A Crime Review Where the Figures Do Not Add Up
At the monthly crime review of a police station in Bilaspur, the station house officer places the quarter's figures on the table. Beat A: 60 theft cases registered, 21 detected. Beat B: 40 registered, 22 detected. Beat C: 75 registered, 15 detected. Beat D: 25 registered, 17 detected. The station has four motorcycles allotted 300 litres of petrol per month in all, each giving about 35 km per litre, and night patrol is fixed at six hours per motorcycle. The SHO proposes to give 50 per cent of the petrol to Beat C because it 'has the most cases'. A clerk's draft note states that 'the station's detection rate for the quarter is 50 per cent'. You prepared the raw figures and are asked to check the note and suggest the fuel allocation. At the Mohalla committee meeting, residents of Beat D argue that because their beat has the best detection rate, it should get more patrols, and that Beat A must be 'full of criminals' because it registers the most thefts.
1. Check the clerk's 50 per cent claim and compute the correct position. Where is the likely error?
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The claim is wrong. The station's detection rate is total cases detected divided by total cases registered, not an average of the four beat rates.
Total registered = 60 + 40 + 75 + 25 = 200. Total detected = 21 + 22 + 15 + 17 = 75. Station detection rate = 75/200 = 37.5 per cent.
Beat rates are: A 21/60 = 35 per cent; B 22/40 = 55 per cent; C 15/75 = 20 per cent; D 17/25 = 68 per cent.
The likely error is that the clerk averaged the four percentages: (35 + 55 + 20 + 68)/4 = 44.5, which is still not 50, so he probably picked the two 'good' beats or simply wrote an impression. Averaging rates is invalid here because the denominators differ widely: Beat C's 75 cases carry three times the weight of Beat D's 25. This is the classic small-denominator trap - Beat D's 68 per cent rests on only 25 cases, so one detection changes it by four percentage points, while one detection in Beat C changes its rate by only 1.3 points. Any comparison of beats must therefore show the raw numbers alongside the rate, and the station figure must be computed from totals.
2. How would you allocate the 300 litres, and why is the SHO's proposal unsound?
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The SHO's proposal is unsound because case volume measures reporting, not patrol need. Beat C has the most cases but also the worst detection rate, which can mean either that it is under-policed or that its cases are being registered honestly while other beats under-register. A flat 50 per cent of fuel would starve three beats and still not fix the detection gap.
300 litres at 35 km per litre gives 10,500 km a month, about 350 km a day for the whole station. A defensible allocation has two parts:
- A guaranteed baseline for every beat so that the fixed six-hour night patrol can run - say 45 litres per beat, 180 litres in all, giving each beat roughly 1,575 km a month.
- The remaining 120 litres distributed by a workload index that combines registered cases and the detection gap: cases share A 30 per cent, B 20 per cent, C 37.5 per cent, D 12.5 per cent gives 36, 24, 45 and 15 litres, so totals are A 81, B 69, C 90, D 60 litres.
I would also add a condition: Beat C's extra fuel is tied to a written night-patrol plan and a review after one month. Fuel is a measurable input; the review should ask whether detections rise. If they do not, the problem is deployment or investigation quality, not litres.
3. How do you answer the Mohalla committee's two claims without either misleading them or dismissing them?
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I would answer with the figures and explain what they can and cannot show.
On Beat D: yes, 68 per cent is the best rate, but it is calculated on only 25 cases, the smallest number in the station. A high rate on a small base can mean good work or it can mean that many incidents are never registered - a theft not reported is not a theft not committed. Patrol need is decided by time-of-day patterns, vulnerable locations such as markets, bus stands and ATM kiosks, and the density of repeat offenders, not by a percentage alone. I would ask the committee for specific locations and timings where they feel unsafe and promise a patrol check at those spots, which is more useful than a fuel share.
On Beat A: the highest number of registered cases is not evidence that the residents are criminals. A beat that registers more cases may simply be the one where complaints are written down instead of being settled on the street. That is the behaviour the department wants. What matters is detection and conviction. I would tell the committee plainly that if anyone has evidence of a particular offender or gang, the station will act on it, and that labelling a whole locality is both unfair and likely to be an offence under the law. The minutes should record the questions and the answers given.