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Help finding formula for zscore spreadsheet

johnlocke3

New member
Joined
Oct 30, 2015
Messages
1
Hello, I was looking for a little help with a spreadsheet I was trying to recreate using zscores. This sheet was used to judge defenses in basketball, but I am having a tough time figuring out what the original creator used to make the calculations. I understand how to get the means and S.D. for the columns listed, and the zscore for (raw z-FG%). But under z-FG% (last column) it looks like he may have used several sources of data to come up with the answers. So, I'm looking for the formula used to calculate z-FG% of 0.4 for row team A. I hope I am posting this in the right spot! Thanks

teamOpp FG%raw z-FG%Opp FGAFGA as % of meanz-FG%
A45.20.582.698.10%0.4
B44.5084.199.90%0
C45.50.688.5105.10%0.7
D44.2-0.283.999.60%-0.2
E42.9-1.185.9102.00%-1.1
F45.10.483.298.80%0.4
G45.90.983.499.00%0.9
H45.90.983.699.30%0.9
I44.80.283.398.90%0.2
J43.1-0.984.6100.50%-0.9
K43.3-0.890106.90%-0.9
L41.1-2.283.699.30%-2.2
M42.8-1.183.198.70%-1.1
44.3-0.182.197.50%-0.1
44.4-0.180.395.40%-0.1
44.4-0.181.897.10%-0.1
43.8-0.581.496.70%-0.5
46.71.488.1104.60%1.5
44-0.385.4101.40%-0.3
45.40.683.398.90%0.6
44.1-0.388104.50%-0.3
46.71.481.296.40%1.4
43.6-0.684.2100.00%-0.6
43.2-0.986.2102.40%-0.9
46.31.287.6104.00%1.2
46.91.687.2103.60%1.6
45.80.884.199.90%0.8
46.71.483.198.70%1.4
40.8-2.479.394.20%-2.3
44-0.382.998.50%-0.3
Means:44.584.2
Standard Deviations:1.52.5
 

Ishuda

Elite Member
Joined
Jul 30, 2014
Messages
3,345
Hello, I was looking for a little help with a spreadsheet I was trying to recreate using zscores. This sheet was used to judge defenses in basketball, but I am having a tough time figuring out what the original creator used to make the calculations. I understand how to get the means and S.D. for the columns listed, and the zscore for (raw z-FG%). But under z-FG% (last column) it looks like he may have used several sources of data to come up with the answers. So, I'm looking for the formula used to calculate z-FG% of 0.4 for row team A. I hope I am posting this in the right spot! Thanks

teamOpp FG%raw z-FG%Opp FGAFGA as % of meanz-FG%
A45.20.582.698.10%0.4
B44.5084.199.90%0
C45.50.688.5105.10%0.7
D44.2-0.283.999.60%-0.2
E42.9-1.185.9102.00%-1.1
F45.10.483.298.80%0.4
G45.90.983.499.00%0.9
H45.90.983.699.30%0.9
I44.80.283.398.90%0.2
J43.1-0.984.6100.50%-0.9
K43.3-0.890106.90%-0.9
L41.1-2.283.699.30%-2.2
M42.8-1.183.198.70%-1.1
44.3-0.182.197.50%-0.1
44.4-0.180.395.40%-0.1
44.4-0.181.897.10%-0.1
43.8-0.581.496.70%-0.5
46.71.488.1104.60%1.5
44-0.385.4101.40%-0.3
45.40.683.398.90%0.6
44.1-0.388104.50%-0.3
46.71.481.296.40%1.4
43.6-0.684.2100.00%-0.6
43.2-0.986.2102.40%-0.9
46.31.287.6104.00%1.2
46.91.687.2103.60%1.6
45.80.884.199.90%0.8
46.71.483.198.70%1.4
40.8-2.479.394.20%-2.3
44-0.382.998.50%-0.3
Means:44.584.2
Standard Deviations:1.52.5
If I'm understanding you correctly, the raw score Z[SUB]r[/SUB] (raw z-FG%) is what is measured. This is turned into a (standard) score Z (z-FG%) by
Z = \(\displaystyle \frac{Z_r\, -\, \mu}{\sigma}\)

Just based on the two scores, a (close to) best fit for \(\displaystyle \mu\) and \(\displaystyle \sigma\) appears to be \(\displaystyle \mu\) = 0, \(\displaystyle \sigma\) = 1.

EDIT:As a pragmatic view of the differences, there may be some round off errors. Suppose that first pair of Z[SUB]r[/SUB] and Z was supposed to be 0.45 and the person filling out the 'raw' colume rounded up to 0.5 and the person filling out the 'standard' column rounded down to 0.4.
 
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