## Wednesday, February 20, 2013

### The slugging percentage and walks.

Question:  The table below has Miguel Cabrera’s hitting statistics for 2012.  Find the definition of slugging percentage on the web and calculate Miguel Cabrera’s 2012 regular season slugging percentage.

Assume that a walk has the same value as a single.  Create a modified slugging percentage that incorporates information about walks.  Calculate this slugging percentage for Miguel Cabrera.

Why might a walk have a lower value than a single?   Assume that a walk is worth 50% of a single. Calculate a modified slugging percentage for Miguel Cabrera based on this assumption.

 Miguel Cabrera Hitting Statistics 2012 Games played 161 At Bats 622 Runs 109 Hits 205 Doubles 40 Triples 0 Homers 44 RBIs 139 Walks 66 Strike Outs 98 Stolen Bases 4 Caught Stealing 1 Hit by Pitch 4 Sacrifice fly ? On Base Percentage ? Slugging Percentage ?

Answer:    The formula for the slugging percentage is total bases divided by at bats

SLG=TB/AB=(1XB+2X2B+3X3B+4X4B)/AB

Where B is the number of bases obtained on a hit. ( B=1 for a single, 2 for a double, 3 for a triple and 4 for a home run.)

Plugging in Miguel Cabrera’s 2012 numbers we get:

SLG=(1X121+2X40+3x0+4X44)/622

SLG=0.606

A modified slugging percentage that incorporates information on walks would add the number of walks in the numerator and the number of walks in the denominator.

SLGM=(TB+W)/(AB+W)

SLGM=(377+66)/(622+66)

SLGM=0.644

A walk is probably worth less than a single because many walks are intentional.  When an intentional walk is granted with two outs and players in scoring position a pitcher can get out of a jam if he or she gets the next (presumably weaker hitter) out.

One way to modify the slugging percentage is to assume a walk is worth 50% of a single.  A formula consistent with this assumption is

SLGM2=(TB+0.5XW)/(AB+0.5XW).

Plugging in the numbers I get

SLGM2=0.626

A second pair of eyes is always useful.  Please check my work.

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