The seven-month dredging job that is usually over in six weeks
Showing the misleading chart
A dredge spotters’ almanac we invented counts the 60 Army Corps of Engineers dredging jobs on the water on one Wednesday in June 2023 and finds that the median one runs 207 days, so there is no hurry to go and see one. Every date is the Corps’ own. But a day out catches jobs in proportion to their length: a year-long job is on the water every day of the year, and a ten-day job is there on only ten of them. Count the jobs instead — the 250 that started in 2023 — and the median is 38 days, and 45.6% were done within a month.
01The claim
A page from a dredge spotters’ almanac — the almanac is ours, the dates are the Corps’ — asks how long a dredge stays once it turns up. The answer comes from the Army Corps of Engineers’ own job records rather than anyone’s memory: on Wednesday 14 June 2023, 60 dredging jobs that have since been completed were underway across the country, and each has a recorded first and last day. Take the full length of every one of them and half run longer than 207 days, the average is 292, a quarter run past a year, and only 4 of the 60 were done inside a month. Nor was that a lucky Wednesday: run the same count for every day of 2023 and the median job on the water never drops below 126 days. Zero-based axis, equal 60-day bins, every job counted once. So the almanac’s advice is to take your time — the typical dredging job outlasts a summer, and the dredge will still be there in the autumn.
02The trick
Every date on the page is right; what sets the picture is how a job got into the count. The almanac counted the jobs that happened to be on the water on the day it looked, and a job’s chance of being underway — between its recorded start and end — on a given day is proportional to its recorded length. A year-long job is underway every day of the year; a ten-day job on only ten of them, so the year-long job is 36.5 times as likely to be caught. A day out therefore samples jobs weighted by their length, which drags the whole distribution to the right — the inspection paradox, the same arithmetic that makes you more likely to reach a bus stop during one of the longer gaps between buses. The sample also reaches back in time: 20 of the 60 jobs underway that June day had started before 2023, long contracts carried over from earlier years, including a Mississippi dustpan-dredge rental that ran 1,630 days. Count the jobs themselves — the 250 completed jobs that started in calendar 2023, each tallied once — and the median is 38 days, not 207; the mean is 83.5, not 292; 114 of them (45.6%) were finished within 30 days, and only 8 (3.2%) ran past a year. Ten more jobs that started in 2023 are still not marked completed; counting them as running until the day we downloaded the records moves the median only to 44 days and the share past a year to 6.2%. Both sets of numbers come from the same records, and neither is wrong: one describes jobs, the other describes days on the water. The almanac asked a question about jobs (“how long does a job last?”) and answered it with a count of days on the water. (Both drawings are ours; the almanac, its spotters and its advice are invented, and every date and count is the Corps’.)
03The fix
Decide whether the sentence is about jobs or about days on the water, and count that. The honest redraw puts the two counts side by side on the same 60-day bins: blue for the 250 jobs that started in 2023, each counted once, and gold for the 60 underway on 14 June. Blue piles up at the left, with 60% of jobs in the first bin, while gold spreads out to the right, with 18% in the first bin and 5% past two years. Beside it, a line for every completed job on the water at some point in 2023, 304 of them, shows why: a vertical rule at 14 June is far more likely to cross a long line than a short one, and the 60 lines it crosses are the longest on the panel. Both answers are useful for different questions. A spotter who wants to know whether the dredge in front of them will still be there next month is asking about days on the water, so the snapshot is the right group to look at — but the number to quote is the time remaining, not the total length, and for the 60 jobs underway on 14 June the median time remaining was 91.5 days, about three months, not seven. A planner budgeting a typical job, or anyone writing “a dredging job lasts seven months”, is asking about jobs and needs one tally per job. Whenever you build a distribution from whatever is present at a moment in time — patients on a ward, guests in a hotel, open tickets in a queue, cars in a car park — ask whether the long ones had more chances to be counted. If they did, either weight each case by one over its length, or start from a cohort, such as every job that started in a given year, and say which you used. A cohort has its own catch: begin it too recently and the long cases have not finished yet. Here the 2023 starters have had more than two years to finish, but ten of them are still open and are left out; counting them as running until today moves the median from 38 to 44 days and the share past a year from 3.2% to 6.2%, and the gap with 207.5 barely moves. The nine jobs underway on 14 June that are not marked completed are left out of the snapshot too. Every one of them has run at least 269 days by its recorded dates or is still open, so leaving them out, if anything, makes the almanac’s figure shorter — with them in, the median job underway that day runs 246 days.