2022-23 Equity Adjustment: Calculations

2022-23 UC DAVIS ACADEMIC SALARY EQUITY PROGRAM

Calculations

Salary Equity Adjustment Pool

Using data as of May 31, 2022, sum the total salaries within each equity group; This equals total salary expenditure (TSE).
Multiply the TSE by the equity adjustment factor of 1.5%. This will provide our total equity pool for each group (TPE).

Document Changes and Exclusions

Using vetted data from the various Schools and Colleges, update any off-scales that have changed due a retention offer. These individual off-scales will be used to determine an individual's proportion (that is, how far away from the mean they are).
Exclude anyone from equity group that does not meet eligibility criteria.

Mean Off-scale within Equity Group

On Scale
- Using data as of May 31, 2022, determine the mean offscale for each on scale equity group by taking the average of all offscales within that specific equity group. This will provide our Average Off Scale (AOS).
Above Scale
- For each Above Scale equity group, find the corresponding On-Scale equity group. Determine the mean proportion of total salary comprised of off-scale for those in the on-scale equivalent equity group. This is our Average Proportion of Offscale.
- For each member of the Above Scale Equity Group, multiply their total salary by the Average Proportion of Offscale calculated above. This provides our Pseudo Off-Scale.
- Determine the average of all Pseudo Off-Scales. This will provide our Average Pseudo Off Scale (APO).

Individual Equity Calculations

Step 1. Calculate each faculty member's "residual" from the mean off-scale (AOS or APO) within their equity group
- The residual is the arithmetic difference between each individual’s actual off-scale or pseudo-off-scale salary and the mean off-scale salary for their comparison unit (calculated above). Every individual has a potentially unique residual, although in reality some will have the same one because some faculty have identical off-scale salaries. A residual < 0 indicates that an individual’s off-scale salary is below the mean for her/his comparison unit; a residual > 0 indicates that an individual’s off-scale salary is above the mean for her/his comparison unit.
Step 2. Create the "delta" variable for individuals who fulfill eligibility.
- The delta is the absolute value of residual if the residual is < 0. If the residual is >0, then delta is = null
Step 3. Create the adjustment weights that are proportional to the magnitude of the residual.
- Sum all non-null deltas who are eligible for equity adjustments.
- Divide each individual's non-null delta by the sum of all non-null deltas
- Note that weights are constrained to a sum of 1
- No weights are assigned for individuals who are ineligible for equity adjustments.
Step 4. Calculate each eligible individual's adjustment to off-scale salary.
- Multiply the individual's adjustment weight by the Total Equity Pool.
Step 5. Cap the adjustment no higher than the mean
- If the individual adjustment + original off-scale salary is greater than the average offscale in equity group, then cap the individual level adjustment so that it does not go higher than the mean.
Step 6. Examine Total Equity Pool (TPE) for excess funds.
- If there are excess funds:
  - Raise the lowest off-scale/pseudo off-scale until it equals the next lowest. Any additional excess funds can then be added to the two lowest until it equals the next lowest, and so on.
  - When the total cost to raise the lowest to the next lowest is greater than the remainder of the equity pool, calculate a fractional equity adjustment by dividing the remainder of the equity pool by the number of individuals with the same lowest off-scale in that equity group. Add this fractional equity adjustment to those individuals.
  - The individual-equity adjustment is the difference from the newly calculated off-scale/pseudo off-scale and the individual's original offscale/pseudo-offscale.
- If there are no excess funds, the individual-level equity adjustment is what was calculated in step 5.

Examples

Examples of calculations for on-scale and above-scale equity comparison groups can be found below. These examples follow our methodology closely, with some steps abbreviated for simplicity.

On-Scale Example

Let's say an equity comparison group is comprised of the following members:

Person	UCOFF1	UCANNL	Total Compensation	FTE	Total Compensation at FTE
Annie A	N/A	$115,400	$115,400	0.4	$46,160
Bert B	N/A	$154,400	$154,500	0.25	$38,625
Chris C	$14,800	$124,300	$139,100	1	$139,100
Dianne D	$22,100	$108,900	$131,000	0.5	$65,500

1. Determine the Total Equity Pool
- Total Salary Expenditure = $289,385 ($46,160 + $38,625 + $139,100 + $65,500)
- Total Equity Pool = $4340.78 (1.5% * $289,385)
2. Calculate the Mean Off-scale in Equity Group
- Sum of Offscales: $36,900 ($0 + $0 + $14,800 + $22,100)
  Headcount in group: 4
- Mean Off-scale: $9,225 ($36,900/4)

3. Determine each faculty member's "residual", "delta", and "adjustment weights"

Residual: Take the difference between the average off-scale and the individual's offscale.
Delta: Take the absolute value of residual if the residual is <0.
Sum of Deltas: $18,450 ($9,225 + $9,225)
Adjustment weight: Divide individual's Delta by the Sum of Deltas

Person	UCOFF1	Average Off-scale	Residual	Delta	Adjustment Weight
Annie A	N/A	$9,225	- $9,225	$9,225	0.5
Bert B	N/A	$9,225	- $9,225	$9,225	0.5
Chris C	$14,800	$9,225	$5,575	Null	N/A
Dianne D	$22,100	$9,225	$12,875	Null	N/A

4. Calculate each individual adjustment to off-scale salary
- Annie A: $2170.39 (0.5 * $4340.78)
- Bert B: $2170.39 (0.5 * $4340.78)
- Chris C: $0
- Dianne D: $0

5. Cap the adjustment if higher than the mean and determine the final rounded equity adjustments to match the corresponding salary table rounding. (e.g. Professor tables are rounded to the nearest $100)

Person	Original UCOFF1	Equity Adjustment	Updated UCOFF1	Check if adjustment is higher than mean	Final Rounded UCOFF1 (including individual-level adjustment)
Annie A	$0	$2170.39	$2170.39	Ok	$2,200
Bert B	$0	$2170.39	$2170.39	Ok	$2,200
Chris C	$14,800	$0	$14,800	N/A	$14,800
Dianne D	$22,100	$0	$22,100	N/A	$22,100

As you can see, the positionality (ranking) of the faculty off-scales is preserved, and neither Annie A. nor Bert B. has moved above the mean.

Above-Scale Example

Let's say the Above-scale equity group is comprised of the following members:

Person	UCABVE	FTE	Total Compensation at FTE
Alex A	$225,400	1	$225,400
Belinda B	$239,400	0.33	$79,002
Charlie C	$343,200	.25	$85,800

1. Determine the Total Equity Pool
- Total Salary Expenditure = $390,202 ($225,400 + $79,002 + $85,800)
- Total Equity Pool = $5853.03 (1.5% * $390,202)

2. Calculate the Average Proportion of Offscale
To calculate the average proportion of off-scale, we'll need to look at the corresponding on-scale equity group (from on-scale example above)

Annie A: 0 (0/$115,400)
Bert B: 0 (0/$154,500)
Chris C: 0.106398 ($14,800/$139,100)
Dianne D: 0.168702 ($22,100/$131,00)
Average Proportion of Offscale: 0.068775 ((0 + 0 + 0.106398 + 0.168702)/4)

3. Use the average Proportion of Offscale to determine Pseudo Offscales

Person	UCABVE	Pseudo Off-scale
Alex A	$225,300	$15,501.89
Belinda B	$239,400	$16,464.74
Charlie C	$343,200	$23,603.58

4. Calculate the Average Pseudo Off-scale
- Sum of Pseudo Offscales: $55,570.43 ($15,501.89 + $16,464.74 + $23,603.58)
  Headcount in group: 3
- Average Pseudo Off-scale: $18,523 ($55,570.43/3)

5. Determine each faculty member's "residual", "delta", and "adjustment weights"

Residual: Take the difference between the average off-scale and the individual's offscale.
Delta: Take the absolute value of residual if the residual is <0.
Sum of Deltas: $5,080.33 ($3021.59 + $2,058.74)
Adjustment weight: Divide individual's Delta by the Sum of Deltas

Person	Pseudo Off-scale	Average Pseudo Off-scale	Residual	Delta	Adjustment Weight
Alex A	$15,501.89	$18,523.48	-$3,021.59	$3021.59	0.594779
Belinda B	$16,464.74	$18,523.48	-$2058.74	$2,058.74	0.405249
Charlie C	$23,603.8	$18,523.48	$5,080.32	Null	N/A

6. Calculate each individual adjustment to pseudo off-scale salary
- Alex A: $3,481.26 (0.594779 * $5,853.03)
- Belinda B: $2,371.93 (0.405249* $5,853.03)
- Charlie C: $0

7. Cap the adjustment if higher than the mean

Person	Pseudo-Offscale	Equity Adjustment	Updated Pseudo-Offscale	Check if adjustment is higher than mean	Capped at Mean Pseudo Off-scale	Capped Equity Amount
Alex A	$15,501.89	$3,481.26	$18,983.15	Higher	$18,523.48	$3,021.59
Belinda B	$16,464.74	$2,371.93	$18,836.67	Higher	$18,523.48	$2,058.74
Charlie C	$23,603.8	$0	$23,603.8	N/A	N/A	N/A

8. Examine the Total Equity Pool for excess funds
- Funds spent so far: $5,080.33
  Total Equity Pool: $5,853.03
  Total Funds Remaining: $772.7
9. Determine if there are enough funds to bring the lowest pseudo off-scales to the second lowest.
- Lowest Pseudo Off-scale: $18,523.48 (Alex A & Belinda B)
- Second Lowest Off-scale: $23,603.8 (Charlie C)
- Cost to bring Lowest Pseudo Off-scale to Second Lowest: $10,160.64
10. Since there is not enough remaining in the Total Equity Pool, evenly distribute the remaining funds among the lowest pseudo off-scales.
- Remaining Funds: $772.7
  Alex A: $3,407.94 ($386.35 + $3,021.59)
- Belinda B: $2,445.09 ($386.35 + $2,058.74 )

11. Determine the final rounded equity adjustments to match the corresponding salary table rounding. (e.g. Professor tables are rounded to the nearest $100)

Person	UCABVE	Equity Adjustment	Equity (Rounded)	Updated UCABVE
Alex A	$225,400	$3,407.94	$3,400	$228,800
Belinda B	$239,400	$2,445.09	$2,400	$241,800
Charlie C	$343,200	$0	$0	$343,200

As you can see, the positionality (ranking) of the faculty off-scales is preserved. Both Alex A and Belinda B have moved above the original mean, but are still lower than Charlie C. The most dramatic effect is to raise Alex A much closer to their colleagues than before. Belinda B still receives a benefit, but because they were closer to the mean, the effect was smaller, as expected.