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
Let's formulate It! This is one in a series of articles on forecasting
Strat-O-Matic baseball cards. Bruce Bundy has been at h since 1968 and says
he achieves up to 95_{ }percent accuracy. But keep in mind that only
the game company has the correct formulas, that many of them rely on
statistics not readily available and that some ratings are subjective. Comments should be directed to: Let's Formulate
It!, c/o Bruce Bundy, 4474 Outlook Dr., Brooklyn, OH 44144 |
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.
EXAMPLES:
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
ERA =9*ER/IP
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