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

| team | Opp FG% | raw z-FG% | Opp FGA | FGA as % of mean | z-FG% |

| A | 45.2 | 0.5 | 82.6 | 98.10% | 0.4 |

| B | 44.5 | 0 | 84.1 | 99.90% | 0 |

| C | 45.5 | 0.6 | 88.5 | 105.10% | 0.7 |

| D | 44.2 | -0.2 | 83.9 | 99.60% | -0.2 |

| E | 42.9 | -1.1 | 85.9 | 102.00% | -1.1 |

| F | 45.1 | 0.4 | 83.2 | 98.80% | 0.4 |

| G | 45.9 | 0.9 | 83.4 | 99.00% | 0.9 |

| H | 45.9 | 0.9 | 83.6 | 99.30% | 0.9 |

| I | 44.8 | 0.2 | 83.3 | 98.90% | 0.2 |

| J | 43.1 | -0.9 | 84.6 | 100.50% | -0.9 |

| K | 43.3 | -0.8 | 90 | 106.90% | -0.9 |

| L | 41.1 | -2.2 | 83.6 | 99.30% | -2.2 |

| M | 42.8 | -1.1 | 83.1 | 98.70% | -1.1 |

| | 44.3 | -0.1 | 82.1 | 97.50% | -0.1 |

| | 44.4 | -0.1 | 80.3 | 95.40% | -0.1 |

| | 44.4 | -0.1 | 81.8 | 97.10% | -0.1 |

| | 43.8 | -0.5 | 81.4 | 96.70% | -0.5 |

| | 46.7 | 1.4 | 88.1 | 104.60% | 1.5 |

| | 44 | -0.3 | 85.4 | 101.40% | -0.3 |

| | 45.4 | 0.6 | 83.3 | 98.90% | 0.6 |

| | 44.1 | -0.3 | 88 | 104.50% | -0.3 |

| | 46.7 | 1.4 | 81.2 | 96.40% | 1.4 |

| | 43.6 | -0.6 | 84.2 | 100.00% | -0.6 |

| | 43.2 | -0.9 | 86.2 | 102.40% | -0.9 |

| | 46.3 | 1.2 | 87.6 | 104.00% | 1.2 |

| | 46.9 | 1.6 | 87.2 | 103.60% | 1.6 |

| | 45.8 | 0.8 | 84.1 | 99.90% | 0.8 |

| | 46.7 | 1.4 | 83.1 | 98.70% | 1.4 |

| | 40.8 | -2.4 | 79.3 | 94.20% | -2.3 |

| | 44 | -0.3 | 82.9 | 98.50% | -0.3 |

| | | | | | |

| | | | | | |

Means: | | 44.5 | | 84.2 | | |

Standard Deviations: | | 1.5 | | 2.5 | | |

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.