http://www.whatifsports.com/mlb-l/playerprofile.asp?ID=32192829&pr=False&pl=0&type=1

Manny has a .990 OPS vs. lefties, .996 vs. righties.  His overall OPS?  .999

I guess he pounded that guy who threw with his foot...

Just one of those funny things that happen in math sometimes when you combine averages.

Here's another one (I made these numbers up, but I've seen it before in real life).

Player A hits .200 vs LHP and .300 vs RHP.
Player B hits .225 vs LHP and .310 vs RHP.

So player B hits better against both LHP and RHP.

But player A hits better overall: .267 vc .253.

How?  Player A is 20-100 vs LHP (.200) and 60-200 vs RHP (.300), so overall 80-300 (.267)
Player B is 45-200 vs LHP (.225) and 31-100 vs RHP (.310), so overall 76-300. (.253).

Or try this one...you drive 60 miles in one direction averaging 30 MPH.  How fast do you have to drive on the return trip in order to average 60MPH for the trip as a whole?  Answer: you can't do it.  In order to average 60 MPH for the whole trip (120 miles) you have to do the whole thing in 2 hours.  But you used up your 2 hours in the first leg.  No matter how fast you drive on the return trip, your overall average speed will be less than 60 MPH.

Posted by dahsdebater on 8/12/2011 3:25:00 PM (view original):
http://www.whatifsports.com/mlb-l/playerprofile.asp?ID=32192829&pr=False&pl=0&type=1

Manny has a .990 OPS vs. lefties, .996 vs. righties.  His overall OPS?  .999

It is because the components of OPS do not have a common denominator.  A combined avg, obp and slg must always fall between the left and right components.  However since ops is average plus slugging and each component has a different porportion from the left or right side OPS does not have to be between OPSr and OPSl. 

i don't think that is what it is

Posted by bagchucker on 8/15/2011 7:05:00 PM (view original):
i don't think that is what it is

If you are refering to my post, I acn explain further.  Any straight average (e.g. avg, slg, obp) will always be between to right and left components.  That should be intuitive, but can be proven:
let...
a = avg
b= avg  vs rhp
c = avg vs lhp
x = porpotion of ab (or pa) against rhp

a = bx + c(1-x)
a = bx + c -cx

b > a   and c > a
b > bx + c - cx                      c > bx + c - cx 
b - bx > c - cx                        0 > bx -cx
b (1-x) > c (1-x)                    cx > bx
b > c                                        c > b

Obviously b> c and c>b are mutualy exclusive and this proves a can't be less than both b and c.  You could reverse the ">" to a "<" and prove a can't be greater than both b and c.

The same concept doesn't apply for OPS because obs and slg have differenr denominators.
a = obp
b= obp  vs rhp
c = obp vs lhp
x = porpotion of pa against rhp
d = slg vs rhp
e = slg vs lhp
y = porportion of ab against rhp
z = ops

ops vs rhp = b+d
ops vs lhp = c+e

z = (bx + c - cx) + (dy + e -ey)

b+d > z   and c +e > z                              
 
b +d > (bx + c - cx) + (dy + e -ey)                    c+e > (bx + c - cx) + (dy + e -ey)
b-bx + d-dy > c-cx+e-ey                                        0 > bx-cx+dy-ey
b(1-x)+d(1-y) > c(1-x)+e(1-y)                           cx+ey > bx+dy

These two equations only contradict when  x=y.  So like I said as long as a player has a different number of PA and AB, his OPS doesn't need to fall between the left and right components.

What a nerdfest

A more succinct answer would be that WIS just screwed up the formula somewhere.

Occam's Razor and all...

Posted by toddcommish on 8/16/2011 4:52:00 PM (view original):
A more succinct answer would be that WIS just screwed up the formula somewhere.

Occam's Razor and all...

Um, no the formula isn't screwed up.