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For homicide detectives, the clock starts ticking the moment they are called. Their chance of solving a murder is cut in half if they don't get a lead within the first 48 hours.

This was the lead in message for the "Investigation Discovery" channel program The First 48.

Is this true? If so, what are actual odds of solving a murder before and after this time limit? Is this time limit started at the time of the crime or the time the crime is discovered? Is there a more fine grained analysis of the odds of a murder being solved given a timeline of when the first clues are found?

N.B.: The quote specifies having a lead, not being solved in 48 hours. Some parts of answers seem to bias toward being solved or solvable within that period.

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    I've always wondered if investigators just kind of give up after this timeframe, thus making it self-fulfilling – fredsbend Sep 7 at 0:42
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    I think there are cases that are easy to solve, and cases that are hard to solve. If you spent 48 hours searching for clues and didn’t find any, the case is likely a harder one. But if the police was called only after 48 hours, it may still be an easy case. Of course at some point evidence starts deteriorating. Rain wiping blood away, out-of-town witnesses returning home etc. – gnasher729 Sep 7 at 9:09
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    Strangely, after some years chances go up. Friends of suspects are not friends anymore, people afraid to come forward are not afraid anymore, and so on. – gnasher729 Sep 7 at 9:11
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    @gnasher729 that certainly seems reasonable. Is there any where you can look for data to back up your theory? – psaxton Sep 8 at 1:44
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    @gnasher729 I agree, the first example that comes up to illustrate is to replace "solving a murder" with "finding my car keys." Most of the time you'll find them within two days, the rest of the time they're likely in a sewer drain. – Cristobol Polychronopolis Sep 9 at 20:49
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The best research I'm aware of is a Washington Post investigation of 8,000 murder arrests. Their data journalists found that half of the arrests happened in 10 days or fewer, not 48 hours.

A Washington Post examination of 8,000 homicide arrests across 25 major U.S. cities since 2007 found that in half of the cases, an arrest was made in 10 days or fewer.

The analysis underscores what police leaders and homicide experts have said about the passage of time working against detectives. But it also dispels the notion of a “48-hour rule” that most cases, if solved, are wrapped up in two days. Only 30 percent of the cases led to an arrest within that time frame, the analysis found.

So the frequently given 48-hour rule of thumb doesn't seem very accurate, at least for homicide cases. However, a graphic further down in the Post article does show that the likelihood of an arrest declines steeply within just a few days.

Of course 'finding a lead' is an ill defined term and not necessarily the same as arresting a suspect. The Washington Post piece quotes a police sergeant who argues that 48 hours for 'identifying a suspect' isn't far off:

Evidence collection and lab tests often delay an arrest beyond a couple days. “It’s probably more accurate to say that you had a suspect identified in the first 48 hours,” said Sgt. Greg Van Heyst, who supervises the Tampa Police Department homicide unit.

Ultimately one would need to come up with a clear set of criteria for what constitutes a 'lead' to accurately confirm or dispel the claim.

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    I would think a "lead" is a person suspected to be either a witness or the perpetrator. That seems how the term is typically used. – fredsbend Sep 9 at 14:28
  • @fredsbend that's one possible definition. It seems difficult to systematically analyse from police reports though. Witnesses in particular can include a number of people who become part of the investigation files because they might have relevant information and later turn out to be totally irrelevant – waltzfordebs Sep 9 at 19:39
  • Note that this is ignoring the part of the statement "...are cut in half...". It doesn't say it suddenly becomes impossible. Only that it becomes harder. – Keith Morrison Sep 10 at 20:21
  • I'd listen to @KeithMorrison if I were talking about solving crimes. – Ink blot Sep 13 at 22:23
  • The median time to an arrest is not obviously related to the probability of solving a murder case given the time at which the first lead is identified (whatever "solving" means, and, for that matter, "lead"). – phoog Sep 15 at 14:22
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This question does not have a country tag, although there seems to be an implicit US assumption. In order for the claim to be feasible there needs to be a significant proportion of murders that go unsolved.

This seems to be the case in the US, where around 40% of murders are unsolved (source, not super reliable but they claim to quote the FBI which should know about this). However, this is not the case in for example Germany where less than 10% of murder cases go unsolved (source in German).

Hence unless you believe that the German police solves almost all murders in less than 48 hours, their chances of solving a murder after 48 hours must still be well above 50% to get to over 90% total solved cases, so they chances to solve the case can't be halved. I believe the proportion of solved cases is approximately similar to Germany in most other EU countries but haven't looked for any sources.

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    Why shouldn't we believe that German police have leads in the first 48 hours for most cases? – Oddthinking Sep 10 at 0:02
  • You are correct the program is US based. I didn't post a location tag because the claim doesn't specify a location. I considered adding an applicable region to the large list of questions I've already asked, but don't want to expand the scope of the question any further. – psaxton Sep 10 at 1:50
  • If someone can provide a data set confirming or confounding the claim, maybe a region for where the claim is true could be extracted. – psaxton Sep 10 at 1:52
  • "there needs to be a significant proportion of murders that go unsolved": That doesn't follow at all. For example, if the proportion of cases in which a lead is found in under 48 hours is very high then the proportion of cases solved overall will be very close to the probability of solving such cases. If that probability is very high then the proportion of unsolved cases will be small even if the probability of solving other cases is less than half as great. Granted, those two figures probably aren't that high, but there isn't anything given in the question to support such an assumption. – phoog Sep 15 at 14:36
  • The claim isn't about whether the case is solved within 48 hours but whether it is solved eventually considering whether the first lead is developed within 48 hours. So it is not necessary to believe that German police solve almost all murders within 48 hours to accept the claim as stated. – phoog Sep 15 at 14:45

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