What the March Incident Numbers Actually Show
The shift commander asks you to review the March incident summary for Rolling Hills Correctional Center before a staffing meeting. Average daily population for March: 1,150. March has 31 days. The summary table lists incidents logged by shift, with staffed posts per day:
| Shift | Hours | Incidents logged | Staffed posts |
|---|---|---|---|
| Day | 0700–1500 | 9 | 8 |
| Evening | 1500–2300 | 15 | 6 |
| Night | 2300–0700 | 6 | 5 |
Two notes appear beneath the table. First, three of the evening shift's 15 incidents are separate reports generated from a single dining hall fight involving six inmates; facility practice is one log entry per event, but each involved inmate also receives a separate disciplinary report. Second, two of the day shift's 9 entries are slip-and-fall injury reports with no security component. A draft memo states: 'The evening shift accounts for 60 percent of all incidents and is therefore the most dangerous shift in the facility.'
1. Compute each shift's share of total logged incidents and the facility-wide incident rate per 1,000 inmate-days. Show your arithmetic.
Read the worked answer
Totals. Incidents logged = 9 + 15 + 6 = 30.
Shares of the 30.
- Day: 9 ÷ 30 = 0.30 → 30.0%
- Evening: 15 ÷ 30 = 0.50 → 50.0%
- Night: 6 ÷ 30 = 0.20 → 20.0% Sum check: 30 + 50 + 20 = 100%. Correct.
Facility rate. Inmate-days = 1,150 inmates × 31 days = 35,650 inmate-days. Rate per 1,000 inmate-days = (30 ÷ 35,650) × 1,000 = 0.000842 × 1,000 ≈ 0.84 incidents per 1,000 inmate-days. Equivalently, 30 ÷ 1,150 × 100 = 2.6 incidents per 100 inmates for the month.
Sanity check on magnitude. A rate below 1 per 1,000 inmate-days is plausible for a medium-security facility, which tells you the base is large and the counts are small. With only 30 events, a single fight moves shares by several percentage points - so any conclusion drawn from this table alone must be stated cautiously. A reviewer who reports '0.84' without showing the 35,650 denominator has given a number nobody can verify.
2. Evaluate the memo's 60 percent claim and its 'most dangerous shift' conclusion. Recompute after correcting the double counting.
Read the worked answer
The 60 percent figure is wrong twice over. Raw data gives 15 of 30, which is 50%, not 60%. The memo appears to have compared evening incidents to a wrong total or dropped the night shift entirely.
Correcting the double counting. Three reports from one fight should be one event: evening becomes 15 − 2 = 13, total becomes 30 − 2 = 28. Evening share = 13 ÷ 28 = 46.4%. Day = 9 ÷ 28 = 32.1%; night = 6 ÷ 28 = 21.4%. Evening is still the largest share, but no longer a majority.
Removing the non-security entries. Day has two injury reports with no security component: day becomes 7, total 26. Day = 26.9%, evening = 13 ÷ 26 = 50.0%, night = 23.1%.
'Most dangerous' does not follow. Raw counts ignore exposure. Each shift covers 8 hours, so post-hours are: day 8 × 8 = 64; evening 6 × 8 = 48; night 5 × 8 = 40. Incidents per post-hour: day 9 ÷ 64 = 0.14; evening 15 ÷ 48 = 0.31; night 6 ÷ 40 = 0.15. Using the consolidated evening count, 13 ÷ 48 = 0.27.
Conclusion. Evening carries roughly twice the incident load per staffed post-hour, which is a real workload finding and a stronger argument than the memo's inflated percentage. But fewer staff on duty and more inmate movement during program hours are competing explanations that the table cannot separate.
3. The warden proposes moving two posts from day shift to evening shift based on this table. What additional data do you request, and what risk does the proposal carry?
Read the worked answer
Data to request. (1) Incident times within each shift, not just shift totals - a 1900 program movement problem is not fixed by adding a post at 2200. (2) Incident type and severity, separated into security events, medical and injury reports, and inmate-on-inmate versus inmate-on-staff. (3) Whether the same inmates or the same housing units generated repeated events; a concentrated problem may call for a targeted fix rather than a shift-wide post. (4) Three to six prior months, to distinguish a trend from a bad month; 30 events is a small base. (5) Staffing actually filled versus authorized on each shift, including vacancies and overtime, because incidents per post-hour changes if evening posts were frequently vacant. (6) Population present and out of cell by hour, since exposure drives counts.
Risk in the proposal. Day shift's 8 posts are not sitting idle while evening runs 6 - day posts typically cover programs, visits, medical escorts, and court movement, and those movements do not stop because the shift has fewer staff; they slow down or go unescorted. Cutting day posts can reduce recorded incidents while increasing unreported risk, which is the classic measurement trap: the number improves because the observation capacity that produced it was removed. Any reallocation should be paired with a defined review period and the same incident definitions used before and after.