# The Hardball Times

## Pitching Runs Created Again

by David Gassko
January 27, 2006

Friday’s article on Pitching Runs Created generated many questions and comments, so instead of, as one blog put it, coming up with a new statistic for every week of the year, I’m going to try to answer some of the most common questions about PRC, and hopefully give you a better idea of what they are and what they mean.

So what are Pitching Runs Created, exactly?

Pitching Runs Created take a pitcher’s performance and find his expected number of wins. That number is then translated to the number of runs an offense would have had to score to have the same winning percentage in the same number of “games.”

Why are they useful?

Pitching Runs Created is the first pitching metric that acknowledges and adjusts for the fact that a run saved is not equal to a run scored. Let’s say we’re in a league where the average team scores five runs a game. You can choose a pitching staff that allows one run per game, or a lineup that will score 9. Which one do you go with? The pitching staff, right, because the only way you can lose is to get shut out?

But a metric like Runs Above Average will tell you that the two are equal: Both the lineup and the pitching staff are 4 Runs Above Average. However, if you choose the pitching staff, you end up winning 93.6% of your games, while with the offense you’ll only win 77.8%. That’s where Pitching Runs Created come in; they establish the offensive equivalency of a pitcher.

How are they calculated?

Well, I’ve actually changed the process ever-so-slightly, but here’s a step-by-step example:

1. Find a player’s custom Pythagorean exponent. The Pythagorean theorem in its basic form is RS^2/(RS^2 + RA^2) = W%. But in reality, depending on the run environment, the exponent you want to use will vary. It’s not always two. In fact, on average it’s 1.9. So I raise a pitcher’s run environment, which is simply the league average runs scored per game plus his runs allowed per game, to .287, and use the result as my exponent. This process was originated by US Patriot and David Smyth. For example, Johan Santana had a 2.99 RA and the average AL offense scored 4.76 runs per game. So Santana’s run environment is 2.99 + 4.76 = 7.75, and his custom exponent is 7.75^.287 = 1.8.

2. Find a player’s expected win percentage. That’s pretty straightforward: I use the Pythagorean win percentage with a custom exponent. For runs scored, I insert the league average runs scored per game. So what we’re looking at here is a pitcher’s win percentage with an average offense. Santana’s expected win percentage would be 4.76^1.8/(4.76^1.8 + 2.99^1.8) = .698.

3. Convert that win percentage to a runs scored per game number. This is the key to Pitching Runs Created. I’ve algebraically played around with the Pythagorean formula to figure out how to do this in one step. Santana’s offensive equivalent would be a team that scores 7.58 runs per game.

4. Multiply that runs scored per game number by (Innings Pitched)/9. That should be pretty straight-forward.

5. Adjust for defense. At first, I was making two adjustments—one earlier in the process for batting average on balls in play—but I have re-thought the BABIP adjustment and am taking it out until I have a better grasp of what I want to do with that. And since PRC is very much a value method, maybe BABIP shouldn’t play into the equation at all.

Anyway, the one adjustment I do make is for strikeouts per nine innings. My findings indicate that pitchers have more control over their RA at higher strikeout per nine innings levels, and therefore should get more credit. Studes has made similar findings. Anyway, I fitted a curve to my data to find out precisely how much credit pitchers should get at various strikeout per nine innings levels. Since some have asked to see it, here’s a graph of it:

The average pitcher will get about 69% of all credit. Major league pitchers will generally range from about 60%-85%.

So does this mean we have a statistic that we can use to compare pitchers directly to offensive players?

Yes and no. Obviously, PRC come out in the same format, and with roughly the same range as Runs Created for hitters. But if you’re using a correct Runs Created version (or any other system that is linear), you’ll find out how many runs a player is responsible for in the context of his or an average lineup.

Strangely enough, you want to use the wrong Runs Created to compare to pitchers, OBP*SLG*AB, because we’re saying how much would a lineup have to score to win as often as a given pitcher. So on the flipside we want to know how many runs a lineup of a given offensive player will score.

The easiest thing to do is to convert PRC, and a batter’s line, into wins.

What do Pitcher Runs Created tell us about Win Shares?

Well mainly, I think, Pitching Runs Created give insight as to why Win Shares work the way they do, and where the limits of Win Shares fall apart. First of all, it’s easy see why Bill James decided on a 48/52 split for offense and defense. Because, in the context of an otherwise average team, a run saved is worth more than a run scored, using a straight 50/50 split will tend to undervalue good pitching (and fielding, for that matter). A better ratio is 52/48, though, as Pitching Runs Created demonstrates, not perfectly.

When you’re dealing with a player like Johan Santana, though, all that gets thrown out the window. He’s so good that any linear system—as Win Shares are—won’t work with him. James uses many machinations to try and get around that issue, like the 52/48 split, and like using marginal runs, which allow extra credit to be allocated to better players. But when it comes to judging extreme pitchers (and we’re generally only interested in the great ones, aren’t we?), Win Shares break down.

So what’s next?

While Pitching Runs Created are fun to use, I’m working on a simpler but more important system that will express everything in wins and losses using the same basic methodology. See, Pitching Runs Created and the system I’m working on now are value methods. They don’t tell us anything about future performance; they judge past play. And just like you wouldn’t compare Barry Bonds’ Runs Created to Carl Yaztremski’s, you can’t compare Pedro Martinez’s Pitching Runs Created to Sandy Koufax’s.

And anyway, all that matters in baseball are wins and losses. So my plan is to apply my system to every year in history, and then, we’ll see where it goes from there. For now, here’s a list of 12 randomly selected great seasons, ordered by Wins Above Average using my system (Credit refers to the percentage of credit for their accomplishments I assign to each pitcher based on strikeout rate).
```playerID yearID   teamID   lgID     W%       PRC      Wins     Losses   WAA      Credit
Radbourn 1884     PRO      NL       0.769    512      40.93    12.29    14.32    0.706
Johnson  1913     WAS      AL       0.833    241      23.05    4.62     9.22     0.72
Gibson   1968     STL      NL       0.796    180      20.49    5.25     7.62     0.761
Pedro    2000     BOS      AL       0.867    250      17.45    2.68     7.39     0.835
Koufax   1966     LAD      NL       0.76     197      21.3     6.72     7.29     0.781
Cy Young 1901     BOS      AL       0.775    249      20.21    5.87     7.17     0.632
Clemens  1997     TOR      AL       0.803    226      18.92    4.64     7.14     0.803
Carlton  1972     PHI      NL       0.727    190      21.37    8.02     6.68     0.764
Cy Young 1892     CLE      NL       0.709    240      21.72    8.92     6.4      0.609
Pedro    1999     BOS      AL       0.809    209      16.43    3.88     6.28     0.857
Grove    1931     PHI      AL       0.771    203      17.15    5.09     6.03     0.694
RJ       2002     ARI      NL       0.707    166      16.98    7.04     4.97     0.831```

David Gassko is a former consultant to a major league team. He welcomes comments via e-mail.