# Summing up Game Score

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:

Num | Name | GS |
---|---|---|

1 | Clayton Kershaw | 2089.33 |

2 | Justin Verlander | 2072.66 |

3 | R.A. Dickey | 2057.33 |

4 | Felix Hernandez | 1969.66 |

5 | Matt Cain | 1947.66 |

6 | Zack Greinke | 1917.66 |

7 | David Price | 1914.99 |

8 | Gio Gonzalez | 1912.66 |

9 | Johnny Cueto | 1907 |

10 | James Shields | 1893.33 |

11 | Kyle Lohse | 1885 |

12 | Mat Latos | 1870 |

13 | Jake Peavy | 1862.99 |

14 | Cole Hamels | 1859.66 |

15 | Hiroki Kuroda | 1858.33 |

16 | Madison Bumgarner | 1837.66 |

17 | Yovani Gallardo | 1828.66 |

18 | Jordan Zimmermann | 1797 |

19 | C.J. Wilson | 1796.33 |

20 | Jason Vargas | 1787.66 |

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:

Num | Name | Runs GS |
---|---|---|

1 | Clayton Kershaw | 2077.06 |

2 | R.A. Dickey | 2049.06 |

3 | Justin Verlander | 2035.33 |

4 | Johnny Cueto | 1978.8 |

5 | Felix Hernandez | 1964.8 |

6 | David Price | 1960.39 |

7 | Matt Cain | 1953.73 |

8 | Kyle Lohse | 1940.4 |

9 | Zack Greinke | 1878.93 |

10 | Hiroki Kuroda | 1865.86 |

11 | Gio Gonzalez | 1865.73 |

12 | Jordan Zimmermann | 1842.26 |

13 | Matt Harrison | 1825.33 |

14 | Cole Hamels | 1818.13 |

15 | Jake Peavy | 1801.59 |

16 | Mat Latos | 1789.73 |

17 | Jason Vargas | 1780.93 |

18 | Jered Weaver | 1777.46 |

19 | Yovani Gallardo | 1765.6 |

20 | Cliff Lee | 1760.4 |

### 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:

Num | Name | KBB GS |
---|---|---|

1 | Justin Verlander | 1958.33 |

2 | R.A. Dickey | 1947.06 |

3 | Clayton Kershaw | 1924.06 |

4 | Felix Hernandez | 1913.8 |

5 | James Shields | 1912.06 |

6 | Zack Greinke | 1882.93 |

7 | Max Scherzer | 1874.06 |

8 | Cole Hamels | 1827.13 |

9 | Cliff Lee | 1821.4 |

10 | Ian Kennedy | 1811.33 |

11 | Madison Bumgarner | 1807.33 |

12 | Jake Peavy | 1805.59 |

13 | Matt Cain | 1796.73 |

14 | Mat Latos | 1793.73 |

15 | Johnny Cueto | 1784.8 |

16 | Yovani Gallardo | 1779.6 |

17 | David Price | 1768.39 |

18 | Adam Wainwright | 1764.46 |

19 | Hiroki Kuroda | 1761.86 |

20 | Gio Gonzalez | 1761.73 |

### 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:

Num | Name | FIP GS |
---|---|---|

1 | Felix Hernandez | 1996 |

2 | Justin Verlander | 1972.83 |

3 | Clayton Kershaw | 1965.16 |

4 | R.A. Dickey | 1906.66 |

5 | Zack Greinke | 1894.83 |

6 | Johnny Cueto | 1875.5 |

7 | Gio Gonzalez | 1856.33 |

8 | James Shields | 1842.16 |

9 | Adam Wainwright | 1802.66 |

10 | David Price | 1798.49 |

11 | Matt Cain | 1791.33 |

12 | Kyle Lohse | 1775.5 |

13 | Madison Bumgarner | 1754.83 |

14 | Cole Hamels | 1751.33 |

15 | Max Scherzer | 1738.16 |

16 | Hiroki Kuroda | 1731.16 |

17 | Mat Latos | 1723.33 |

18 | Jake Peavy | 1720.49 |

19 | Cliff Lee | 1719.5 |

20 | Jordan Zimmermann | 1718.16 |

### 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:

Num | Name | LWTS GS |
---|---|---|

1 | Clayton Kershaw | 2080.39 |

2 | Justin Verlander | 2035.99 |

3 | R.A. Dickey | 1984.39 |

4 | Felix Hernandez | 1943.8 |

5 | Matt Cain | 1919.39 |

6 | Gio Gonzalez | 1918.4 |

7 | Kyle Lohse | 1869.4 |

8 | Johnny Cueto | 1865.8 |

9 | David Price | 1848.39 |

10 | Zack Greinke | 1837.59 |

11 | James Shields | 1824.39 |

12 | Mat Latos | 1818.39 |

13 | Jake Peavy | 1804.59 |

14 | Madison Bumgarner | 1801.99 |

15 | Hiroki Kuroda | 1793.19 |

16 | Cole Hamels | 1759.8 |

17 | Jered Weaver | 1754.79 |

18 | C.J. Wilson | 1735.6 |

19 | Jordan Zimmermann | 1726.6 |

20 | Adam Wainwright | 1701.8 |

### 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.

Num | Name | Avg GS |
---|---|---|

1 | Clayton Kershaw | 2027.2 |

2 | Justin Verlander | 2015.028 |

3 | R.A. Dickey | 1988.9 |

4 | Felix Hernandez | 1957.612 |

5 | Zack Greinke | 1882.388 |

6 | Johnny Cueto | 1882.38 |

7 | Matt Cain | 1881.768 |

8 | Gio Gonzalez | 1862.97 |

9 | David Price | 1858.13 |

10 | James Shields | 1845.8 |

11 | Kyle Lohse | 1838.54 |

12 | Cole Hamels | 1803.21 |

13 | Hiroki Kuroda | 1802.08 |

14 | Jake Peavy | 1799.05 |

15 | Mat Latos | 1799.036 |

16 | Madison Bumgarner | 1789.028 |

17 | Jordan Zimmermann | 1755.656 |

18 | Cliff Lee | 1744.14 |

19 | Yovani Gallardo | 1741.292 |

20 | Max Scherzer | 1732.132 |

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.*

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Thanks for the feedback MrMan. You’re completely correct, and I should have taken more care in presenting these tables well. I’ll keep your suggestions in mind for future tables, graphs, and charts.

If you take off the 50 free points per start then you can subtract 1650 from both Kershaw and Verlander and probably others. This takes care of the comma problem for those who don’t read numbers well.

I guess another reason for the 50 points is if a pitcher starts throws one pitch that is not hit and then departs, his game score is 50. Wow!

PS> Tom Tango, Loved the original article and remembered it as soon as I clicked on the link above.

Carl’s Game Score:

Take the prior year’s winning percentage for each IP/ER combo and multiply that percentage for the correspondnig IP/ER for each start. The individual games will be a % of win earned and the sum of a pitcher’s individual games will be his total wins. Subtract starts from the adjusted wins to get Adjusted Losses.

By using entire starts, eliminates the situation where a starter is domninent one night, terrible the next yet his .500 record looks unfair due to lots of K’s, low walks, etc. Also, eliminates knuckle ballers (and other pitchers such as Hudson) who outperform their FIP.

I guess what bothers me about such efforts is the lumping into the ‘bad’ bin all walks. I’ve seen situations where the walks did turn out bad for the defense, but I tend to remember more times when the walk of a hot hitter lead to the scoreless end of the inning. Conversely, I’ve seen hits by a slow runner clog up the bases enough so that instead of being a blowout inning, a couple runs are picked up.

Some sort of different approach is needed, where the results of an inning factor back into the events.

I can’t stand decimals either, in situations like this.

—-

Heh, I guess it’s just a glitch in the way the clocks in clock sports operate, but it amuses/irks me that the timers in, say, basketball start running decimals in the last minute, and that announcers feel obligated to include them. “Time out, Lakers, with 57.6 seconds to play …” I mean, there DOES come a point when the decimals matter to actual strategy, but that point is with 3.8 or 5.1 seconds to go, and not much sooner.

Jim: we’re arguing for rounding, not truncating.

I can’t believe you would use the plot device of Superman III to make your case. (And I can’t believe they made a worse Superman movie after that one.)

Carl: you can get it at Baseball-Reference.com’s Play Index.

But, you are going to find what can be explained by PythagenPat. If league average is 4.3 runs per 9 IP, and if you have a pitcher that gave up say 1 runs in 6 IP, this is what you have:

Team Runs scored = 4.3

Team Runs allowed = 1 + 4.3/9*3 = 2.43

And that will give you a win% of 72.5%.

My game score for that is:

Game Score = 6.4*6 – 10*1 + 40 = 68.4.

Which seems close enough for a crude measure.

If my paycheck is 100.60 cents, I’d get 101$. If someone else’s paycheck is 100.40 cents, he’d get 100$. Either way, our company is paying out 201$. That’s why rounding works, because given a large enough number of employees, things will work out.

***

Carl, I just wrote this up:

http://tangotiger.com/index.php/site/article/tangos-lab-deconstructing-game-score

For those of you who don’t like decimals, would you send me everything to the right of the decimal on your pay check? If it’s not important to you, I will be able to use it. You guys are scared of number, methinks.

After admittedly scrolling rather quickly through all the discussion about decimal places, we are still left to wonder why there are any fractions in the first table. The Bill James formula always yields an integer. The sum of a column of integers should always be an integer.

Right, as I noted in the comments on my blog, I made a mistake. A team that AVERAGES allowing 2 runs will win 78% of the time, but if they allow EXACTLY 2 runs, the calculation will be different.

As for the Bill James Game Score, since the decimals are all the .33 and .66 variety, it’s clear that Matt gave out points for partial innings, which is not correct.

Apologies, I must have had an error in my formula somehow.

Thanks for all the fantastic feedback, everyone. Definitely lots of material to think about and improve on for the future.

I do love watching people fail at statistics. Makes for quite the friday night.

IIRC, sending fractions of a cent into your own account was a plot point in “Office Space.” It worked out to be a little more than the penny-ante (literally) thieves thought it would.