Confused about PX index explanation in MW

[Kneale]

"Even more worrisome, though, is Guzman's declining power trend. Remember that PX is an index, where 100 is league average. Currently, nearly half of all batters in the Majors are hitting with more authority that Guzman. "

If 100 is the average, then by the above definition wouldn't about half the players be over 100 and half under? If so, wouldn't Guzman's 2004 PX of 53 indicate that a much higher than 50 percent of the players would hit with more authority than Guzman?

Just when I thought I finally was getting the handle on all the toolbox stuff, this pops up. Drat! Can someone show me where my logic is off?

Thanks,
Kneale

[PD@HQ]

Because for there to be an even split of players above and below 100 PX, it would have to be a median of leaguewide LWPr, and it is not. Nor is it an "average" in the sense that you can calculcate it by summing all the LWPr scores and divinding by the number counted.

100 PX is an aggregate league LWPr, the result of the formula for LWPr applied to the totals of all players' ABs, 2Bs, 3Bs and HRs.

Imagine a league where you have Barry Bonds and nine copies of Endy Chavez. Bonds' LWPr in 2003 was 76, Chavez' was 23.

The average LWPr for this league is 28 (it is not the average of the 10 LWPrs above, as noted above). Bonds in this league would have a PX of 271 (76/28*100), while all the Endys (Endies?) would have PXes of 82. One super slugger pulls the aggregate LWPr (and therefore the 100-level PX) upwards and leaves all the Endys (Endies?) under the bar.

In fact, a quick check of AL 2003 shows 112 players over 100 PX and 185 under, which isn't unusual considering the upward pull from the relatively few sluggers versus the dilutive effect of the many banjo-hitting others. The aggregate AL LWPR was 33.6, but the median (the value at which half of all players are above and half below) was 29. As it happens, the average was also 29.

PX is meant to standardize the metric year-over-year, not to compare players within years to some "average" standard.

[Kneale]

Kneale

Davitt,

It took a few read throughs, and I'm still not quite there, but the picture is looking a more clear with regards to this PX thing and the whole "average" issue. I'm going to keep playing with the numbers.

Here's another question that may help me with understanding the explanation on Guzman:

How can I figure out that half of the league has a PX above 53? Or that y% of the league has a PX above z?

Thankx,
Kneale

[PD@HQ]

Re: Kneale

Originally posted by Kneale
How can I figure out that half of the league has a PX above 53? Of that y% of the league has a PX above z?

You can't do it by formula because it changes with every PA. But if you have the data in an Excel sheet, say the PX numbers are in column AB from row 3 to 290, then go to another cell and enter:

=MEDIAN($AB$3:$AB$290)

and that will give you the value at which half the players are above and half below.