How to calculate a weekly productivity average and a pay-period average
Averaging percentages is not the same as averaging the days behind them.
Adding up five daily percentages and dividing by five gives the right weekly productivity average only when every day has the same paid minutes. The method that works for any week is total treatment minutes divided by total paid minutes, times 100.
Paid minutes differ most on part-time and split-shift days, which the guide to part-time therapy productivity covers.
Some employers judge productivity across a week or a two-week pay period instead of a single day. The sections below show the weighted average, the pay-period version, and how to work out what each remaining day needs.
Why a simple weekly productivity average goes wrong
Say you work five days and record 90.0%, 88.0%, 60.8%, 85.1% and 91.1%. Adding them and dividing by five gives 83.0%.
That is only correct if every day had the same paid minutes. If Wednesday was a 4-hour shift and the other days were full days, the 60.8% covers fewer minutes than any other day. A simple average still counts it as a full fifth of the week.
The correct calculation totals the minutes behind the percentages.
Period productivity = total treatment minutes ÷ total paid minutes × 100
Weighted average: a worked example
This example assumes four full days of 450 paid minutes (an 8-hour shift with a 30-minute unpaid lunch). Wednesday is a 4-hour day with no unpaid break, so it has 240 paid minutes.
| Day | Paid minutes | Treatment minutes | Day % |
|---|---|---|---|
| Monday | 450 | 405 | 90.0 |
| Tuesday | 450 | 396 | 88.0 |
| Wednesday | 240 | 146 | 60.8 |
| Thursday | 450 | 383 | 85.1 |
| Friday | 450 | 410 | 91.1 |
| Total | 2,040 | 1,740 | 85.3 |
The simple average of the five percentages is 83.0%. The weighted average, 1,740 ÷ 2,040, is 85.3%. The difference is 2.3 points, and it decides whether this week is on an 85% target or below it.
If your employer reports a simple average, ask about it. A simple average gives a short day the same weight as a full one. It penalizes anyone whose bad day fell on a short shift, as here, and it flatters anyone whose best day was a short one.
What each remaining day needs
Mid-week, the practical question is what each remaining day requires to finish on target.
Needed each remaining day = (target × total days − average so far × days worked) ÷ days left
Example: an 85% target, a five-day week, and two days done at an average of 74%.
- Budget: 85 × 5 = 425
- Banked: 74 × 2 = 148
- Left to find: 425 − 148 = 277, across three days
- Needed: 277 ÷ 3 = 92.3% a day
The weekly productivity calculator runs this sum and gives a verdict. On track means the days left need your target or less. Recoverable means up to 5 points above target each day. Steep means more than 5 points above. Not reachable means more than 100%. At 7.3 points above target, this example is steep, but possible.
The percentage version assumes every day has the same paid minutes, as the calculator does. If your days differ in length, run it in minutes instead. Multiply the week's total paid minutes by the target, subtract the treatment minutes banked, and divide by the paid minutes left.
Using the table above, with Monday and Tuesday done:
- Week's target minutes: 2,040 × 0.85 = 1,734
- Banked: 405 + 396 = 801
- Left to find: 1,734 − 801 = 933
- Paid minutes left: 240 + 450 + 450 = 1,140
- Needed: 933 ÷ 1,140 = 81.8% across the rest of the week
Pay period productivity: the ten-day version
Across a two-week pay period of ten working days, each day is one tenth of the result instead of one fifth. Example: an 85% target, with three days done at an average of 70%.
- Budget: 85 × 10 = 850
- Banked: 70 × 3 = 210
- Needed across seven days: (850 − 210) ÷ 7 = 640 ÷ 7 = 91.4% a day
This is a bigger shortfall than the five-day example. Three days at 15 points below target is 45 points to make up, against 22 points (two days at 11 below) in the week. Seven days share it, so each needs 91.4%, slightly less than the 92.3% the week asked for.
For a like-for-like comparison, put the same two days at 74% into a ten-day pay period. The other eight days need (850 − 148) ÷ 8 = 87.75, so 87.8% a day, against 92.3% over three days in a week. With seven or eight days left, one more bad day also changes the requirement less.
When the period is already lost
If the required figure comes out above 100%, the target can't be reached. Work out the best close you can reach instead.
Best possible = (average so far × days worked + 100 × days left) ÷ total days
Two days at 40% with three days left: (80 + 300) ÷ 5 = 76%. That is the ceiling even at 100% on every remaining day. It is better to know it on Wednesday than at a review. The guide on how to recover a bad productivity week covers what to do next.
Reference: what you need for the rest of the week
Five-day week, 85% target, equal-length days. Each cell is the percentage needed on each remaining day.
| Average so far | After 1 day | After 2 days | After 3 days | After 4 days |
|---|---|---|---|---|
| 60% | 91.3 | 101.7 | 122.5 | 185.0 |
| 70% | 88.8 | 95.0 | 107.5 | 145.0 |
| 75% | 87.5 | 91.7 | 100.0 | 125.0 |
| 80% | 86.3 | 88.3 | 92.5 | 105.0 |
| 85% | 85.0 | 85.0 | 85.0 | 85.0 |
Anything above 100 can't be reached. A 75% average after four days needs 125% on Friday, while the same average after one day needs 87.5% across the remaining four.
Which period your employer uses, and how to find out
Ask directly. If the answer is unclear, watch how the reported number moves. A daily measure jumps around. A weekly average smooths within the week and resets on Monday. A pay-period average smooths across two weeks and resets on the pay date.
Two weeks of watching the reported figure will usually show which one you are on.
Part weeks, leave and holidays
A week with annual leave should have fewer days in the calculation, not a zero for each day off. If you work three days and take two as leave, the week should be measured across the three days worked.
A system that counts leave as a zero-productivity day penalizes you for taking leave, and the effect is large. At 85% on the three days worked, two leave days counted as zero report the week as (85 × 3) ÷ 5 = 51%. If your figures drop sharply in weeks with leave or holidays, raise it as a reporting error, not a performance issue.
Using the average to decide about staying late
The weekly view usually argues against staying late. Extra time on one day adds to both the treatment minutes and the paid minutes of a much larger weekly total.
Take a week of 2,250 paid minutes (five days of 450) running at 85%, which is 1,912.5 treatment minutes.
- Filling an empty slot with one 45-minute treatment: 1,957.5 ÷ 2,250 = 87.0%, up 2.0 points
- Staying 45 minutes late to treat one more patient: 1,957.5 ÷ 2,295 = 85.3%, up 0.3 points
- Staying 30 minutes, paid, to write notes: 1,912.5 ÷ 2,280 = 83.9%, down 1.1 points