# Help me understand the concept of "85th Percentile." November 26, 2014 10:51 AM   Subscribe

I am part of a group working on a policy document for the mitigation of traffic issues (e.g. speeding). Stakeholders are having a hard time with a particular criteria which reads as follows: "85th percentile speed is in excess of the signed speed limit by 5 mph or more."

The engineers who wrote and will enforce the policy cannot explain to stakeholders how and why this doesn't mean "85% of drivers are speeding," and neither can I! So what does it mean? Of the total drivers on a segment of roadway in a given day, how many are speeding in this condition?

I know this is a traffic engineering standard, and of course I was able to google lots of very technical explanations about what percentiles mean, even in the context of traffic engineering, but they mean nothing to me or the neighborhood folks that I work with and represent for my job. Can you explain this concept to me the way you would explain it to someone with say a 6th-grade concept of math and/or statistics?
posted by M.C. Lo-Carb! to Law & Government (22 answers total) 2 users marked this as a favorite

There is no way to answer the question "Of the total drivers on a segment of roadway in a given day, how many are speeding in this condition?" with the given data. What it means that the top 15% of drivers are going at least 5 MPH over the speed limit. the other 85% are going slower than that -- but it doesn't specify how many are going between 1-4 MPH over the limit and how many are going at or under the limit.
posted by brainmouse at 10:57 AM on November 26, 2014 [11 favorites]

I think this means that 85% of drivers are not speeding -- and defines speeding as driving the speed limit plus more than 5 mph. If you looked at the speed of all drivers, and then divided their speeds into one hundred groups (or percentiles), 85 of these groups of drivers would be driving slower than the speed limit + 5 mph.
posted by chesty_a_arthur at 10:58 AM on November 26, 2014 [1 favorite]

85% of drivers drive slower than 5mph over the limit.
15% of drivers drive 5 or more mph over the limit.
posted by EndsOfInvention at 10:59 AM on November 26, 2014 [10 favorites]

If you're in the 85th percentile of something, that means that you are ahead of 85% of people for that something. So, "85th percentile speed is in excess of the signed speed limit by 5 mph or more" means that if you take the folks in the 85th percentile of speed (those people who are driving faster than 85% of people), the speed they're going at is 5mph faster, or more, than the speed limit.

You can't answer your second question without knowing quite a bit more-- in this situation, for example, it's possible that *everyone* is speeding, slightly, and the 85th percentile is just doing it more.
posted by damayanti at 10:59 AM on November 26, 2014 [1 favorite]

While I was typing a response, brainmouse answered the question correctly.

To put some numbers on the idea, here are two (highly contrived) examples. Say there is a road that has a 20 mph speed limit and 10 drivers on it per day.

Example 1: Drivers 1-8 drive at 20 mph, driver 9 drives at 30 mph, and driver 10 drives at 50 mph. In that case, the 85th percentile speed is 30 mph (and in excess of 5 mph over the speed limit), although only 20% of the drivers are speeding.

Example 2: Drivers 1-9 drive at 22 mph, driver 10 drives at 30 mph. In that case, the 85th percentile speed is 22 mph, although 100% of the drivers are speeding.
posted by saeculorum at 11:00 AM on November 26, 2014 [2 favorites]

I think damayanti has it, and think the other answers are slightly off. I'm not a traffic engineer, but I think the plain-English interpretation of that statement would be something like: at least 15% of drivers are speeding by 5 mph or more.

It doesn't tell you what percentage of drivers are speeding by 5 mph or more - it could be 16%, or 50%, or 100%. And it doesn't tell you what speed the drivers at the 85th percentile are traveling - they could be at 5mph over the limit, or 10, or 100.
posted by burden at 11:02 AM on November 26, 2014 [1 favorite]

Best answer: Lets say you go to the road and observe ten cars with a radar gun. If you write down the speeds, they are, in increasing order, 24 25 27 29 29 30 31 31 33 37. The 80th percentile speed is 33 mph. So if the limit is 25 mph, then the 80th percentile speed is 8 mph over the limit, so traffic mitigation is called for.

The real traffic study will have hundreds of observations, but that's the basic idea.
posted by wnissen at 11:03 AM on November 26, 2014 [4 favorites]

Does it help if you think of it as "15% of the drivers will be considered fair game for a speeding ticket, as cops often tend to not issue tickets for going less than 5 miles over the limit?"
posted by doctor tough love at 11:04 AM on November 26, 2014

Yeah, wnissen has it. They're determining the 85th %ile of speed -- faster than 85% of other drivers -- and comparing it to the speed limit.
posted by katemonster at 11:08 AM on November 26, 2014

To make this more understandable, avoid any variation of "percent." You might be surprised how many adults do not understand what percentages mean, let alone percentiles.

How about: "On average, of every one hundred cars that pass, at least fifteen are going faster than five miles per hour over the posted speed limit"?
posted by Snerd at 11:27 AM on November 26, 2014 [3 favorites]

Think of the '85th percentile speed' as you would 'average speed'.

If the average speed was higher than the speed limit, you'd say you had a speeding problem, right?

But that would be waiting a long time to act, and you'd be counting people going 1 mph over the limit. So give people the benefit of the doubt that they were trying to observe the limit, and only count the people who are 5 mph or more over as "speeders."

So, the criteria then becomes, average speed on the road is 5 mph over the limit.

But! If average speed is over your action level, that's a lot of people! Let's not wait until 50% of everyone speeds. So instead of average, let's use 85th percentile. Instead of 50% speeding/50% not, we'll act when 15% are speeding/85% not.

And that's exactly what your criteria says: when 15% of everyone is more than 5 mph over the limit.
posted by ctmf at 11:32 AM on November 26, 2014

I'm going to answer this a little differently, as I'm interpreting it as a specification, not an observation about a traffic study. To understand, I'm going tack on an implied prefix of the idea "You're going to design some traffic mitigation controls, and those controls will be considered unsuccessful if the" (85th percentile speed is in excess of the signed speed limit by 5 mph or more). Meaning that when you're done, you have not met your design conditions if more than 15% of the drivers are going faster than 5 MPH over the speed limit.

As others have said, the 85th percentile speed is the speed at which 85% of the traffic is at or below, and 15% is above. It's useful to point out that if you characterize the speeds of two different groups of traffic, and one of them has an 85th percentile speed of 60MPH, and the other has the 84th percentile speed of 60MPH, the second group is in general travelling faster.
posted by achrise at 11:34 AM on November 26, 2014 [1 favorite]

The important thing to understand is that the engineers are not talking about one person behaves, or even hundreds of people individually behave; but about a population of hundreds/thousands of people, and trying to describe how that population behaves. When they are talking about the population, they assume a bell-shaped distribution. (Maybe you can draw this on a board.)

You can intuitively understand a bell curve/normal distribution with something like height: if, say, the average height of the people in your room is 5 feet, seven inches, that doesn't mean that every single person is 5'7". It probably means, in practical terms, that you'll get a small number of people who are 4'11", 5'0", and 5'2", a small number of people who are 5'11" and 6'2", and a larger number of people who vary in between, with an especially large number of people who hover around 5'6", 5'7", and 5'8". If you were to make a bar graph with height increasing from left to right on the horizontal axis and the number of people with each height on the vertical axis, the shape of the bar graph would probably look a lot like your bell-shaped graph. (That's not really how it's created, it actually has to do with the area under the curve and a lot of other statistical stuff, but it might do for a simple 'aha'-type explanation.) The point is that a simple average (add everybody up, divide by the number of people you have) loses the nuance of the way the varying heights are distributed in a way which the bell curve/normal distribution tries to pick up.

You might, at this point, be able to bring out a graphic like the one here, of percentile ranking. Notice how different slices of the curve have percentages of the population associated with them: for instance, between the lines labeled "0" and "+1σ," it shows that 34.13% of people fall within that part of the curve. In your room-height comparison, that probably means something like 1/3 of the people in the room are between, say, 5'7" and 5'11". Looking at that percentile chart and where the +1σ mark is located, you could say that 5'11" is the 84.1th percentile of height in your group. That is, ~84% of people in your group are probably 5'11" or shorter.

It may be that no particular person in your group actually is 5'11"; but this may still be a helpful way of thinking about your group heights--for instance, if you wanted to hang pictures on your meeting room walls and wanted to know what was a reasonable eye level. Or if you wanted to stock the shelves of the closet where you keep your office supplies, it might be helpful to know that a majority of the people can only reach so far. The actual average height of your group may be a number which might not reflect the percentages of people inside it, but the percentile (as opposed to just plain percent) tries to use the number as a signpost showing percentages of the population above or below it. That's one of the reasons why it's frequently used for test scores--people who score in the "99th percentile" have done better than the vast majority of their peers. A school might target students who score in the, say, 25th percentile for extra tutoring. A score in the 25th percentile might be a 77% on the test--it's all about the distribution compared to one's peers.

While I was typing and thinking, I think your question got pretty adequately and succinctly answered. "85th percentile speed is in excess of the signed speed limit by 5 mph or more." I believe that means that if your speed limit was 45 mph in one location, and you were to take 100 measurements of the speeds of people who went by, 85% of them would be traveling at 50 mph or slower. If somewhere else had the limit of 25 mph and 85% of people in that area travel at 32 mph or slower; and somewhere else has a limit of 55 mph and 85% of people in that area travel at 65 mph or slower, then I might describe the conglomerate of the speed measurements in your area using the sentence you quoted.

I know my explanation is not perfect (people who know better should let me know where there may be flaws), but maybe it can help.
posted by spelunkingplato at 11:53 AM on November 26, 2014

Reading back over my explanation, I think I started off the second paragraph talking about the "average"/arithmetic mean (add all the heights up, divide by the number of people) when I should have been talking about the median (take all the measurements, line them up from lowest to highest, pick the one in the middle), or "50th percentile." The arithmetic mean gives you a number which better represents the spread between extreme highest and extreme lowest, and the median gives you a number which better represents the actual way the data is weighted or distributed.
posted by spelunkingplato at 12:12 PM on November 26, 2014

I don't think that it's accurate to rephrase "85th percentile speed is in excess of the signed speed limit by 5 mph or more" as "84th percentile speed is less than 5 mph over the signed speed limit." "85th percentile speed is in excess of the signed speed limit by 5 mph or more," to me, means that the driver driving faster than 84% of the other drivers is going at least 5 mph over the speed limit, but it doesn't tell you how much faster he or she is going.

OP's phrase "85th percentile speed is in excess of the signed speed limit by 5 mph or more" is true if the driver at the 85th percentile is going 5 mph over the limit, or 10 mph over the limit, or 50 mph over the limit. Since we don't know exactly how much the driver at the 85th percentile is speeding, we don't know if the driver at the 84th percentile is speeding, or by how much. It could be that the driver at the 85th percentile is going 10 mph over the limit, and the driver at the 84th percentile is going 9 mph over the limit - the phrase would still be true under these conditions.

Things would be different if the OP's phrase was "85th percentile speed is in excess of the signed speed limit by exactly 5 mph" - if that were true, we would know that the driver at the 85th percentile is going exactly 5 mph over the speed limit, which would mean that the driver at the 84th percentile is traveling somewhat slower than 5 mph over the speed limit.
posted by burden at 12:22 PM on November 26, 2014 [3 favorites]

I'm the only one that mentioned "84th percentile speed", and I didn't rephrase in the way you characterized. I do, however, agree with you completely, and that phrasing is why I'm looking at this in terms of a specification to meet, not a description of an observed condition.
posted by achrise at 12:35 PM on November 26, 2014

Right, I was talking more about the first three comments, plus spelunkingplato's first, which I think are close to right, but not completely accurate, for the reason I explained. I think the conceptualization of this phrase as a specification is helpful.

posted by burden at 12:43 PM on November 26, 2014 [1 favorite]

Best answer: Pretty sure it means in context "We propose to act when at least 15% of drivers are going more than 5 over the speed limit"
posted by zug at 12:45 PM on November 26, 2014 [1 favorite]

Response by poster: Wow -- you've all provided some very helpful answers, thank you!
posted by M.C. Lo-Carb! at 12:45 PM on November 26, 2014

Best answer: In the civil engineering world, 85th percentile is kinda a term of art. It is used as a design goal and measurement for how to spend money/time solving a problem. If 85% of a population using the infrastructure (road/sewer/path/sidewalk/cross walk/etc) is being well served by it (such as obeying the posted speed limit) then you have met your responsibility and no further design work is necessary. To design/build something to handle the highest peak demand seen would be obscenely expensive and only be utilized a very small amount of time. So if most road users are going the speed limit (or close to it) than the road is A. properly designed for that speed and B. meeting user expectations.

So what it means to engineers is if the performance being measured is meeting the demand of 85% of the population or more than it is properly designed and functioning well and needs no further work from an engineering cost-benefit analysis. If it isn't than you need to look closer and what can be done to raise it to 85% and is that worth it (this is usually passed on to the people who control the money and they decide) or will it reduce some other performance measure below 85% (this is the law of unintended results and it is a harsh mistress).

So know you now why the engineers look at you weird when asked about this and don't answer right-fish don't see water, we live and breathe this terms every day and have internalized it so it is very hard to explain to an outside group.
posted by bartonlong at 12:59 PM on November 26, 2014 [8 favorites]

I think most answers here have it backwards. I believe your criteria explains when a speed limit is set too low:

"85th percentile speed is in excess of the signed speed limit by 5 mph or more."

It starts with the assumption that most people will drive at the speed they feel comfortable with, regardless of the posted speed limit. The 85th Percentile guide says that for a given stretch of road, the speed limit should be set such that 85% of drivers are within it, and 15% are over the limit (as 15% of people tend to drive faster than is safe for that stretch of road).

In your example, where the 85th percentile of speed is 5mph faster than the speed limit, that would indicate that the speed limit is set too low, and therefore more than 15% of drivers will be exceeding the speed limit.

To give a specific example, if the 85th percentile speed is 35MPH, but the posted speed limit is 30 MPH, that means that more than 15% of drivers are speeding over 30 MPH. And, this means that the 30 MPH speed limit is too low, because speed limits should not be set below the 85th percentile speed.

See the Texas DOT's Procedures for Establishing Speed Zones for a detailed explanation of how they use the 85th percentile speed to set speed limits.
posted by reeddavid at 10:39 AM on December 1, 2014

I think that's the same thing. Part of the actions the engineers will do when the criteria are met is to ask the whys. Too many people are speeding: fact. That could mean any number of things, one of which is the posting is too low for the conditions. That leads to another decision: raise the limit, or change the conditions such that people don't feel comfortable speeding?

But you have to set some tripwire for starting to ask the questions.
posted by ctmf at 3:35 AM on December 2, 2014

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