Appraisal Bell Curves: How a Merit Budget Becomes Your Hike

The matrix and the budget

A merit matrix gives a target percentage for each combination of rating and position in the pay band. These numbers are invented for illustration.

The budget is a separate decision, usually a percentage of the team's total fixed payroll. Here it is 6% of ₹1,65,00,000, or ₹9,90,000.

The team and the forced distribution

A bell curve, or forced distribution, fixes how many people may receive each rating. This team of ten follows a 1/2/4/2/1 pattern.

Applied as printed, the matrix costs ₹10,11,000, which is ₹21,000 over budget. So every cell is scaled by 9,90,000 ÷ 10,11,000, or 0.9792. P2's 12% becomes 11.75%, a rise of ₹1,76,261. P1's 13% becomes 12.73%.

When the distribution shifts

Now suppose a calibration meeting moves P5 and P6 from 3 to 4. Neither is below the midpoint, so they move to the 10% cell. The raw cost rises to ₹11,43,000, while the budget is still ₹9,90,000, so the scale factor falls to 0.8661.

Everyone whose rating did not change got a smaller hike. That is the arithmetic of a fixed pot, not a judgement about their work. It is also why managers often resist moving people up at calibration.

# Synthetic team and matrix. Scales matrix percentages to a fixed merit budget.
MATRIX = {5: (16, 13, 10), 4: (12, 10, 8), 3: (8, 6, 4), 2: (3, 2, 0), 1: (0, 0, 0)}
BANDS = ("below", "at", "above")

team = [("P1", 1800000, 5, "at"), ("P2", 1500000, 4, "below"),
        ("P3", 2100000, 4, "above"), ("P4", 1400000, 3, "below"),
        ("P5", 1600000, 3, "at"), ("P6", 1700000, 3, "at"),
        ("P7", 2000000, 3, "above"), ("P8", 1300000, 2, "below"),
        ("P9", 1900000, 2, "above"), ("P10", 1200000, 1, "below")]

def hikes(team, budget_pct):
    payroll = sum(s for _, s, _, _ in team)
    raw = {n: s * MATRIX[r][BANDS.index(b)] / 100 for n, s, r, b in team}
    scale = payroll * budget_pct / 100 / sum(raw.values())
    return scale, {n: round(MATRIX[r][BANDS.index(b)] * scale, 2)
                   for n, s, r, b in team}

scale, pct = hikes(team, 6)
print(round(scale, 4), pct["P1"], pct["P2"])          # 0.9792 12.73 11.75

moved = [(n, s, 4 if n in ("P5", "P6") else r, b) for n, s, r, b in team]
scale, pct = hikes(moved, 6)
print(round(scale, 4), pct["P1"], pct["P2"], pct["P5"])  # 0.8661 11.26 10.39 8.66

Change the budget to 8% and the scale factor rises above 1, so every cell is paid more than printed. The ratios between cells never change; only the budget and the distribution move the absolute figures.

What this tells you as an employee

• Your rating is only one input. Band position and the ratings of everyone else sharing the pot matter too.
• Being below the midpoint helps. At the same rating, P2 below the midpoint gets 11.75% while P3 above it gets 7.83%. If you were hired high in the band, expect smaller percentages.
• The budget is set before your review. Arguing your rating up after calibration is hard because it takes money from someone else.

Checking your own letter against the model

If HR shares the matrix and the budget percentage, you can test your letter. Divide your hike percentage by your matrix cell to get the implied scale factor. For P2 in the first run, 11.75 ÷ 12 is about 0.98. If colleagues in the same pot report factors that differ widely, either the pots are separate or individual adjustments were made after scaling. Both are legitimate, but they are worth knowing about, because the next cycle will work the same way.

Questions worth asking HR

1. 1Is the merit budget set as a percentage of payroll, and is it the same across teams?
2. 2Is there a forced distribution, and at what level: team, department or company?
3. 3Where does my pay sit against the midpoint of my band?
4. 4Is the variable pay multiplier tied to the same rating? Reading a variable pay plan covers how that second matrix works.

Once you have your percentage, salary hike percentages helps check what it means after tax in tax year 2026-27, using the department's slab page.

Scaling an allocation to a constraint and testing how it responds to changes in inputs is a small optimisation exercise. That style of modelling is practised in our Data Science programme, live online with optional in-person labs at our Noida centre.