the scores. I left them as is and they fluctuate between positive and negative values, just like regular +/-..... but this is NO +/- !!!  This is much closer (I hope) to what people have been looking for. It is quite literally DEFENCE..... just defence and nothing else. 

 

Now, I know what people are going to say: "But guys are still being punished for offence..."  (That comment makes me cringe.) No player is ever technically "punished" for offence. They're just not able to boost their DEFENCE rating by scoring points. That's it. If you're the worst defensive player in the league, you can't score 100 goals, boost your stat, and then turn around and claim a Selke trophy. This isn't +/-. Just like you can't erase ERRORS in baseball by hitting more home runs. It doesn't make sense. If you commit 50 errors in baseball, the only way you can get better is to stop making errors... and if you play long enough error-free, you will eventually raise your fielding percentage to a respectable level. But the bottom line is that you can't hit your way out of bad fielding stats.

 

(Whew!)

 

Okay, so how does this work now? It starts with the Minus stat (as described previously) but now I take TOI (Time On Ice in minutes) and divide it by 60. That value gets added to the score. So for every game you play without committing a "-", your defence score will go up. Notice that this accomplishes a few things: It sort of considers "quality of opposition" into the stat (because your best players play the most) but it also rewards the players who contribute the most to your team. 

 

I still don't know if I have anything viable here, but it gives me a good feeling this time around.   

 

[WordsOfWisdom]

Doing an updated Q&A:

 

Q: If it doesn't punish offence, why are Tavares, Marner, and Nylander the three worst Leafs?

A: Because they're -2, +1, and +1 respectively.  They wouldn't be last if they improved their +/- scores.

 

Q: Why do you have Minus and Defence?

A: "Minus" is +/- with the offensive component (+) removed.  "Defence" is Minus + the TOI adjustment.

 

Q: What is wrong with Morgan Rielly's ice time (ATOI)?

A: Microsoft Excel reads it as a date/time field, and values above 24 are "invalid". I'm only using the TOI field.

 

Q: Why don't you just give players a point for defence every time they score?

A: That's what the +/- statistic does. This isn't +/-.

 

Q: So if a player scores a goal, according to your formula, their Defence stat goes down right?

A: No, it doesn't. It remains exactly as it is. 

 

Q: But you're subtracting points! How can it not be that way?

A: Points are subtracted from +/-, and only the points that boost a player's +/- are removed.

 

Q: So now you're saying Cody Ceci is the best Leafs player defensively?

A: He has the highest score on the team at +15, so yes. He plays 21:33 per game and has a +/- of +9. If not Ceci, then who?

 

 

 

[WordsOfWisdom]

Final thoughts:

 

It's important to recognize my goal here. I wanted to find something that could evaluate defence using only the most common, most readily available hockey stats. Are there more "advanced" stats out there? Probably. If I could create my perfect stat, it would be a stat tracking the number of times that a mistake by one player led to a scoring chance by the opposition. But that's not only difficult to track, it's difficult to track consistently given the fluid nature of hockey. I wanted something simple. Something that wasn't hard to calculate and something that is more "absolute" in nature. 

 

Is there room for more tinkering/modification?  Perhaps. Look, it's easy to tear apart someone's work... not so easy to come up with original work of your own. In the time that I've been here at HF I've created three different hockey statistics. Not many people can say that. I've also done the same for MLB, although baseball is far more "crowded" when it comes to statistics. Not to "toot my own horn" here but by age 16 (while still in high school) I had already created a stat called "Total" that tried to determine the overall value of a baseball player to their team. This was long before anyone knew about WAR (Wins Above Replacement) and other such metrics. I actually beat them to it. So in many ways, I've been "cutting edge" in the work I do. There are more failures than there are successes of course. Most of these stats never catch on. Some don't work the way I want them to. Other times my idea sort of "ignites"/"fuels" the concept and is later done better by someone else. Someone who read my post here first, studied my work, and then took it further. (Most of these guys have a PhD in math who crunch these numbers.) But they do find posts like this on internet forums and read them.    

 

Anyway, I think I'll let this play out for the season and see where the players on Toronto wind up. Then I can do a post-mortem after the season.   

[JR Ewing]

3 hours ago, WordsOfWisdom said:

Final thoughts:

 

It's important to recognize my goal here. I wanted to find something that could evaluate defence using only the most common, most readily available hockey stats. Are there more "advanced" stats out there? Probably. If I could create my perfect stat, it would be a stat tracking the number of times that a mistake by one player led to a scoring chance by the opposition. But that's not only difficult to track, it's difficult to track consistently given the fluid nature of hockey. I wanted something simple. Something that wasn't hard to calculate and something that is more "absolute" in nature. 

 

I will say that version 2 is better than your previous iteration. Allow me that compliment.

 

Strongest correlation coefficients to Minus Score v1

-0.84, Points scored

-I actually had intended to do a top 3 or 5 on this, but will sum it up quickly: the least damaging offensive statistic (G) was a -0.75. A correlation coefficient of +0.6 or greater or -0.6 or less is enough to show a good relationship between two sets of data, while a +1 or -1 would show a perfect linear relationship. A correlation of -0.8 is enough to show a significant negative relationship. In this instance, the more points a player accumulates, the more damaging it is to his Minus Score.

 

Correlation between +/- and Minus Score v1 score: 0.21

 

In other words, there's enough of a correlation between a player's Minus Score and his +/- to show a relation between the two numbers, and it was very very far away from the negative relationship between offense and Minus Score.

 

Version 2 *does* improve in this area:

 

Strongest correlation coefficients to Minus Score v2

-a tie between Points (-0.61) and Power-Play Points (0-.60). In v1, these were also very close, almost all equally as damaging. That has been mitigated in v2, but is still relational.

 

Correlation between +/- and Minus Score v2: 0.35. It is an improvement, but a good +/- minus is still only contributes to Minus Score half as much as scoring points lowers a player's Score.

 

Keep plugging and improving, but keep in mind that, due to the nature of +/- itself:

-It will still punish players with bad goaltending and reward those whose is good.

-It will still unfairly rewards and punishes players for being on the ice when empty net goals are scored: a time when the odds of an empty-netter are far higher than a tying goal being scored.

-It still punishes good players on bad teams and rewards mediocre players on strong teams.

 

Quote

Is there room for more tinkering/modification?  Perhaps. Look, it's easy to tear apart someone's work... not so easy to come up with original work of your own. In the time that I've been here at HF I've created three different hockey statistics. Not many people can say that.

 

I've not come in to tear apart your work, though I am offering criticism where I see parts which I think need re-shaping. And I *do* speak from experience on this as I've done a hell of it with hockey. The sheer number of spreadsheets I've populated my various hard drives over the last 25ish years with is a hell of a thing, from working on seeing if we can accurately predict who will win the Hart Trophy (we can, btw) to estimating ice time back to the 1960s (that works, too).

 

I don't do much of it any more, and I let my website lapse well over a decade ago. I got out before the blog revolution and Corsi and scraping huge amounts of situational game data became a thing . J0e Thornton, here on our site, would probably remember when I was quite active. Now, I just get some mentions in a few books on sports data mining, and for some reason a statistical society in Quebec.

 

I remember when having the audacity to publicly suggest that a goalie's SV% is more important than how many games he win meant that I had to write about 10 "Dear Idiot" letters per week. Trust me, I get it.

 

Oh, and for what it's worth: Pete Palmer and John Thorn published their work on Linear Weights and Total Player Ratings for baseball about 35 years ago. We all stand on the shoulders of giants.

 

Edited December 27, 2019 by JR Ewing

[WordsOfWisdom]

2 hours ago, JR Ewing said:

I will say that version 2 is better than your previous iteration. Allow me that compliment.

 

 

Thank ya!  

 

2 hours ago, JR Ewing said:

Strongest correlation coefficients to Minus Score v1

-0.84, Points scored

-I actually had intended to do a top 3 or 5 on this, but will sum it up quickly: the least damaging offensive statistic (G) was a -0.75. A correlation coefficient of +0.6 or greater or -0.6 or less is enough to show a good relationship between two sets of data, while a +1 or -1 would show a perfect linear relationship. A correlation of -0.8 is enough to show a significant negative relationship. In this instance, the more points a player accumulates, the more damaging it is to his Minus Score.

 

Yeah, I see when I look at the spread sheet and the top point getters are near the bottom of the list. My question is WHY? Why can't someone lead the league in points AND +/-?  Has there been a player that led the league in both?  

 

I'm just wondering if that's the nature of the game or if those players are at the bottom because the top point producers are the worst players defensively. It seems like common sense in a way but I doubt most teams put their top line out to kill penalties. They're not on the ice to defend, so is it possible that each team's top line is only thinking offence and doesn't care one iota about defending? 

 

In theory, if they do their job, they control the play in the offensive zone, score a goal, and nobody ever needs to defend. But if they're not scoring goals, and they're not controlling the puck in the offensive zone, are they a tremendous liability on the ice?  I don't know.

 

2 hours ago, JR Ewing said:

Strongest correlation coefficients to Minus Score v2

-a tie between Points (-0.61) and Power-Play Points (0-.60). In v1, these were also very close, almost all equally as damaging. That has been mitigated in v2, but is still relational.

 

Power play points are not subtracted from the Minus score in either version.  If you're a player with 100 points and all 100 of them were scored on the power play, you would have a +/- of 0 and your Minus score would be completely unaffected.

 

Only even strength points and short handed points are subtracted away.   

 

2 hours ago, JR Ewing said:

Correlation between +/- and Minus Score v2: 0.35. It is an improvement, but a good +/- minus is still only contributes to Minus Score half as much as scoring points lowers a player's Score.

 

To avoid confusion, I will refer to this as "Defence" from now on, because there is no "Minus v2.0" technically, it's a new stat entirely. There should be no correlation between a player's Defence score and his +/-. Actually, I take that back. Since +/- is 50% offence, 50% defence, there will be a slight correlation between them... but certainly not much. 

 

I'll continue this post in a minute.....   

Edited December 27, 2019 by WordsOfWisdom

[WordsOfWisdom]

2 hours ago, JR Ewing said:

Keep plugging and improving, but keep in mind that, due to the nature of +/- itself:

1. It will still punish players with bad goaltending and reward those whose is good.

2. It will still unfairly rewards and punishes players for being on the ice when empty net goals are scored: a time when the odds of an empty-netter are far higher than a tying goal being scored.

3. It still punishes good players on bad teams and rewards mediocre players on strong teams.

 

For #1, I'd just chalk that up to "the nature of team sports". Every statistic is team based, line based, and so on... and I'd venture to guess that it's impossible to truly separate the player from the team. In hockey especially, the players are like different colors of fluid placed into one container (the team). They are impossibly mixed together.  Like McDavid and Draisitle: Who powers who in that scoring relationship? We know (by observation) who it might be, but there's nothing to indicate that in the stats. All we get is points. 

 

For #2, I'm actually shocked that players would receive a "-" on an empty net goal. I thought (given how much thought went into the +/- stat) that it would be smarter than that.  Perhaps #2 is the reason why top scorers have lower Defence scores. They're always going to be the players on the ice in the final minute of a game trying to tie the game and so will always suffer a "-" here if their team loses.

 

For #3, it's a bit of chicken-and-egg here too. Do strong teams have mediocre players or are they "under-rated"?  But this sort of gets back to #1 again. You can't separate the player from the team, at least not entirely. This affects scoring and everything else too.

 

3 hours ago, JR Ewing said:

I've not come in to tear apart your work, though I am offering criticism where I see parts which I think need re-shaping. And I *do* speak from experience on this as I've done a hell of it with hockey. The sheer number of spreadsheets I've populated my various hard drives over the last 25ish years with is a hell of a thing, from working on seeing if we can accurately predict who will win the Hart Trophy (we can, btw) to estimating ice time back to the 1960s (that works, too).

 

Cool.  

 

3 hours ago, JR Ewing said:

I remember when having the audacity to publicly suggest that a goalie's SV% is more important than how many games he win meant that I had to write about 10 "Dear Idiot" letters per week. Trust me, I get it.

 

lol.   

 

3 hours ago, JR Ewing said:

Oh, and for what it's worth: Pete Palmer and John Thorn published their work on Linear Weights and Total Player Ratings for baseball about 35 years ago. We all stand on the shoulders of giants.

 

True, although I had heard nothing about it at the time I did my version, as is so often the case. Many of these works remain almost entirely hidden from fans until many years later. So it's like an invention that nobody knows about (unless you specifically go looking for it). In scenarios like that, things often get "invented" over and over again until someone finally puts it into widespread use. 

 

But yes, there are lots of smart minds out there.   

[WordsOfWisdom]

Well, in the loss to the Rangers last night (a game I could actually watch lol) the three Leafs players on the ice for the OT goal were Marner, Matthews, and Barrie. All three of them will have had their Defence score reduced on that play, and not surprisingly they're near the bottom of the team because I'm sure this happens frequently. 

 

In many ways, the relationship between Points and Defence is that you can have one or the other but you can't have both. 

 

[WordsOfWisdom]

[WordsOfWisdom]

UPDATE: Apparently there's a stat called "TGA" (Total Goals Against while player is on the ice). There are also stats for goals for, power play, and so on... the breakdown of components that make up +/-. You'll have to forgive me for not knowing about them... since I doubt anyone else has ever heard of them either. They never appear in any publication anywhere other than a well-buried Misc. section on Hockey Reference.com ... and even then it's only on players from yester-year, before the days of Ice Time stats.  

 

So long story short, an analysis of TGA - TGAPP (whatever it's called, who cares) relative to TOI would be ideal.... but since the goal here was to use only readily available hockey stats (the most commonly published) then TGA is out and I'm going to continue forward with +/- as the building block to get to Minus and then Minus and TOI as the building blocks to ultimately to Defence.

 

Out of all the major pro team sports, hockey is probably the most poorly represented statistically. So it is what it is and I can live with it.