Offensive and Defensive PER: A new way to show a player's Offensive/Defensive Value!

[BlueBull]

Welcome to a new age: the age of Offensive and Defensive PER!
These two beauties are a new art in the league to show how good a player is in their own end, and their opponents end.
If you don't know what the word PER means, here is some context.

About 5 years ago, John Hollinger, an Analyst on ESPN, created a new advanced stat for the NBA, called Player Efficiency Rating (or PER), which was a way of showing how good a player is. A player should be able to stay in the league if they have at least a 12-13 PER. 15 is average. If you have a PER above 27, you might win the MVP that year. If you have a PER above 30, you might be one of the best players of all time. Jordan and Lebron have Career PERs very close to each other, Jordan has a 27.9 PER while Lebron has a 27.6 PER.

The Calculation for PER is very complicated in the NBA. No seriously, it's REALLY complicated: Calculating PER | Basketball-Reference.com
That does not mean that the NHL's soon to be brand new equivalent created by myself has to be complicated too, though. My version seperates it into two seperate PERs, Offensive PER (How good a player is Offensively) and Defensive PER (How good a player is Defensively). Here are my Formulas:

Offensive PER:

((Goals * 1.4) + (Assists))
/Team GF per Game

Example: 1998-99 Al MacInnis: 24.22 Offensive PER
(Note: this would make the average player's Offensive PER in 2018 be a 9.38)

Defensive PER:

((Hits* 0.56) + (Blocked shots*1.44)) * Takeaway Giveaway Ratio{If you know what that is}
/1.PIM
/Team GA per Game

Example: 2011-12 Rick Nash 48.16 Defensive PER
(Note: Any season pre 2007-08 can't have Defensive PER since Hockey Reference only Tracks all of the stats in the Parentheses above 2007-08 and beyond.)

2 Bonus PERs:
1981-82 Wayne Gretzky would have an Offensive PER of 47.73
2016-17 Connor Mcdavid would have an Offensive PER of 39.97 and a Defensive PER of 26.95 for a total PER of 66.92.

If you wanted to normalize to a good average do the following formula:
OFF/DEF/TOT PER * (x / League Average OFF/DEF/TOT PER)

This is just an early 1.0 Version of Offensive/Defensive PER. I think that the Defensive PER might be a bit off due to the wide changes in Takeaway Giveaway Ratio, but we can fix that as we move along. I hope this Post was Interesting for you, and I hope this contributes to the HF board community in a good way.
A Value statistic was my idea I have been trying to make over the last 24 Hours. It's not perfected, but it is a good start.

-BlueBull

Click to read more...

 

[BlueBull]

Update: for players who did not play full seasons, adjust their OFF/DEF PER by simply doing this:
Games in Season / Games Player has Played

 

[morehockeystats]

Ok, now the money questions:
If we have a roster of aggregate OPER O1 and DPER D1, and another roster of OPER O2 and DPER D2, what is the probability of Pw1 = f1(O1, D1, O2, D2) that team 1 wins?
What is the probability P31 = f2(O1, D2) that team 1 scores more than 3 goals?

Or we may get tactical:
If we have 5 players from team1 on the start of the power play with the combined OPER Opp, and the team2's PK is of combined DPER Dpk, what is the probability of team1 scoring the goal on the PP Ppp=f3(Opp, Dpk)?

 

[BlueBull]

1.1.0 Update: For the time being, I will make two seperate DPERs to hopefully fix some of my mess ups with Takeaway/Giveaway Ratios. One includes TK/GV Ratio in the equation and one does not. unadjusted DPER (uDPER) is no TK/GV ratio and adjusted DPER (aDPER) has TK/GV ratio.

1.1.1 Update: This is an expanded definition for 1.0.1. For people midway through the year, enhance their stats to an 82 game season with the Equation from the 1.0.1 update. This update has been made since PER is an efficiency/per game stat, and not a total stat. For example, Lars Eller would have a 29.91 TPER [11.57 OPER and 18.34 aDPER] pre 1.1.1 update. Post 1.1.1 update, Eller now has a 40.89 TPER (15.82 OPER and 25.07 DPER).

Hopefully, this can make this more or less fair for Dmen who are not as good as forwards on offense and have a bad TK/GV ratio (*cough* Zdeno Chara *cough*) and make it more fair for comparing TPERs over the last 10 years and OPERs throughout the history of the NHL and other leagues even.
OPER is easier to track over time than u/a DPER.

 

[BlueBull]

1.2.0 Update: I did it. After 5 days with some help from other people, I did it. A Fair DPER Formula.
The formula makes the difference way smaller difference for ta/ga ratios. Instead of 50;1 from best to worst its now 2.69;1. The Formula goes like this:
((Hits*0.56) + (Blocked Shots*1.44)) * log (TK/GV Ratio *100)
/1.PIM
/Team Average Goals per Game

PIM part of the formula might be changed in the future, but other than that DPER looks polished enough.

 

[BlueBull]

Example for new DPER formula:
Zdeno Chara (0.58 TK/GV Ratio, great defender)
1.1.1 aDPER: 44.98 1.2.0 DPER: 136.76
Eric Staal (1.95 TK/GV Ratio, Forward who is solid at defending)
1.1.1 aDPER: 51.35 1.2.0 DPER: 60.30
all of those numbers are adjusted to 82 games.
This makes defenders look like they are good at defense.

 

[613Leafer]

Aren't NHL giveaway/takeaway stats well known to be pretty inconsistently counted, especially between different arenas?

Also, I would personally put more weight on primary assists than secondary assists. I've read a few articles out there about how primary assists are a repeatable skill whereas secondary assists are much more luck-based, which intuitively makes sense. My opinion from watching hockey is that 2nd assists are mostly (not always, but mostly) basic/safe cycle passes or breakout passes and not really directly involved in creating the goal.

 

[BlueBull]

1.2.1 Update: Need to address the PIM in the DPER formula here.
Eg. (a) 2 PIM = /1.02
(b) 20 PIM = /1.2
(c) 200 PIM = /3

 

[BlueBull]

1.2.2 Update: During the DPER formula... If your player has played less games than his team has, adjust his pre-log adjust numbers (just after adding the Hits and Blocked shots together) to the games the team has played. Then post-formula, adjust the teams GP to 82 games and his numbers with them to get the final DPER.
Just making my formula more clear