Making Sense of Formulas
By Bruce Bundy
For eight months, we have given you a dizzying array of formulas to help forecast or create hitters' cards. Undoubtedly, you are dizzier still if math is not your first language and all the parentheses, asterisks and other symbols have looked like hieroglyphics.
If so, here is some elementary instruction that will let you catch up. Like anything else, it takes a little practice. You can practice with previous issues of STRAT FAN, or just keep this guide handy next month, when we begin examining pitchers' card formulas.
The standard vehicle for baseball statistic number crunching is called a linear equation. All the statistics (batting average, slugging percentage, ERA, etc.) seen in the weekly or final statistics are the result of math performed in linear equations. Likewise, all the formulas seen in the "Let's Formulate It!" articles are linear equations.
Home-computer spreadsheet software can read and perform linear equations. It is essential to baseball statistical analysis that the user learn to read these formulas. It is quintessential that statistic formulators master these tools.
A linear equation is an equation. An equation is a mathematical statement. It must be true. A linear equation is an equation that is limited to numbers in the 1St power (no numbers to the Nth power). A linear equation shown on a graph will always be a straight line.
For example, x + ( y * 2 ) = 9 is a linear equation; x3+(y*2)=9 is not a linear equation, but is known as a quadratic equation
with multiple results.
Linear equations only use the four basic math functions: multiplication, division, addition, and subtraction. All math functions are performed in the order of these priorities:
1. BRACKETS () : There should be only as many as necessary. For every open bracket
- (- there must be a close bracket ).
Calculate the result within each bracket before calculating the portions of the formula outside the bracket.
2. MULTIPLICATION * and DIVISION /
In a linear equation without brackets, all multiplication and division must be resolved before any addition or subtraction.
3. ADDITION + and SUBTRACTION -
In a linear equation without brackets, addition and subtraction are resolved last.
On Base Percentage (OB%) = (Hits + Walks + Hit By Pitches) /( At Bats + Walks + Hit By Pitches + Double Plays)
OB% =(H+W+HBP)/(AB+W+HBP + DP)
In this formula, division must wait until all math is resolved within the brackets, even though the math is addition.
Slugging Percentage (SLUG) = ( Hits + Doubles + (Triples * 2 ) + (Home Runs * 3)) I At Bats
SLUG = (H + D + (T * 2 ) + ( HR * 3)) lAB
In this formula, there are brackets within brackets. In linear equations, each math step must be read and resolved from the deepest brackets. As a result, the multiplication is done first, followed by the addition, and then division.
Note that the singles, doubles, triples, and home runs are already counted once in the hits. A homerun, for example, is 4 bases - a hit plus 3 bases (HR *3).
Earned Run Average (ERA) =9 * Earned Runs I Innings Pitched
In this formula, there are no brackets and two math steps. Since the math in this formula, multiplication and division, have equal priority, the math sequence is interchangeable. Here, you can do any of the following:
9 * ER/IP, ER/IP * 9, or, 9/IP * ER.
The math symbols, however, are not interchangeable. You cannot 9/ ER * IP.
Further investigation should be homework for the studious mind. The CRC Math Table Manual is your source for many of life's linear equations. Most sports encyclopedias have tables explaining their use of any linear equations.
Next month: The inside look at pitchers.
Hall ofFamers' Cards Coming Next Month