Summing up Game Score by Matt Hunter April 18, 2013 I’m on a bit of a pitcher evaluation kick at the moment. Just a couple of days ago, I wrote about crowdsourcing balls in play at Beyond the Box Score. More importantly, two weeks ago I had an idea: instead of measuring starting pitching performances on an inning or plate appearance basis, why don’t we evaluate them on a game-by-game basis? Since (team) wins are the end goal of a pitcher, and since each game is basically independent, we could evaluate an entire season simply by evaluating each start, and summing them up. So how do we evaluate a single start? Traditionally, we have used pitcher wins. Then, those who wanted to ignore the effect of the pitcher’s team offense thought of the Quality Start. But do we really want to say that a six-inning, three-run start (4.50 ERA) is quality? No is the answer. No we don’t. There wasn’t a great way to evaluate a single start, so Bill James, doing what Bill James does best, created something called Game Score. Here’s the formula for Game Score: Game Score = Outs + 2*(innings completed after the fourth) + strikeouts – 2*hits – 4*earned runs – 2*unearned runs – walks + 50 It was a pretty good start, but far from perfect. Weighting earned runs twice as strongly as unearned runs seems arbitrary, as does counting only innings after the fourth. I won’t get into the specifics of what’s wrong with this Game Score, because it doesn’t really matter for my purposes. But, because it will be a good reference, I’ll show you the leader board for the sum of each pitcher’s Game Score for each start in the 2012 season: NumNameGS1Clayton Kershaw2089.332Justin Verlander2072.663R.A. Dickey2057.334Felix Hernandez1969.665Matt Cain1947.666Zack Greinke1917.667David Price1914.998Gio Gonzalez1912.669Johnny Cueto190710James Shields1893.3311Kyle Lohse188512Mat Latos187013Jake Peavy1862.9914Cole Hamels1859.6615Hiroki Kuroda1858.3316Madison Bumgarner1837.6617Yovani Gallardo1828.6618Jordan Zimmermann179719C.J. Wilson1796.3320Jason Vargas1787.66 Looks like it passes the sniff test to me. Let’s move on. A couple years ago, Tom Tango introduced a few alternatives to James’ Game Score, each one based on a different method of evaluating pitchers. Let’s summarize them. Runs The first new version of Game Score cares only about runs allowed. It’s essentially the Game Score version of RA9. Here’s the formula (again, as formulated by Tango): Game Score = 6.4*IP – 10*R + 40 And the 2012 leader boards for total Game Score: NumNameRuns GS1Clayton Kershaw2077.062R.A. Dickey2049.063Justin Verlander2035.334Johnny Cueto1978.85Felix Hernandez1964.86David Price1960.397Matt Cain1953.738Kyle Lohse1940.49Zack Greinke1878.9310Hiroki Kuroda1865.8611Gio Gonzalez1865.7312Jordan Zimmermann1842.2613Matt Harrison1825.3314Cole Hamels1818.1315Jake Peavy1801.5916Mat Latos1789.7317Jason Vargas1780.9318Jered Weaver1777.4619Yovani Gallardo1765.620Cliff Lee1760.4 Strikeouts and walks Here we have the other end of the spectrum; instead of considering only runs allowed, this version is going to be based only on strikeouts and walks, and nothing else. It’s basically the Game Score version of kwERA. Game Score = 0.4*IP + 3*(SO–BB) + 40 And the leader boards: NumNameKBB GS1Justin Verlander1958.332R.A. Dickey1947.063Clayton Kershaw1924.064Felix Hernandez1913.85James Shields1912.066Zack Greinke1882.937Max Scherzer1874.068Cole Hamels1827.139Cliff Lee1821.410Ian Kennedy1811.3311Madison Bumgarner1807.3312Jake Peavy1805.5913Matt Cain1796.7314Mat Latos1793.7315Johnny Cueto1784.816Yovani Gallardo1779.617David Price1768.3918Adam Wainwright1764.4619Hiroki Kuroda1761.8620Gio Gonzalez1761.73 FIP See the previous version, but add home runs, and you have the FIP version. There’s really not too much else to say. As always, Tango’s formula: Game Score = 2.5*IP + 2*SO – 3*BB – 13*HR + 40 Leader board: NumNameFIP GS1Felix Hernandez19962Justin Verlander1972.833Clayton Kershaw1965.164R.A. Dickey1906.665Zack Greinke1894.836Johnny Cueto1875.57Gio Gonzalez1856.338James Shields1842.169Adam Wainwright1802.6610David Price1798.4911Matt Cain1791.3312Kyle Lohse1775.513Madison Bumgarner1754.8314Cole Hamels1751.3315Max Scherzer1738.1616Hiroki Kuroda1731.1617Mat Latos1723.3318Jake Peavy1720.4919Cliff Lee1719.520Jordan Zimmermann1718.16 Linear weights Last one! This time, we’re going to use a simplified version of linear weights, looking only at walks, hits and home runs. Game Score = 8.4*IP – 3*BB – 5*H – 8*HR + 40 Leader board: NumNameLWTS GS1Clayton Kershaw2080.392Justin Verlander2035.993R.A. Dickey1984.394Felix Hernandez1943.85Matt Cain1919.396Gio Gonzalez1918.47Kyle Lohse1869.48Johnny Cueto1865.89David Price1848.3910Zack Greinke1837.5911James Shields1824.3912Mat Latos1818.3913Jake Peavy1804.5914Madison Bumgarner1801.9915Hiroki Kuroda1793.1916Cole Hamels1759.817Jered Weaver1754.7918C.J. Wilson1735.619Jordan Zimmermann1726.620Adam Wainwright1701.8 Average Now, it’s almost certain that none of these versions of Game Score is perfect on its own. However, as Tango said in the article a few years ago, we can assign weights to each one depending on our goals or preferences. Unfortunately, right now, I’m not sure how to do that. Maybe that will be a project for a future article. For now, I’m going to give you the average of all four new versions of Game Score. NumNameAvg GS1Clayton Kershaw2027.22Justin Verlander2015.0283R.A. Dickey1988.94Felix Hernandez1957.6125Zack Greinke1882.3886Johnny Cueto1882.387Matt Cain1881.7688Gio Gonzalez1862.979David Price1858.1310James Shields1845.811Kyle Lohse1838.5412Cole Hamels1803.2113Hiroki Kuroda1802.0814Jake Peavy1799.0515Mat Latos1799.03616Madison Bumgarner1789.02817Jordan Zimmermann1755.65618Cliff Lee1744.1419Yovani Gallardo1741.29220Max Scherzer1732.132 This list looks good, but it is far from a perfect way to evaluate pitchers. It doesn’t take into account park or league factors, which is incredibly important. However, if you’re looking for a different way to evaluate pitchers that takes many different factors into account, this is something to consider. Conclusion There you have it. For your reference, here’s a Google Docs spreadsheet of all the versions of Game Score for every pitcher who made at least one start in 2012. Before I go, because I didn’t do a whole lot of actual analysis, here are some of my ideas at the moment for where to go next with these data: {exp:list_maker} Include park and league factors Combine these versions of Game Score with varying weights Convert Game Score to wins Look at total Game Score over a career Probably much, much more. Stay tuned! {/exp:list_maker} Thanks again to Tom Tango for the inspiration and, honestly, most of the real analysis. Also thanks to James Gentile for the Retrosheet help.