# GOALS CREATED

### Introduction

Once upon a time, I was a huge baseball fan. I still am, to a certain extent - that new ballpark that's mere minutes away from my home helps. In my initial forays into the world of baseball statistics, I came upon a tome known as the Bill James Baseball Abstract. It was difficult to understand, at first - how anyone could say that the Cardinals were so good and my Brewers were, well, not so good was beyond my comprehension at the time. As I read on and understood and learned more, the principles he espoused made even more sense.

The one area that he focused heavily on was the theory that there was a direct relationship between scoring runs and winning baseball games. The basis of this theory was what he called the Law of Competitive Balance:

 "There develops over time separate and unequal strategies adopted by winners and losers; the balance of those strategies favors the losers (or the team that is behind), and thus serves constantly to narrow the difference between the two."

This, of course, is a theory in a vacuum; if it actually worked, the Twins would win the World Series more than twice in their 100-plus year history, and the Detroit Red Wings would put a team out on the ice that the French Olympic Team could beat. However, given enough time, all teams would eventually have an overall record of exactly .500 over their team's existence.

This basic theory leads to another theory: there is a direct relationship between run scoring (or point scoring or goal scoring or tiddlywinks scored) and winning. The theory is known as the Pythagorean Theory, since it resembles the Pythagorean Theorem (the sum of the square of each of the two smaller sides of a triangle equals the square of the longest side). Basically, it goes like this:

``` (Runs Scored)^2       (Wins)
-----------------  =  --------
(Runs Allowed)^2     (Losses)
```

What this means, of course, is that a team that scores as much as it gives up isn't going to be much more than a .500 team, no matter what the sport is. It also can act as a way of analyzing outside factors on a team. For example, as of the 2002 Olympic break, you have two teams that differ in goals scored and allowed by about five goals each way: Montreal (148 GF-153 GA) and Nashville (143-148). The Habs are 24-23 with 11 OT points, while the Preds are 23-25 with 10 OT points. The Pythagorean theorem, however, says that both teams should have 56 points (a .483 winning percentage); Les Glorieux has a scant three points more. Obviously, something has happened with Montreal that hasn't happened in Nashville.

Hockey fans would generally come to this point and say things like, "Oh, that's because of Koivu being out," or some generally snide comment about hockey in the Music City. The statistician in me, however, quotes the immortal lines of Adam Ant: "Must be something inside." And that is where we begin with Goals Created.

### A Duck At The Pond

In the mid-1990's, I really started to like a player drafted by the Mighty Ducks of Anaheim, named Paul Kariya. (Ever heard of him?) I really liked his style of play, and, being a college-educated short-stuff myself, I took a liking to his career. As he toiled away with a Ducks team that was less than extraordinary, I started toying with the question of how much Kariya really meant to his team.

That was when I began to realize that there was a dearth of valuable hockey statistics in the land. Even the best internet site for hockey stats out there, Ralph Slate's Hockey Database, only had the traditional games, goals, assists, points and PIM. For the longest time, all there was for other stats was the News And Observer's Sportserver.com website, which only added things like plus/minus, Power Play and Short Handed Goals, Game Winning/Game Tying goals, and shots on goal. The internet portal site Yahoo started to carry some more stats - they added a fantasy download file, which included things like empty-net, first and unassisted goals, missed penalty shots, and even period-by-period breakdowns of when goals were scored. The NHL official site followed this up a few years ago with their "Real-Time Scoring System" which added things like Average Time On Ice, Shifts per game, Hits, Giveaways and Takeaways. But, way back in those halcyon days of the internet, all I had was the basics. I had just started to peek through The Hockey News for info, and didn't have much background in what hockey's history was like.

Thus, I made some decisions, based on the statistics that I had, towards creating a measure of a player's performance in hockey. The first was that points scored was a relatively good barometer of a player's output on the ice. The scoring of a goal is a very solid measure of a player's worth because, as we have already discussed, goal scoring has a direct relationship to winning and losing. The thing that bothered me, though, was, "What about the guys who aren't the goal scorers?" All that points tell you is that the guy is a good passer and can at least occasionally put the puck in on net. That doesn't tell you anything else about his play. So I tried to figure out a way to use a player's stats to determine adjustments to that total. There were two obvious areas: penalty minutes plus/minus.

Plus/Minus, of course, is the least useful - or most useful - stat on the books, depending on whom you talk to. It is basically the number of goals scored by your team while you are on the ice, less power-play goals, minus the number of goals scored against your team while you are on the ice, less opponent power-play goals. It can be a very unfair statistic, because if you are on a team that doesn't score a lot of goals, and you are not a very prolific goal scorer yourself, you can have a horrendous plus/minus. However, for my purposes, it measured "tangential goals" that may have been created by a player, but was missed because they couldn't add a third assist to a goal. This is where the concept of "goals created" began.

This was a pretty good start - Kariya's 1995-96 totals were 108 points, plus a plus-9 for a total of 117 points. But I knew I had to figure in something regarding goals scored when a player was off the ice because of his own actions - namely, Penalties. I did a quick analysis (thanks to some stats from various sources) of Penalty Minutes, power-play goals, and short-handed goals to come up with a ratio of goals scored per penalty minute for a given team. It didn't take me long to realize two things: using Short Handed goals was redundant, since SHG are counted in plus/minus; and it was a whole lot easier to use the PIM totals for the entire league, to counteract players who were traded from team to team mid-season. So, courtesy of the NHL's own 1996-97 yearbook, I totaled up the PIM's and Power Play goals for the league: 1927 power-play goals, 42,797 penalty minutes, and a 0.04503 PIM ratio. So, since Kariya collected 20 penalty minutes in 1995-96, this would mean 20 x .04503 = 0.9, which subtracted from 117 gives us 116.1. This was good for 12th overall in the NHL for 1996. Here's the list of the top 20 players in Goals Created in the NHL for 1995-96:

PLAYER TM GP PTS +/- PIM GC
Jagr,J PIT 82 149 31 96 175.7
Lemieux,M PIT 70 161 10 54 168.6
Fedorov,S DET 78 107 49 48 153.8
Francis,R PIT 77 119 25 56 141.5
Forsberg,P COL 82 116 26 47 139.9
Lindros,E PHI 73 115 26 163 133.7
Nedved,P PIT 80 99 37 68 132.9
Sakic,J COL 82 120 14 44 132.0
Messier,M NYR 74 99 29 122 122.5
Yzerman,S DET 80 95 29 64 121.1
Mogilny,A VAN 79 107 14 16 120.3
Kariya,P ANA 82 108 9 20 116.1
LeClair,J PHI 82 97 21 64 115.1
Turgeon,P MON 80 96 19 44 113.0
Selanne,T WIN-ANA 79 108 5 22 112.0
Bourque,R BOS 82 82 31 58 110.4
Fleury,T CGY 80 96 17 112 108.0
Oates,A BOS 70 92 16 18 107.2
Verbeek,P NYR 69 82 29 129 105.2
Kozlov,V DET 82 73 33 70 102.8

By the way, Dennis Vial of the Ottawa Senators had the distinction of having a GC of -20.4 for the 1995-96 season. In 64 games, he scored only one goal, five points and was -13 with 276 PIM's.

### Goal Strength - Or is it "Linear Goals"?

When I first found the Yahoo Fantasy Sports Download site, which allowed you to download stats in comma-sorted value format, I immediately started playing around with the period-by-period breakdown of goals. I realized that you could start "weighing" goals by when they occurred in a game with these stats, and award points accordingly. Granted, it was an arbitrary method, but it does have some basis in reality. I simply gave a player four points for each overtime goal, three for each third period goal, two for each second period goal, and one point for every first period goal. Then I started adding and subtracting. Two points for a game-winner, one for a game-tying goal. Empty nets and power-play goals were minus-one point, while I added one point for short-handed goals. I simply decided to call this concoction "Goal Strength Rating", but later just simplified it to Goal Strength. Here are the totals for 1998-99 in the NHL:

PLAYER TM GP G PP SH 1PG 2PG 3PG OT GW GT EN GS
Jaromir Jagr PIT 81 44 9 1 13 14 14 3 7 2 1 102
John Leclair PHI 76 43 16 0 10 12 21 0 7 3 1 97
Tony Amonte CHI 82 44 14 3 12 14 17 1 8 0 4 96
Joe Sakic COL 73 41 12 5 11 18 12 0 6 1 1 88
Miroslav Satan BUF 81 40 13 3 12 13 14 1 6 1 2 85
Martin Straka PIT 80 35 5 4 9 11 15 0 4 1 1 83
Theoren Fleury COL 75 40 7 3 16 12 12 0 5 2 2 82
Teemu Selanne ANA 75 47 25 0 15 19 13 0 7 1 2 80
Alexei Yashin OTT 82 44 19 0 15 12 17 0 5 1 2 80
Pavol Demitra STL 82 37 14 0 13 11 13 0 10 1 1 80

After doing a bit of reading, I realized that I actually had created the hockey answer to Linear Weights. I could assign a value to each of the types of goals and do it like John Thorn and Pete Palmer do with Batting Runs, but then again, I never understood Batting Runs to begin with. So I left it the way it was.

The next logical step was to integrate this into Goals Created. The most obvious way, of course, was to remove the Goals component from the GC formula (very simple: Points minus Goals), then add in Goal Strength. Just like that, you have Adjusted Goals Created. So simple you could probably do it with a good spreadsheet program and the data from Yahoo in a few seconds - which I do on a routine basis during the season.

 PLAYER NAME TM P GP G A PTS +/- PIM PP SH GW GT 1PG 2PG 3PG OT EN S S% GC GS AGC Iginla Jarome CGY RW 82 52 44 96 27 77 16 1 7 2 14 18 19 1 3 311 16.7 119.7 109 176.7 Naslund Markus VAN LW 81 40 50 90 22 50 8 0 6 1 11 10 20 0 4 302 13.2 109.9 92 161.9 Shanahan Brendan DET LW 80 37 38 75 23 118 12 3 7 3 9 13 15 2 1 277 13.4 92.9 95 150.9 Sundin Mats TOR C 82 41 39 80 6 94 10 2 9 2 8 12 19 2 0 262 15.6 82.0 109 150.0 Murray Glen BOS RW 82 41 30 71 31 40 9 0 9 0 16 11 12 2 2 246 16.7 100.3 89 148.3 Gagne Simon PHI LW 79 33 33 66 31 32 4 1 7 0 6 15 12 0 0 199 16.6 95.6 83 145.6 Demitra Pavol STL C 82 35 43 78 14 46 11 0 10 0 9 19 5 2 1 212 16.5 90.0 78 133.0 Tkachuk Keith STL LW 73 38 37 75 21 117 13 0 7 1 13 15 9 2 0 244 15.6 91.0 80 133.0 Daze Eric CHI LW 82 38 32 70 17 36 12 0 5 1 12 9 15 2 1 264 14.4 85.5 81 128.5 Modano Mike DAL C 78 34 43 77 14 38 6 2 5 0 13 9 11 1 2 219 15.5 89.4 72 127.4 Sullivan Steve CHI RW 78 21 39 60 23 67 3 0 8 2 2 7 12 0 1 155 13.5 80.1 66 125.1

No big surprise as to who led the league: Jarome Iginla had a head-and-shoulders year. Look at the huge bump that adding Goal Strength to GC did for Mats Sundin and Brendan Shanahan. While it's very remarkable for Sundin, it's far from unusual for Shanahan. Shanny has scored a lot of gamers and late goals in his career, which leads to great GS totals.

### GC and Teams

The team that created the most goals in the NHL for 2002 is the Detroit Red Wings, with 677.9 GC. They also had the highest Goal Strength rating of 572, and, of course, an Adjusted GC of 998.9. Of the top five teams in Adjusted GC, three of them are also the top five in winning percentage in the NHL. Vancouver, of course, is the notable exception with 937.1 AGC and a winning percentage of .573 and the 13th best record in the NHL. Four out of the five worst teams in the NHL are also the worst teams in AGC. The only exception is (thankfully, for me, at least) the Nashville Predators, who are 24th in AGC and 25th in winning percentage.

Goals Created is not perfect, however, in relationship to winning percentage. Its correlation to winning percentage is extremely high, but not less than five percent. A brief digression into statistics: when two sets of statistics are correlated, it means that for every stat in one group, there is a matching one in the other - one that can be predicted with a high degree of accuracy. An example of this is when you hear about an "error margin" in polls - they're actually talking about a form of correlation. In hockey, win point totals and winning percentage have a correlation coefficient of exactly 1 (at the end of the season; mid-year the correlation fluctuates a bit). Correlation is better the further the number is away from zero, and the closer the number is to 1 - a little like winning percentage. In fact, it's usually referred to as a percentage - the percentage of difference from a perfect correlation.

GC has a correlation of about .934 in both of its incarnations, for a 6.6 percent difference from perfect correlation - what's commonly known as variance. Adjusted GC is slightly better, but not by much (about four times in 10,000 difference). Runs Created, in baseball, generally doesn't have a variance greater than 6 percent, either.

### A Total Player Rating - And Having A Hart

When the NHL decided in 2002 to stop keeping track of Hits, Giveaways and Takeaways, I lost the defensive part of the Total Player Ratings. In years past, I had developed a formula that put those three factors together to form what I called "Selke-Norris Points." However, it was painfully obvious that Hits were dished out unevenly around the league - the Islanders led the league in hits three consecutive years, and if they actually had that many hits, I've got a bridge to sell you.

So, instead of using Selke-Norris Points, I just used the Adjusted Goals Created totals. And you'd think that you'd have a pretty good idea of who the best players in the NHL are, right?

Wrong. Nicklas Lidstrom is barely in the top 20 in AGC, and if he's only the 19th best player in the NHL, then there's something wrong.

This is where Average Time On Ice comes in. Take AGC, multiply by ATOI (expressed in decimal format), and divide by 60 (the typical number of minutes played overall in a game). This gives you a number that is remarkably similar to goals scored. For 2002-03, Milan Hejduk (surprise, surprise) led the NHL with a 61.6 TPR. Eight other players had a TPR of 50 or more: Peter Forsberg (58.4), Nicklas Lidstrom (58.0), Ziggy Palffy (56.7), Mike Modano (54.1), Glen Murray (53.8), Sergei Fedorov (53.7), Joe Thornton (52.7) and Markus Naslund (51.9).

Alas, Milan Hejduk wasn't even nominated for the Hart Trophy last season. Realizing this, I figured that to come up with a Hart-Trophy "Predictor" stat (hereafter called HTP, and abbreviated HART), I'd have to balance some of the stats that aren't as set-in-stone valuable to those who vote for the NHL's hardware.

Namely, Penalty Minutes.

Remember, back in Goals Created, we took away from a player who accumulated a huge number of PIM's. However, if you follow the Don Cherry school of hockey, Penalty Minutes are not such a bad thing. And since there are a significant number of hockey scribes out there who do put faith into such numbers, giving a player credit for PIM's should be part of HTP.

Then, quite by accident, I came upon a scoring system for a hockey pool on the internet. Hockey pools, for those of us who weren't rooting for the boys in Red and White in the Gold Medal game, are the Canadian version of fantasy sports leagues. Think of a combination of Rotisserie, fantasy leagues and football pools and you've got a fair approximation. Anyways, the scoring system gave a player one point for each goal, assist and plus/minus point, two points for each power play goal, and one point for every four penalty minutes (or .25 x PIM). It's not a very scientific system, but it does balance out a lot of things that TPR doesn't take into account when considering Hart Trophy candidates.

It shouldn't be a big surprise that Brendan Shanahan is at the top of the list in this category right now. I would probably wager that if I were to go back and do the totals, he'd probably be among the top ten (if not top five) every year going back to 1993. Of course, his broken hand suffered in the Olympics isn't going to help him keep that record up. Anyways, taking this "Fantasy Total" and adding it to TPR, you get what is called HTP, or Hart Trophy Points. The final leaders for 2002-03:

PLAYER NAME TM Pos GP G A PTS +/- PIM PP SH 1PG 2PG 3PG OT GW GT EN S S% GC GSR AGC FPTS TTOI ATOI AM AS TPR HART
Hejduk Milan COL RW 82 50 48 98 52 32 18 0 17 19 12 2 4 1 2 244 20.5 148.4 88 186.4 176.0 1626.33 19.83 19 50 61.6 119.78
Forsberg Peter COL C 75 29 77 106 52 70 8 0 9 9 10 1 2 0 1 166 17.5 154.4 56 181.4 183.5 1448.75 19.32 19 19 58.4 117.49
Lidstrom Nicklas DET D 82 18 44 62 40 38 8 1 6 5 6 1 4 0 1 175 10.3 100.1 38 120.1 119.5 2378.00 29.00 29 00 58.0 115.79
Thornton Joe BOS C 77 36 65 101 12 109 12 2 9 18 9 0 4 1 2 196 18.4 107.4 69 140.4 152.3 1735.07 22.53 22 32 52.7 109.92
Palffy Zigmund LOS RW 76 37 48 85 22 47 10 2 9 10 17 1 5 0 2 277 13.4 104.6 84 151.6 128.8 1704.93 22.43 22 26 56.7 104.82
Murray Glen BOS RW 82 44 48 92 9 64 12 0 16 13 13 2 5 2 0 331 13.3 97.7 89 142.7 129.0 1853.20 22.60 22 36 53.8 102.36
Bertuzzi Todd VAN RW 82 46 51 97 2 144 25 0 13 14 18 1 7 1 1 243 18.9 91.7 88 133.7 160.0 1686.47 20.57 20 34 45.8 100.66
Naslund Markus VAN LW 82 48 56 104 6 52 24 0 14 21 12 1 12 1 0 294 16.3 107.4 97 156.4 147.0 1631.80 19.90 19 54 51.9 100.61
Modano Mike DAL C 79 28 57 85 34 30 5 2 7 10 9 2 6 0 5 193 14.5 117.5 66 155.5 131.5 1648.47 20.87 20 52 54.1 99.80
Fedorov Sergei DET C 80 36 47 83 15 52 10 2 7 16 11 2 11 0 1 281 12.8 95.4 93 152.4 121.0 1693.33 21.17 21 10 53.7 96.43
MacInnis Al STL D 80 16 52 68 22 61 9 1 6 5 5 0 2 0 1 299 5.4 86.9 26 96.9 114.3 2152.00 26.90 26 54 43.4 94.66
Gonchar Sergei WAS D 82 18 49 67 13 52 7 0 6 8 4 0 2 1 0 224 8.0 77.4 32 91.4 100.0 2178.47 26.57 26 34 40.4 84.73
Jagr Jaromir WAS RW 75 36 41 77 5 38 13 2 11 16 7 2 9 0 0 290 12.4 80.1 79 123.1 104.5 1597.50 21.30 21 18 43.7 80.79
Heatley Dany ATL RW 77 41 48 89 -8 58 19 1 17 13 11 0 6 0 2 252 16.3 78.0 68 105.0 114.5 1690.15 21.95 21 57 38.4 80.32
Demitra Pavol STL C 78 36 57 93 0 32 11 0 10 14 11 1 4 1 1 205 17.6 91.4 72 127.4 112.0 1543.10 19.78 19 47 42.0 78.93
Morrison Brendan VAN C 82 25 46 71 18 36 6 2 12 8 3 2 8 0 0 167 15.0 87.2 57 119.2 104.0 1739.77 21.22 21 13 42.1 78.91
Alfredsson Daniel OTT RW 78 27 52 79 15 42 9 0 4 12 10 1 6 0 2 240 11.3 91.9 63 127.9 113.5 1522.30 19.52 19 31 41.6 78.51
Mogilny Alexander TOR RW 73 33 46 79 4 12 5 3 5 11 17 0 9 0 2 165 20.0 82.4 92 141.4 91.0 1462.43 20.03 20 02 47.2 77.59
Hossa Marian OTT RW 80 45 35 80 8 34 14 0 15 11 18 1 10 1 3 229 19.7 86.3 99 140.3 110.5 1480.00 18.50 18 30 43.2 77.32
Kovalev Alexei NYR RW 78 37 40 77 -9 70 11 0 10 10 17 0 3 1 1 271 13.7 64.4 76 103.4 96.5 1782.30 22.85 22 51 39.4 76.14

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