100 workers with randomly assigned skills compete for full-time jobs at $70,000 a year. The chart shows how many are left behind as the mix of jobs changes. Below it, one draw plays out step by step.
Hover a year or use the arrow keys to read it. Click a year, or press Enter, to run it in the animation below. You can also drop a data file onto the chart.
Each row of the data file sets the number of knowledge, social and physical positions for one year. The page runs 10,000 draws per year, then plots the median share of the 100 workers left behind and, for each kind of job, its fill rate: the percent of that year's positions of that type that get filled. The shaded band holds the middle 90% of draws for Percent Left behind.
Each line is a median across draws. When a worker could fill more than one kind of job, knowledge jobs are filled first, then social, then physical; total hiring is the same either way, but it decides which kind of job shows the vacancies in years when every kind has some.
| Year | Knowledge jobs | Social jobs | Physical jobs | Skills K / S / P | Percent Left behind | 90% of draws | Knowledge fill rate | Social fill rate | Physical fill rate | Vacant positions | Run |
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A plain text file named years.tsv, kept next to this page. One header row, then one row per year, with columns separated by tabs. Commas or spaces also work.
Year Knowledge Social Physical 1980 40 30 30 1990 50 30 20
Year, Knowledge, Social, Physical are required. The three job columns are positions per 100 workers.KnowledgeSkill, SocialSkill, PhysicalSkill set the percent of workers with each skill for that year. Without them, each year uses the skill rates under “Change the assumptions”.# is a comment; the first one is shown above the chart as a note.years.tsv on its own. Use “Load data file…” instead.100 workers. Three skills handed out at random. 100 full-time jobs at $70,000 a year. Who gets one? Click a year on the chart to play it here.
Every position: 40 hours a week, $70,000 a year, no benefits.
People with no matching opening gather here at step 4.
Each worker gets each skill independently at the stated rate, so a person can hold none, one, two or all three. At 30% / 30% / 50%, about 4.5% of people hold all three and about 24.5% hold none.
Jobs are filled the best possible way: the assignment that employs the most people, found by maximum bipartite matching. A real labor market does worse than this, so the left-behind count is a floor. Anyone left behind holds no skill that any remaining opening needs. When a worker could take more than one kind of job, knowledge jobs are filled first, then social, then physical; this changes which jobs are filled, never how many people are hired.