## Friday, March 1, 2013

### Slugging percentage comparisons can be tricky

Often there are subtle differences in questions.  Consider these two problems.

Question One:  After 100 at bats a hitter has 15 singles, 5 doubles, 1 triple and 3 homeruns.  His slugging percentage last year was 25% higher than his current slugging percentage at this point in the season last year.  What was his slugging percentage at this point in the season last year?

Answer:  His current slugging percentage after 100 at bats is

SLGP=(15x1+5x2+1x3+3x4)/100

SLGP=(45/100)=0.450

His slugging percentage last year was

LYSLG =0.450x(1+0.250)=0.5625.

Question Two:  A batter’s slugging percentage was 25% below its level from the previous year.  His current slugging percentage is 0.450.  What was his slugging percentage last year?

Answer:  The slugging percentage last year is denoted by LGSP

0.450=(1-.25)xLGSP

LGSP=0.450/0.75

LGSP=0.600.

(NOTE THAT 25% OF 0.600 IS 0.150 AND THAT 0.600-0.150 IS 0.450.)

Why the difference?

A 25% drop from last year’s high slugging percentage is a larger decline than a 25% increase from the current lower level.

0.25 X 0.450 < 0.25 X 0.600

Is this explanation clear?

If not help me improve it!!!!!