Sabermetric Primer: GSC

February 24, 2010 3:43pm CST

What is a well pitched game? I attempted to address this issue in a previous set of articles dealing with the idea of Quality Starts. Part I dealt with Quality Starts, whereas Part II spoke to Quality Start Percentage. In what follows, I will continue my review of measures that attempt to quantify just what should be considered a "good" start by taking a look at a measure called Game Score (GSC).


GAME SCORE DEFINED
Just how do you explain or quantify what a good game pitched is? Is a complete game (CG) with zero earned runs and four strikeouts a better performance than a complete game with 12 strikeouts and two runs allowed? Writers and fans have spent years trying to answer this question, and while there is still no clear-cut answer, the father of sabermetrics, Bill James, has invented a way that he, and many others, believe can be used to quantify a pitcher's performance. The metric, Game Score, attempts to do just that by quantifying performances based on one continuum.

Here is the formula for GSC.

Start with 50 points.

Add 1 point for each out recorded, (3 points per inning).
Add 2 points for each inning completed after the 4th.
Add 1 point for each strikeout.
Subtract 2 points for each hit allowed.
Subtract 4 points for each earned run allowed.
Subtract 2 points for each unearned run allowed.
Subtract 1 point for each walk.

That definition will certainly lead to some battles with a spreadsheet, but it's still pretty straightforward, isn't it? For those of you are mathematically inclined here is GSC expressed as an equation:

50 + Outs + 2(IP after the 4th) + K - 2(hits) - 4(ER) - 2 (UER) - BB

*UER = Unearned Runs


2009 GAME SCORE LEADERS

So GSC quantifies what it means to pitch a great game by taking out the subjective conjecture and replacing it with a tangible formulaic equation. With that straight forward explanation of what the metric measures, let's spend a moment listing the 2009 GSC leaders. Here are the top-10 pitching performances in each league in 2009.

AL	DATE	IP	H	R	ER	BB	SO	GSC
Mark Buehrle	23-Jul	9	0	0	0	0	6	93
Justin Verlander	8-May	9	2	0	0	2	11	92
Jeff Niemann	3-Jun	9	2	0	0	1	9	91
Roy Halladay	4-Sep	9	1	0	0	3	9	91
Brett Anderson	6-Jul	9	2	0	0	2	9	90
Zack Greinke	30-Aug	9	1	0	0	1	5	89
Jon Lester	6-Jun	9	2	1	1	2	11	88
Josh Beckett	12-Jul	9	3	0	0	0	7	88
Zack Greinke	24-Apr	9	3	1	0	1	10	88
Scott Baker	14-Aug	9	2	0	0	0	5	88

Not surprisingly, the best mark in the Junior Circuit belonged to a guy who threw a perfect game. You'll also notice that AL Cy Young winner Zack Greinke appears on the list twice.

PITCHER	DATE	IP	H	R	ER	BB	SO	GSC
Jonathan Sanchez	10-Jul	9	0	0	0	0	11	98
Chris Carpenter	7-Sep	9	1	0	0	2	10	93
Cliff Lee	19-Aug	9	2	1	0	0	11	92
Cole Hamels	1-Sep	9	2	0	0	1	9	91
Tim Lincecum	29-Jun	9	2	0	0	0	8	91
Aaron Harang	12-Apr	9	3	0	0	0	9	90
Carlos Zambrano	25-Sep	9	2	0	0	1	8	90
Yovani Gallardo	29-Apr	8	2	0	0	1	11	88
Chris Carpenter	25-May	8	2	0	0	0	10	88
Dan Haren	10-Jul	9	4	0	0	1	10	88

The NL leader, the one who produced the best GSC mark in baseball last year, was the Giants' Jonathan Sanchez. He didn't pitch a perfect game, but he did pitch a no-hitter in which he struck out 11 Padres' batters.

*** Every game but one on the lists ended up in a win for that pitcher. Chris Carpenter was saddled with a no-decision in his May 25th outing.

*** Only two outings on the list were efforts that lasted less than nine innings. Carpenter's no-decision went eight innings, the same as the effort from Yovani Gallardo against the Pirates.

*** Only one hurler allowed an earned run in his outing, as Jon Lester permitted one to the Rangers. Two others allowed an unearned run: Greinke on April 24th and Cliff Lee against the D-backs.

*** Six of the 10 outings in the NL had double-digit strikeout efforts, while only three in the AL did.

A quick glance over these two lists gives you a bunch of household names that were drafted in every fantasy league last season, but there were a few outings produced by hurlers who would have found it difficult to crack a fantasy roster in a standard mixed league at the start of last season (Sanchez, Jeff Niemann and Brett Anderson certainly belong on that list). However, because any flunky can have a one great outing, GSC really is nothing more than a cute tool you can use to gauge one performance against another. Moreover, since GSC only records individual games, it isn't really a tool you can use to gauge a pitcher's overall effectiveness, which got me to thinking - why not just take the next step and do the obvious, which is apply GSC to the whole season?


AVERAGE GAME SCORE SEASON

If we are going to bother to record individual Game Scores, why shouldn't we try to do the same thing for the whole season? Average Game Score Season (AGSS) is nothing more than just what it says. AGSS measures what each pitcher's average GSC was for each start he made over the entire year. Here is the formula for AGSS.

AGSS = [(GS x 50) +Outs+2(IP after the 4th)+K-2(Hits)-4(ER)-2(UER)-BB] / GS

The resulting number from this equation is then divided by the number of starts the pitcher made to come up with his AGSS.

Note: If you are interested in seeing the equation actually worked out, see the end of this story for an example.

With that explanation of the metric, let's move right into the leaderboard for 2009.


2009 AGSS LEADERS, THE TOP-26

*This survey took into account every pitcher who made at least 20 starts in 2009.

Pitcher	AGSS	Pitcher	AGSS
Tim Lincecum	64.55	Tommy Hanson	57.83
Zack Greinke	63.51	Jon Lester	57.36
Chris Carpenter	62.12	CC Sabathia	57.35
Javier Vazquez	61.96	Josh Johnson	57.33
Felix Hernandez	60.98	Jair Jurrjens	57.12
Dan Haren	60.84	Ubaldo Jimenez	57.00
Roy Halladay	60.38	Johan Santana	56.85
Adam Wainwright	59.44	Randy Wolf	56.75
Justin Verlander	58.74	Wandy Rodriguez	56.62
Clayton Kershaw	58.50	Yovani Gallardo	56.28
Ted Lilly	58.44	Cliff Lee	55.66
J.A. Happ	58.39	Josh Beckett	55.43
Matt Cain	58.13	Matt Garza	54.72

The top of the list is populated by exactly the names you would expect to see. The two Cy Young winners finished 1-2, and NL ERA leader, Chris Carpenter, comes in third. In the fourth spot is new Yankee Javier Vazquez, who really did pitch excellently last year no matter which measure you look at (2010 might be a different story). Rounding out the top-5 is King Felix, another well earned addition to the top of the heap.

Dan Haren comes in sixth. If not for his traditional second half fade he would have been higher.

The new Phillies' ace, Roy Halladay, is next in line, just ahead of the other Cardinal on the leader board, Adam Wainwright.

The leagues most potent strikeout arm belonged to Justin Verlander, and he just finished ahead of the power arm that belongs to Clayton Kershaw which I reviewed yesterday in my Breaking Down piece.

I was surprised to find Happ finish ahead of another rookie, Tommy Hanson. Just goes to show you that not all measures relate to the fantasy game.

Overall there are nine lefties on the list. Long live the southpaw.

Some notable omissions from the AGSS leaderboard include the following hurlers.

John Lackey (53.17, 35th overall) - The Red Sox would be happy with a repeat effort this season, though it is a bit shocking to see that he finished last season with the same mark as Carlos Zambrano, who didn't really tear it up.

Rich Harden (53.12, 37th) - Obviously his stuff is not indicative of his placement on the list. The reason he fell so far down is obvious to all - he just didn't throw enough innings (141).

Jonathan Sanchez (52.95, 40th) - The single-game leader for last year falls way down the season list due to his up and down efforts.

Scott Baker (52.36, 44th) - A sneaky play in 2010, that outside ball yard in Minnesota could help him to curtail his home run tendencies a bit. If so, he could easily be a top-20 hurler.

Cole Hamels (51.54, 53rd) - There's no sugar coating it - last year was a disappointment for the lefty. He finished behind such luminaries as Kevin Millwood (52.24) and Barry Zito (51.85) last year.

James Shields (51.31, 55th) - He suffered a slight misstep last year but was still plenty good enough to be a middle of the rotation arm. He finished a smidgen ahead of Mr. Perfect Game, Mark Buehrle (51.29).

Brett Anderson (51.19, 57th) - Anderson is Fantasyland's preseason darling this season after a wonderful second half last year. He was slightly better than another lefty, veteran Yankee hurler Andy Pettitte (50.67).

Ricky Nolasco (50.71, 59th) - He was far too uneven in his performance last season and that resulted in a poor mark here.

Rick Porcello (49.30, 71st) - As with other measures, he just doesn't profile as a pitcher of note, though that is drastically different than what he actually provides the Tigers when on the field.

The three worst pitchers who made at least 20 starts last season? Not a big surprise if you scan the stats from last season: Manny Parra (40.78), Fausto Carmona (40.49) and Jason Berken (39.26).


So there it is. A brief look into the world of Games Scores. While AGS and AGSS may not be something you use to argue the strength or weakness of a pitcher with your league mates, it can help you in determining the relative consistency of a pitcher that you might consider for fantasy staff this year. Consistency is a wonderful thing, and hopefully this measure will give you some insight into how to best roster men that can help you to attain that on your fantasy squad.


AVERAGE GAME SCORE SEASON - EQUATION

STEP I
You begin with the games started total of a pitcher. Pedro Martinez started 31 games in 2005. Here are his pitching numbers from that campaign: 217 IP (651 Outs), 208 Ks, 159 Hits, 68 ER, 69 Runs (therefore 1 UER), 47 BB

STEP II
The next step in the process is to take the GS total and multiple that number by 50 (since the original GSC starts out with a baseline of 50).

GS (31) x 50 = 1550, which equals our GSC Points for the Season.

STEP III
For the IP after the 4th inning you would figure out the total like this:

2 [IP - (GS x 4)]
Pedro pitched 217 innings.
2 [217 - (31 X 4)]
2 [217-124]
2[93] = 186
186 points for IP after the 4th inning for the equation.

STEP IV
Simply figure the pitchers' AGSS for the entire season.

Pedro:
= 1550 + Outs + 2(IP after the 4th)+K- 2(Hits) - 4(ER)- 2(UER)- BB
= (1550 + 651 + 2[186] + 208)- 4(68) - 2(1) - 47- 2(159)
= 2201 + 394 - 272 - 2 - 47 - 318
= 2595 - 639
= 1956

STEP V
You then take the final number from Step IV and divide that by the Games Started total in order to arrive out our final score...our Average Game Score Season (AGSS).

Pedro: 1956 / GS 31

AGSS = 63.1

What AGSS says is that for each start Pedro made in 2005, his Average Game Score was 63.1.


One last note. The numbers used for innings pitched after the 4th inning are "guesstimates." I worked under the assumption that in every game the pitcher was on the mound he threw at least four innings, so I multiplied each hurlers games started total by four in order to find out how many innings pitched he had that exceeding the 4th inning. Obviously, this is not the case in all instances, as sometimes outings don't even last four innings, so if you would like to make this part of the equation more accurate, simply go through each pitchers game log to find out which games he did not pitch at least four innings and make the necessary adjustments to his innings pitched "bonus" point total.