## Calculating Z score for batting average

Moderator: Baseball Moderators

### Calculating Z score for batting average

I checked out a link with tangos instructions for calculating, but am having trouble following how he calculates the z for batting average.

For HR's, sb's etc I;m taking (projection-mean for group)/SD for group

I understand with avg (as with era or whip) the number of ab's should be a factor.

Can someone clarify?
Mike_nyc
College Coach

Posts: 326
(Past Year: -2)
Joined: 21 Mar 2006
Home Cafe: Baseball

### Re: Calculating Z score for batting average

Good question. Yes, the AB's need to be counted. Player A who has a .320 average over 200 ABs might actually contribute less than play B who has a .310 average over 600 ABs.

I'll tell you what I do, would be interested in hearing if others have different methods. I assume I already have the rest of my team in place, and it's a completely league average team. That would be about a .270 average. Say I already had 10 hitters in place averaging 500 ABs. That would be 5000 AB for my team, at .270, they would have 1350 hits. The numbers for average change a bit using different roster sizes, so I change the formula based on the league I want values for.

So for each player, I add his ABs and hits to my league total, then see what my team BA would be. Let's use ARod's CHONE projections as an example. ARod is projected to hit 159/541 = .294. So add ARod's 159 hits to my existing 1350, and his 541 ABs to my 5000. We then have my team BA is 1509/5541 = .2723. So ARod brings my team BA up .0023 or 2.3 points if you will. Do the same thing for every player and take z-scores.
TheRock
General Manager

Posts: 3037
(Past Year: -15)
Joined: 16 Apr 2003
Home Cafe: Baseball
Location: America's Heartland

### Re: Calculating Z score for batting average

I do like Rock does in a way. If I'm trying to determine the value of a 2B within the draftable 2B universe (15 players let's say), the value of a player's BA will be weighted by how many ABs I have projected for him relative to the average of all 15.
RugbyD
Hall of Fame Hero

Posts: 5589
(Past Year: -2)
Joined: 7 Dec 2004
Home Cafe: Baseball
Location: punting small dogs and being surly

### Re: Calculating Z score for batting average

Thanks alot - do you use IP and work it the same way for era and whip?
Mike_nyc
College Coach

Posts: 326
(Past Year: -2)
Joined: 21 Mar 2006
Home Cafe: Baseball

### Re: Calculating Z score for batting average

Mike_nyc wrote:Thanks alot - do you use IP and work it the same way for era and whip?

Sure do
TheRock
General Manager

Posts: 3037
(Past Year: -15)
Joined: 16 Apr 2003
Home Cafe: Baseball
Location: America's Heartland

### Re: Calculating Z score for batting average

I think TheRock's way works, but here's another way to think about it:

First find what the average BA of the entire draft pool would be: Take all 168 hitters drafted (or however many your league drafts) and get the league average BA. Let's say it ends up at .270.

The basic formula Tango suggests is:

H - (AB * league_average)

So if A-Rod gets 159 H in 549 AB:

159 - (541 * .270) = 159 - 146 = 13

Here's what that formula is doing: Let's suppose that a league average player (the .270 hitter) gets the same number of AB as A-Rod (541). In that situation, how many hits would he have? He would get 146 hits (541 * .270).

Now A-Rod is projected to get 159 hits. When we subtract the pro-rated hits of the average player (146), we find that A-Rod is projected to get 13 more hits than the league average. That 13 is what Tango uses for xH.

EDIT: I can't subtract.
Mays
Little League Legend

Posts: 17
Joined: 19 Feb 2009
Home Cafe: Baseball

### Re: Calculating Z score for batting average

Note that this general formula works to convert any rate stat into a counting stat:

numerator - (denominator * league_average)

So ,for example, OBP:

xOBP = (H + BB + HBP) - ( (AB + BB + HBP + SF) * league_average)

For stats where a small number is good, all you have to do is multiply by -1:

xERA = ( ER - (IP * league_average) ) * -1
xWHIP - ( (BB + H) - (IP * league_average) ) * -1

EDIT: Note that for ERA I'm assuming for simplicity that it's ER/IP, and the league average is the league average ER/IP. It would work the same if you prefer multiplying/dividing everything by 9.
Mays
Little League Legend

Posts: 17
Joined: 19 Feb 2009
Home Cafe: Baseball

### Re: Calculating Z score for batting average

this has been great info thanks alot. after calculating all the xH's, he calculates the SD of these values as part of his formula, correct?
Mike_nyc
College Coach

Posts: 326
(Past Year: -2)
Joined: 21 Mar 2006
Home Cafe: Baseball

### Re: Calculating Z score for batting average

Mays wrote:I think TheRock's way works, but here's another way to think about it:

First find what the average BA of the entire draft pool would be: Take all 168 hitters drafted (or however many your league drafts) and get the league average BA. Let's say it ends up at .270.

The basic formula Tango suggests is:

H - (AB * league_average)

So if A-Rod gets 159 H in 549 AB:

159 - (541 * .270) = 159 - 146 = 13

Here's what that formula is doing: Let's suppose that a league average player (the .270 hitter) gets the same number of AB as A-Rod (541). In that situation, how many hits would he have? He would get 146 hits (541 * .270).

Now A-Rod is projected to get 159 hits. When we subtract the pro-rated hits of the average player (146), we find that A-Rod is projected to get 13 more hits than the league average. That 13 is what Tango uses for xH.

EDIT: I can't subtract.

In the end, this actually takes ABs back out the equation. xH tells us how much a players performance increases the overall team numerator when computing team BA, but not how much it increases the denominator. And you need both to know the value.

I.e. ARod has 13 hits over average. My team altogether has 60 hits over average. Some other team also has 60 hits over average. The winner is whichever team attained that in the fewest at bats. It's information you need to know.

But as a rough guide of value, it does have its purpose.
TheRock
General Manager

Posts: 3037
(Past Year: -15)
Joined: 16 Apr 2003
Home Cafe: Baseball
Location: America's Heartland

### Re: Calculating Z score for batting average

another question if i may -

I have a player pool of 250 hitters. For a league where 150 are used i use the top 150 values for each statistical category correct? Then for a league with only 100 batters i just cut down the values used to the top 100 for each?
Mike_nyc
College Coach

Posts: 326
(Past Year: -2)
Joined: 21 Mar 2006
Home Cafe: Baseball

Next