A More Accurate ERA

The January issue of the .NET Developer's Journal will include an editorial by Jon Box where Jon is nice enough to mention my MLB Pocket Manager application as an example of using the .NET Compact Framework. Through Derek Ferguson I discovered that the CEO of Expand Beyond Corporation Ari Kaplan is also interested in baseball statistics.

Ari has done some very interesting work in evaluating pitchers (especially relief pitchers), work that Orioles, Expos, and Padres paid him to do. In short Kaplan devised at least three measures:

• RE (Reliever's Effectiveness) - the number of runs a pitcher allows in a given situation divided by the number of runs expected. This stat is based on run expectancy tables like the one I used to build my pocket manager. The reason this stat is useful is that some pitchers enter a game more frequently with runners on base and some without. After all, ERA was devised during a time when most starters completed their games as shown in the following graph. The percentage of complete games today is down around 4.5%.

• PERA (Potential ERA) - what the pitcher's ERA would be if none of the runners on base when he left the game scored
• WERA (Worst Case ERA) - what a pitcher's ERA would be if all runners he left on base scored

To these I'll add two other independent measures that can be used to evaluate pitchers:

Component ERA (CERA)

Definition: A statistic that estimates what a pitcher's ERA should have been, based on his pitching performance.
ERC=(((H+BB+HBP)*PTB)/(BFP*IP))*9-.56

PTB in the formula is calculated as:
PTB=.89*(1.255*(H-HR)+4*HR)+.56*(BB+HBP-IBB)

When intentional walk data is not available you can use:
PTB=.89*(1.255*(H-HR)+4*HR)+.475*(BB+HBP)

Also, if the ERC is less than 2.24 the formula is adjusted as follows:
ERC=(((H+BB+HBP)*PTB)/(BFP*IP))*9*.75

History: The formula here is at it appears in the 2004 edition of The Bill James Handbook.

Expected ERA (XERA)

Description: xERA represents the expected ERA of the pitcher based on a normal distribution of his statistics. It is not influenced by situation-dependent factors. xERA erases the inequity between starters' and relievers' ERAs, eliminating the effect that a pitcher's success or failure has on another pitcher's ERA. Similar to other gauges, the accuracy of this formula changes with the level of competition from one season to the next. The normalizing factor allows us to better approximate a pitcher's actual ERA. This value is usually somewhere around 2.77 and varies by league and year.

XERA = (.575 * H/9 ) + (.94 * HR/9 ) + (.28 * BB/9 ) - (.01 * K/9 ) - Normalizing Factor

History: By Gill and Reeve as found on http://www.baseballhq.com/. No formula for calculating the Normalizing Factor is found on the site.