There are many of ways to estimate runs. If you want to find out how many runs a team should have scored, for example, you can use estimated runs produced (ERP), extrapolated runs (XR), or one of many runs created (RC) formulas . If you want to find out how many runs a picher should have given up, you could use component ERA (CERA) or expected ERA (XERA) formulas. Most of these approaches, however, are only useful because they have been tweaked to work in the major league context. These methods are not robust and tend to fall apart when applied to other contexts or extreme examples of run production. David Smyth once pointed out that if a team hits 500 consecutive home runs, James' RC method estimates about 2,000 runs scored although we know the team would score about 500 runs.

Base Runs, in contrast, is a technique for run estimation that actually models the run scoring environment and is accurate in a wide range of contexts. The formula can be described this way:
Runs = Baserunners * The Proportion of Baserunners Who Score + Home Runs

This model is commonly used to estimate team run totals, but it can also be used to estimate how many runs a pitcher will surrender. This is exactly what BsRA9 is designed to do; use component statistics (suc as hits, walks, and home runs) to estimate how many runs allowed a pitcher will give up over nine innings.

Method
Base Runs Allowed per 9 innings (BsRA9) = ((A * (B/(B+C)) +D)/IP)*9
A = H + BB - HR
B = (1.4*(1.12*H + 4*HR) -.6*H -3*HR +.1*BB) * 1.1
C = 3*IP
D = HR

The base run run estimates reported on this site are constructed with a league-specific B multiplier. At the MLB level, the 1.1 value in the above formula is usually about right. There is notable variability across leagues and years, but the B multiplier is usually close to 1.15 in AAA leagues, 1.2 in AA leagues, and 1.3 in A leagues.

For example, Chien-Ming Wang allowed 4.49 runs per nine innings in 2005. If we want to estimate how many runs he should have allowed in a neutral situation, we can plug his component numbers into the above formula. The B multiplier for the AL in 2005 is 1.11, so his BsRA would look like this:
BsRA = (113 + 32 - 9) * ((1.4*(1.12*113 + 4*9) -.6*113 -3*9 +.1*32) * 1.11) / (((1.4*(1.12*113 + 4*9) -.6*113 -3*9 +.1*32) * 1.11) + (3 * 116.33)) + 9

That gives you an estimate of total runs allowed (about 50 runs). When you divide the above estimate by number of innings pitched and divide by nine, the result is the expected runs allowed per nine innings. In Wang's case, the BsRA9 statistic suggests he should have allowed 3.84 runs per nine innings, a figure that is signficantly lower than the 4.49 runs he did allow.

Situational factors determine whether or not a pitcher will actually more or fewer runs allowed than the model predicts, but BsRA9 is a better indicator of the pitchers' ability than other descriptive statsitics, including runs allowed per nine innings (RA9). I believe it is the best contemporary run estimator, and I believe BsRA9 is the single best estimate of a pitcher's ability to prevent runs.

Application
Although this is really a descriptive statistic, BsRA9 may also be somewhat predictive because it allows us to see which pitchers were luckier than others. If you divide a pitchers' expected runs allowed (as measured by BsRA9) by the actual runs allowed, you get the BsRA%. This is also listed in the statistics tables on this site. Most pitchers' BsRA9 estimate is very similar to actual RA9, so most BsRA% are close to 100. A low BsRA% (below 90) suggests an unlucky pitcher allowed more runs than predicted by the BsRA9 estimate. A high BsRA% (above 110) suggests a lucky pitcher allowed fewer runs than expected. In general, we would expect these pitchers to give up more runs in the future. As a simple assessment of this claim, the following table lists MLB starting pitchers with the highest BsRA% in 2004 and describes how they fared in 2005.

Pitcher	2004 RA9	2004 BsRA9	BsRA%	2005 RA9	2005 BsRA9
J. Peavy	2.65	3.42	129%	3.10	3.06
O. Hernadez	3.30	4.10	124%	5.30	5.34
J. Marquis	4.02	4.91	122%	4.78	4.69
J. Kennedy	3.77	4.54	120%	6.71	6.23
C. Silva	4.43	5.24	118%	3.97	4.42
R. Lopez	3.74	4.41	118%	5.42	5.18
T. Ohka	4.25	4.99	117%	4.39	4.64
J. Lima	4.28	4.99	117%	7.47	6.87
Z. Greinke	3.97	4.66	117%	6.15	5.88
R. Ortiz	4.50	5.12	114%	5.78	6.15

All but one pitcher, the enigmatic Carlos Silva, gave up more runs per nine innings in 2005. The BsRA9 estimate was a better predictor of runs allowed in the next year than actual runs allowed. Furthermore, the table suggests this estimator is useful for a wide range of pitchers, including the very good (Peavy) and the very bad (Lima). Although more work is needed to establish the predictive validity of BsRA9, this evidence suggests BsRA9 can be used to evaluate which pitchers were lucky and unlucky in any given year.

By now I'm sure you expect me to tell you who were the luckiest pitchers in 2005. Or you might be wondering which minor league pitchers may be underrated because of unusually high runs allowed totals. Or maybe you want to know who the best candidates are to allow fewer runs in 2006. We will explore these question in the coming weeks. For now, I'll just warn you to be wary of Tim Hudson. Oh, and don't dismiss Homer Bailey; his 2005 season was better than his runs allowed total suggests.