# Waypoint error - is it additive?

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When I first started the game years ago it was explained to me that errors in the hider's and finder's GPSr might add if they were trying to find the same waypoint. If both GPSrs had an error of plus or minus 20 ft, then when searching for a cache your GPS might tell you you're at GZ but you might be anywhere from GZ to 40 feet away.

The logic was simple enough to believe:

Worst Case -

If the hider was standing at A but his GPS had a 20 foot error and told him he was actually at B, then he'd list the cache as being located at B.

If a finder then walked to C because his GPS also had the same error but in the opposite direction, he'd think he was actually at B. He'd then be 40 feet away from A while looking for the cache at C.

However, some time in the past someone in the forums stated that this just wasn't true but they didn't explain why at the time. This came up recently in conversation with a friend and I decided to ask those of you that would know for sure. Is what I've explained above true for worst case error in a pair of GPS readings?

I've seen that explained to me a number of times and it really sounds logical but only works out in the very worst case scenario. Obviously, the typical error will be less than that.

However - Fizzymagic has stated several times that we are incorrect to ever add them together (I believe jis exact phase is "it doesn't work that way" - so maybe he could jump in and explain why??

Here's a better picture

The hider is at A but his GPS has 20 ft of error so it returned the coordinate at B. The finder's GPS also has 20 feet of error. When his GPS reads B, he might be anywhere on circle C. The worse case he would be 40 feet from from the cache, but he may also be right on the cache. The expected error is the square root of 800 or about 28.28 feet.

Edited by tozainamboku

I don't know if that's necessarily better, since they both make the same point.. But it sounds like you're saying the same thing I did in my summary above, that "you might be anywhere from GZ to 40 feet away." And only the worst case is 40 feet - but it can happen.

So that's 2 for "sounds reasonable to me".

If there is anyone that thinks otherwise, Fizzy or anyone else, I'd love to hear an explanation of why you can't add the two errors to get worst case.

I have my own theory... but if you take Toz's diagram... and then rotate the C around the point A, I think it fits better with mine.

Reason... B can be anywhere inside A's circle... However, the average says that most of the time C and A will be closer together, as Toz and even FM have stated. Absolute worst case would be B on one side of A circle and C actually on the furthest side of that{C}circle... a very specific case... that is based on the fact that he can be at any point in C while still showing the same coords as A. But they just make that possible at one point.

Based on a couple of years using an older GPS 45xl to cache... and the same for using it since 96 for navigation... when the normal EPE was closer to 10 metres (30 ft) we got to see lots of extra territory... add lack of sensitive receiver and older software... well... The map 60cx I got last year is a joy, was still the best I could afford.

Doug 7rxc

Edited by 7rxc

If you have a GPSr that indicates an "EPE" in feet, that number is actually an 80% confidence number.

In other words, if it tells you the EPE is 100 feet, it is only 80% of the time that you are within the 100 feet. The high EPE numbers happen when only 4 satellites are visible and 3 of them are in the same quadrant of the sky. If you are in a canyon or among tall buildings you may not get clear signals from enough satellites. I observed a USGS technician set up a GPS antenna on a tripod over a benchmark. The tripod and fancy GPS remained in place for 48 hours. With a 48 hour fix the USGS got the location within an inch horizontal and vertical.

Before geocaching was invented, I used to locate property corners and take 3 3 minute shots with a \$5000 GPSr. After using Differential Correction, the best of the 3 by DOPS (Dilution of Precision) was used.

Occasionally, I had to go back to a corner if none of the waypoints was good.

More than half the time, I find the cache less than half the indicated EPE from where I call GZ.

I leave my caching bag with GPSr on at the first indicated GZ and search for up to 5 minutes. If I have not found the cache by then, I will check just outside the area I have checked in the quadrant the arrow is now pointing to.

The magic only works if both you and the hider had good satellite geometry and 5-10 satellites in view.

Based on high school math/physics (we're going back over 30 years here, so expect this to be wrong), I would guess that with two readings with a likely error of 20 feet, the overall error is likely to be around 28 feet (20 squared = 400; 400 + 400 = 800; square root of 800 is about 28).

I don't have a lot of time right now, so I will explain better tonight. The true answer is kind of an in-between situation.

When you do an experiment, there are 2 kinds of error. The first is experimental noise, or statistical error. I am sure everybody is familiar with that concept.

Statistical errors are incoherent in that they are not correlated; when you flip a coin heads it does not impact the next flip. So a statistical error that goes one way today will just as likely go a different way tomorrow. A good way to look at this is to remember that statistical errors tend to cancel out over time. If you flip a coin twice, it's common to get all heads, but if you flip it 100 times, it would be very unusual to get all heads (with a fair coin, of course).

The second kind of error is a systematic error, where there is something in your equipment that is off that will always be off in the same way no matter how many times you do the experiment. Systematic errors always go the same way, and are referred to as coherent.

Simplifying a lot of math, the way you deal with the two kinds of errors is that you add incoherent errors in quadrature (the error of two measures is the square root of the sum of the squared errors) and coherent errors linearly (the two errors added).

The error in GPS position for two people measuring at two different times are a combination of incoherent errors (satellite geometry, timing jitter, ionospheric delay, etc.) and coherent errors (multipath from a large building near the site, errors in the GPS position reconstruction software, etc.) So the actual error is a combination of the two.

However, the incoherent errors are almost always dominant, so that means that the errors are mostly uncorrelated and should therefore be added in quadrature.

So if cacher 1 has an error of 20 feet and cacher 2 has an error of 20 feet, then statistically the expected error is sqrt(20^2 + 20^2) = sqrt(2) * 20 = 28 feet. So, in my (technical) opinion, that's how they should be added.

But the most interesting thing about this is that even though the error equation is symmetric (that is, the expected error doesn't depend on whose error is which), in practice it turns out that the error of the hider is much more significant than that of the finder. I'll explain that later if people are interested.

But the most interesting thing about this is that even though the error equation is symmetric (that is, the expected error doesn't depend on whose error is which), in practice it turns out that the error of the hider is much more significant than that of the finder. I'll explain that later if people are interested.

I, for one, am interested.

But the most interesting thing about this is that even though the error equation is symmetric (that is, the expected error doesn't depend on whose error is which), in practice it turns out that the error of the hider is much more significant than that of the finder. I'll explain that later if people are interested.

I, for one, am interested.

I'm interested, also. I'll throw out my guess that it's because the hider just provides one single reading, while the finder has a tendency to use multiple readings. In other words, he'll look where the GPS initially takes him, when he doesn't find the cache, he'll look at the GPS again, which is now pointing 12 feet over there. Lather, rinse, repeat.

But the most interesting thing about this is that even though the error equation is symmetric (that is, the expected error doesn't depend on whose error is which), in practice it turns out that the error of the hider is much more significant than that of the finder. I'll explain that later if people are interested.

I, for one, am interested.

So am I.

Bated breath here. Not that I'm likely to understand it.

Bated breath here. Not that I'm likely to understand it.

WHEW!!! Yo, dawg, that breath!! Have a bisquit or someting...

Bated breath here. Not that I'm likely to understand it.

WHEW!!! Yo, dawg, that breath!! Have a bisquit or someting...

OK. So now to explain why the accuracy of the hider is so much more important than that of the finder.

Lil Devil hit it right on the nose: the main difference between the finder's coords and the hider's coords is that the finder can perform multiple measurements but the hider cannot. The site generally encourages you to publish a single set of coordinates for each cache.

The finder can always bring multiple GPS units or get a more accurate one or come back multiple times, but no matter how great the finder's accuracy it, the total error can never be less than the hider's error. Unless somebody posts better coords, that is.

The point here is that if the finder doesn't find the cache, they can do many things to get better coords, so their accuracy is limited by the hider's accuracy. So even though the equation I showed is symmetric, it doesn't completely capture the information of the situation.

I know that many people post that they take a single measurement and they never get complaints about coords. I believe them. For the vast majority of caches, having coords accurate to 10 feet is not really necessary.

However, if I hide a difficult-to-find cache, I take it as a point of honor to post the very best coords I can, so that the finder is challenged by my hide and not by bad coords. I average; I take readings from multiple directions; sometimes I come back a couple days later. It's because I know that bad coords are, usually, forever!

Here, by the way, is a picture that reflects the probabilistic nature of the GPS error a little better.

I have a bunch more images of some calculations I did a few years back, which show some interesting stuff, but I am not sure they would be terribly useful.

There is one more amusing factoid, though: assuming that the probability density is Gaussian (also called "normal,") then the distance from the true coordinates that your GPS is most likely to indicate is actually not at the coordinates! That's because the available area gets larger as the square of the distance from the true coords, so even if the probability distribution is centered at the correct coords the most likely distance is not zero. Weird mathematical fact.

So if cacher 1 has an error of 20 feet and cacher 2 has an error of 20 feet, then statistically the expected error is sqrt(20^2 + 20^2) = sqrt(2) * 20 = 28 feet. So, in my (technical) opinion, that's how they should be added.

I won't insist that I understand the explanation fully, but surely it answers a different question?

The expected error might be 28 feet, but the question was about the "worst case possible"; and this still seems to me to be 40 feet (on the assumption that the hider suffered from a 20 foot inaccuracy and then the seeker also suffered from a 20 foot inaccuracy).

There's no probability calculation necessary.

So if cacher 1 has an error of 20 feet and cacher 2 has an error of 20 feet, then statistically the expected error is sqrt(20^2 + 20^2) = sqrt(2) * 20 = 28 feet. So, in my (technical) opinion, that's how they should be added.

I won't insist that I understand the explanation fully, but surely it answers a different question?

The expected error might be 28 feet, but the question was about the "worst case possible"; and this still seems to me to be 40 feet (on the assumption that the hider suffered from a 20 foot inaccuracy and then the seeker also suffered from a 20 foot inaccuracy).

There's no probability calculation necessary.

If I understand the answer given (and a few things I looked up since then) - that is a correct answer to the "worst case" question. The answer is: "the total error will probably never exceed 28 feet when each reading is 20 foot estimated error."

Fizzy (as usual) seems (I think)to have a very correct analysis - it simply is not something you ever add together. Not all things calculate so easily into a concrete answer.

So if cacher 1 has an error of 20 feet and cacher 2 has an error of 20 feet, then statistically the expected error is sqrt(20^2 + 20^2) = sqrt(2) * 20 = 28 feet. So, in my (technical) opinion, that's how they should be added.

I won't insist that I understand the explanation fully, but surely it answers a different question?

The expected error might be 28 feet, but the question was about the "worst case possible"; and this still seems to me to be 40 feet (on the assumption that the hider suffered from a 20 foot inaccuracy and then the seeker also suffered from a 20 foot inaccuracy).

There's no probability calculation necessary.

There is no "worst case possible" distance, because the inaccuracies aren't 20 feet (and not an inch more).

If the 20 foot error is the "Estimated Position Error" (EPE) reading on the GPSr, then that means there's a 50 percent chance that the searcher's displayed GZ is within 20 feet of the published cache coordinates. It also means there's a 50 percent chance that that the searcher is more than 20 feet away. Sometimes they will be 30 feet away. In rarer cases, they could be 50 feet away (or more).

The correct question isn't the unanswerable: "How far away am I from the hidden cache in the worse case scenario?" The correct question is more along the lines of: "How likely is it that I am within 40 feet of the hidden cache?"

Trying to give a short summary:

As tomfuller & Quill states, the "accuracy" indicated by the GPS is not the "maximum error" or something similar, but a confidence interval, ie. "with some (80%?) probability we expect the coords to be within the given distance". If we had two "max errors", we could just add them, but not in case of confidence numbers.

These can be "combined" as fizzymagic states, to calculate a new confidence interval (for example, 28 feet if both had 20 feet accuracy). Problem with this is of course that we don't know the hider's accuracy. And again it doesn't mean that the cache is necessarily within this distance, as there's no way to know or calculate a "maximum error".

The expected error might be 28 feet, but the question was about the "worst case possible"; and this still seems to me to be 40 feet (on the assumption that the hider suffered from a 20 foot inaccuracy and then the seeker also suffered from a 20 foot inaccuracy).

There's no probability calculation necessary.

There's simply no way to calculate a worst case possible, because there's no way for the GPS to know it's worst case error.

Edited by luzian
I'll throw out my guess that it's because the hider just provides one single reading, while the finder has a tendency to use multiple readings. In other words, he'll look where the GPS initially takes him, when he doesn't find the cache, he'll look at the GPS again, which is now pointing 12 feet over there. Lather, rinse, repeat.

Yes, although to complicate that a bit, the hider typically (I hope) takes a reading after the GPSr has been sitting at GZ for several minutes while the cache is placed. And the accuracy precision goodness of the GPS reading is substantially dependent on the signals which have been received in the last few minutes. Compared to that, the seeker is typically wondering around from tree to tree, and the GPSr never truly settles down. (Of course, this could all just be taking place in my imagination.)

A common scenario for me when hunting a cache is to spend 10 minutes looking for the cache, finally find it when the arrow says the cache is 40 feet away, grumble, make note to complain about the coordinates, kneel down, place GPSr on the ground, sign log, trade, etc, then get up and find that the arrow now says 3 feet.

There's no probability calculation necessary.

I'm enjoying this thread almost as much as discussing whether the ratio of favorites votes to some subset of the number of finders is a good statistic. Only here I agree with fizzymagic and most of the other posters.

It's not particularly useful to say "what's the worse case distance I can be from the cache given the inaccuracy of the hiders measurement and the innaccuracy of my measurment". It is more useful for a finder to to look at what is a likely "worse" case.

If your GPSr says the EPE is 20 feet, it doesn't mean that 100% of the time you will be within 20 feet of your target. Instead, EPE gives a confidence interval such as there is better that 80% chance the measured coodinate is less than this distance from the actual coordinates. The 80% confidence for the combined error is something less than the sum (and if the errors are uncorrelated then a formula has been give to determine the 80% confidence).

But if you don't like probablity, you can use fizzy's explanation of why the hider's accuracy is more important to understand why the additive result doesn't provide much help to the finder. The finder isn't likely to go to one spot where his GPS zeros out and then stop looking. More likely, if the finder doesn't find the cache within a short distance of where he first zeros out he will look at the GPS again. That will take him to a new spot. At most one of those two spots was the "worse" case, so the cache is less than the "worse" case for at least one of the places he zeroed out. If the finder keeps repeating this, particularly if he comes back to look on different days, he would move around in his "circle" of inaccuracy. Over a number of tries, his average "worse" distance will be the distance given in the formula.

Of course, the situation on the ground may mean there are times when a finder spots a likely hiding spot 40 ft from where he first zeros out and goes directly there to find the cache. Also we seldom know what the error of the hider was, so even if you move around to try different spots, the cache might be further away if the hider really did have bad coordinates. So for some people, it may be easier to ignore statistics and just use a rule of thumb to search an area twice what their EPE shows.

Wow. You guys probably like watching paint dry to.

I won't insist that I understand the explanation fully, but surely it answers a different question?

The expected error might be 28 feet, but the question was about the "worst case possible"; and this still seems to me to be 40 feet (on the assumption that the hider suffered from a 20 foot inaccuracy and then the seeker also suffered from a 20 foot inaccuracy).

There's no probability calculation necessary.

If I understand the answer given (and a few things I looked up since then) - that is a correct answer to the "worst case" question. The answer is: "the total error will probably never exceed 28 feet when each reading is 20 foot estimated error."

You understand quite well.

I'll put it in a slightly different way. First, I think most companies make the EPE a 90% confidence level; that is, 90% of the time the true coordinates are within the EPE of the point your GPS zeroes at. But I could easily be wrong about that.

So if the hider has a 90% chance of being within his EPE of the true position and you have a 90% chance of being within your EPE of the coordinates the hider posted (which are not the cache position, BTW) then in order for you to be the sum of those distances (or farther) away from the true position, his error had to be in his worst 10%, your error has to be in your worst 10%, and the errors had to be in the same direction!

Let's do the math. The probability that both your errors are in that 10% outside the EPE is pretty close to 10% * 10% = 1%. The probability that they are the same direction is harder to estimate; I will be generous and say that if they are within 45 degrees they are in the "same direction," which reduces the probability anothe1 factor of 8. So your "worst case" scenario has an expected probability of happening that is about .1 * .1 * .125 = .00125, or just over 1 time in 1000.

So the "worst case" scenario can happen, but it is quite rare.

Thanks for all the answers. I like getting more details about how things work, and even if it's information I didn't request it's still welcomed!!!

But to go back to the OP, the specific question asked was, "Is what I've explained above true for worst case error in a pair of GPS readings?"

A few of the answers have been "you probably won't get worse case, and instead you distance will more likely be...." and this answers a different question than was asked. Sort of like if someone asked "If the strongest baseball player hit the fastest baseball pitched on the exact sweet spot of the bat, could he hit it over that wall?" and someone answering with, "Well most of the time the batter won't be the strongest ever, or even in the top 49%, and then the baseball might be a curve, slow ball, or a slider instead of a fastball, and it's really rare that the bat hits the ball right in the sweet spot, etc."

Not that the information given wasn't fun to read, it was very interesting and informative. As a mechanical engineer I'm always interested in learning more about concepts, ideas, methods, etc.

So I'll accept the fact that it's rare for the errors in readings to add up to where the finder is the sum of the errors away. But the question was, in the worst case, do errors in readings add together, or is there some reason the errors in two readings aren't additive and can only combine in some unexpected way".

I think I did get the answer in there that yes, in the worst case, the errors just add together. At least I think that's what I read.

Actually, another "worst case" is that both devices are off by 1000 feet in the same direction and you end up 2000 feet from the cache. It can happen! Remember that the EPE is only the 90% confidence level; the measurement can, in principle, be arbitrarily far off. The probability is tiny, but it could happen.

That's why it is so much more helpful to talk about these things in terms of probabilities than in terms of "worst cases." Your "worst case" is at most a 1 in 1000 occurrence, so even though it could happen, it is so unlikely that for most practical purposes you should ignore it, because it is trivially fixed by making multiple measurements.

The expected error is much more useful in terms of guidance about what to actually, well, expect at the cache site.

But to go back to the OP, the specific question asked was, "Is what I've explained above true for worst case error in a pair of GPS readings?"

The problem is that the way the question was asked, it can't just be answered with a simple Yes or No. Let's look again at "what you've explained above":

When I first started the game years ago it was explained to me that errors in the hider's and finder's GPSr might add if they were trying to find the same waypoint. If both GPSrs had an error of plus or minus 20 ft, then when searching for a cache your GPS might tell you you're at GZ but you might be anywhere from GZ to 40 feet away.

I highlighted the two significant parts. The problem is that "error of plus or minus 20ft" is a misunderstanding of the displayed value. The displayed 20ft EPE doesn't mean that anything is within plus or minus 20ft, it means it probably is within this range. So the display values is already about probabilities. 20ft EPE means we're 90% sure that we're within 20ft of the displayed coords (that's what we call "confidence interval"), but it also means that there's 10% chance to be outside. Which means it could be 1% chance to be something like 50ft or 100ft away, or worst case even more. 20ft confidence interval means we're "quite confident" we're within 20ft.

Now adding two of these confidence intervals together, of course you can say the worst cases would add together. But the worst case was never 20 feet, so the new worst case is also never 40ft. In theory, the cache could be 100 or 200ft or 2 miles away, just that's highly unlikely (very low probability) given the accuracy of the GPS system. So that's why it was suggested to calculate your new "confidence interval", which for the same level of confidence (90%) would be 28 feet.

But the question was, in the worst case, do errors in readings add together, or is there some reason the errors in two readings aren't additive and can only combine in some unexpected way".

I think I did get the answer in there that yes, in the worst case, the errors just add together. At least I think that's what I read.

The answer is actually a simple Yes and No:

Yes, in the worst case, two errors could add together.

But no, you can't use this to calculate the worst case error.

In other words, it seems like a simple question but there's no simple answer. That's why you receive long answers about probabilities, nuclear physics and the start of the universe...

Edit: fizzymagic was faster but what we say is probably the same...

Edited by luzian
Now adding two of these confidence intervals together, of course you can say the worst cases would add together. But the worst case was never 20 feet, so the new worst case is also never 40ft. In theory, the cache could be 100 or 200ft or 2 miles away, just that's highly unlikely (very low probability) given the accuracy of the GPS system. So that's why it was suggested to calculate your new "confidence interval", which for the same level of confidence (90%) would be 28 feet.

Exactly right.

Another way of saying it is that the coords had a certain amount of "badness" in being 20 feet off. The same level of "badness" for the combined measurement of the finder + hider would result in being 28 feet off.

Or another way of putting it: the EPE tells you where it is best to concentrate your search for given true coordinates. Combining that value with the hider's EPE tells you where to concentrate your search for the cache. To answer THAT question, you would use 28 feet if both EPEs had been 20 feet.

One final comment: in the forums, people often make the following argument: "the hider's error was 20 feet and your error is 20 feet so it's completely reasonable to expect to be 40 feet from the cache." That argument is not correct. With 2 EPEs of 20 feet, being 40 feet from the cache is quite unlikely, and so should not be expected.

But to go back to the OP, the specific question asked was, "Is what I've explained above true for worst case error in a pair of GPS readings?"
The problem is that the way the question was asked, it can't just be answered with a simple Yes or No. Let's look again at "what you've explained above":
When I first started the game years ago it was explained to me that errors in the hider's and finder's GPSr might add if they were trying to find the same waypoint. If both GPSrs had an error of plus or minus 20 ft, then when searching for a cache your GPS might tell you you're at GZ but you might be anywhere from GZ to 40 feet away.
I highlighted the two significant parts. The problem is that "error of plus or minus 20ft" is a misunderstanding of the displayed value.

In that case I blame the misunderstanding on my lack of communication skills. I just meant that if the GPS was off by 20 feet, not that the EPE displayed value of approximate error was 20 feet.

A GPS is going to be off by some amount nearly always, and that value is going to fluctuate constantly. The question had more to do with how errors in readings added up together, and less to do with what a displayed EPE value meant with respect to accuracy.

So IF both GPS units were off by 20 feet, in the worst case could the cumulative error be 40? And the answer seems to be yes.

I could have said if one was off by 15 and the other off by 34, in the worst case could the cumulative error be 49? And the answer would also be yes.

One final comment: in the forums, people often make the following argument: "the hider's error was 20 feet and your error is 20 feet so it's completely reasonable to expect to be 40 feet from the cache." That argument is not correct. With 2 EPEs of 20 feet, being 40 feet from the cache is quite unlikely, and so should not be expected.

And this is exactly where my original question comes from. And now that I've read all this, I understand that it's not "completely reasonable to expect" to be 40 feet from the cache. But... 40 feet seems to be about the furthest you'd need to look in that situation, and you'll almost always be within 20 or 30 feet instead. 40 feet would very rarely be the case, within 20 is almost a sure bet.

I just meant that if the GPS was off by 20 feet, not that the EPE displayed value of approximate error was 20 feet.

A GPS is going to be off by some amount nearly always, and that value is going to fluctuate constantly. The question had more to do with how errors in readings added up together, and less to do with what a displayed EPE value meant with respect to accuracy.

So IF both GPS units were off by 20 feet, in the worst case could the cumulative error be 40? And the answer seems to be yes.

I could have said if one was off by 15 and the other off by 34, in the worst case could the cumulative error be 49? And the answer would also be yes.

But how would you know how much the hider's coordinates are off, let alone your coordinates. All you can do is see how far the GPS says the cache is from the posted coordinates once you have found it, and then know the total error. If the hider was 40 off and you were spot on then you would find the cache 40 ft away. If the hider was spot on, and you were 40 ft off, you would find the cache 40 ft away. But if each of you were 20 ft off, you might find the cache 40 ft or you might find it spot on. On average you will find it 28 ft away.

One final comment: in the forums, people often make the following argument: "the hider's error was 20 feet and your error is 20 feet so it's completely reasonable to expect to be 40 feet from the cache." That argument is not correct. With 2 EPEs of 20 feet, being 40 feet from the cache is quite unlikely, and so should not be expected.

And this is exactly where my original question comes from. And now that I've read all this, I understand that it's not "completely reasonable to expect" to be 40 feet from the cache. But... 40 feet seems to be about the furthest you'd need to look in that situation, and you'll almost always be within 20 or 30 feet instead. 40 feet would very rarely be the case, within 20 is almost a sure bet.

As I said above, depending on the situation on the ground you might see a likely hiding spot 40 from the cache, and you would search that spot and perhaps even find the cache there. You can't just look a the EPE reading and assume the cache is within double that distance because you generally don't know what EPE the hider had. Even if the hider says on the cache page what their EPE was, they are probably much closer - though there is also a possibility that 10% of the time they will be further away. If it works for you to have a rule of thumb to search up to twice the distance that your EPE shows, that's fine. I think that would work for a lot of people. The odds will be very small that the cache is farther away than that ... unless the hider had really bad coordinates in the first place.
But how would you know how much the hider's coordinates are off, let alone your coordinates. All you can do is see how far the GPS says the cache is from the posted coordinates once you have found it, and then know the total error. If the hider was 40 off and you were spot on then you would find the cache 40 ft away. If the hider was spot on, and you were 40 ft off, you would find the cache 40 ft away. But if each of you were 20 ft off, you might find the cache 40 ft or you might find it spot on. On average you will find it 28 ft away.

But that's not what it means. It means that most of the time you'll find it within 28 feet, and not at 28 feet. That's a big difference.

While this is an interesting academic discussion, I fail to see how this actually relates to geocaching. How often do y'all know what the hider's EPE was anyways? And even if you *did* know that the hider's EPE was 20 feet, and you know you're own EPE is 20 feet, does that mean you're going to stray out to 28 or 40 feet and stop and say "there's no way the cache is that far so I'll just stop here." No, you're going to look in all the likely spots within what you feel is a reasonable area, and then walk away and log the DNF.

So other than academic trivia, what are we really learning here?

It could be 40 feet, but the probability is closer to what fizzy posted at 28 feet. However both cachers could have the exact same coords also, despite both saying 20 feet off.

While this is an interesting academic discussion, I fail to see how this actually relates to geocaching. How often do y'all know what the hider's EPE was anyways? And even if you *did* know that the hider's EPE was 20 feet, and you know you're own EPE is 20 feet, does that mean you're going to stray out to 28 or 40 feet and stop and say "there's no way the cache is that far so I'll just stop here." No, you're going to look in all the likely spots within what you feel is a reasonable area, and then walk away and log the DNF.

So other than academic trivia, what are we really learning here?

Actually, about 90% of the time I walk away after finding the cache and then I log my find.

Very interesting discussion.

Edited by WRASTRO
While this is an interesting academic discussion, I fail to see how this actually relates to geocaching. How often do y'all know what the hider's EPE was anyways? And even if you *did* know that the hider's EPE was 20 feet, and you know you're own EPE is 20 feet, does that mean you're going to stray out to 28 or 40 feet and stop and say "there's no way the cache is that far so I'll just stop here." No, you're going to look in all the likely spots within what you feel is a reasonable area, and then walk away and log the DNF.

So other than academic trivia, what are we really learning here?

That's exactly why I said that it wasn't EPE that I was talking about, rather the accepted average distance that anyone's GPS might be off.

The conversation where I first heard about it was while looking for a cache as a noob cacher, and someone that knew more about the game than I did was explaining it to me. He said, "Usually you're not going to be led directly to the cache, the GPS is going to probably only be within about 20 or 30 feet of being accurate. But keep in mind that if the person that hid the cache was 20 feet off, and your GPS is also 20 feet off, you could be as far as 40 feet away and still be within the acceptable accuracy range that the GPS can provide."

Then later I read someone in the forums say something (according to my failing memory) like, "This isn't true. If each GPS is off by 20 feet you can't add them together and get a worse case of 40 feet. GPS errors in readings don't add together that way". But then I never heard why.

So again, it's not EPE readings that each say 20 feet off.

And again, it's not "how do I find a cache when I can be as far as 40 feet away".

It's only, "Can errors in readings add together in worst case"? And the answer is yes. So I must have remembered wrong when someone had earlier said that they can't.

Edited by Mushtang

The conversation where I first heard about it was while looking for a cache as a noob cacher, and someone that knew more about the game than I did was explaining it to me. He said, "Usually you're not going to be led directly to the cache, the GPS is going to probably only be within about 20 or 30 feet of being accurate. But keep in mind that if the person that hid the cache was 20 feet off, and your GPS is also 20 feet off, you could be as far as 40 feet away and still be within the acceptable accuracy range that the GPS can provide."

So your talking about a simplification that is usually told to beginners when they expect the GPS to lead them exactly to the cache. First you tell them, "Your GPS usually will get you to with 10 feet, but sometimes it can be off by 20 feet" Then you tell them, "Remember that the hider's GPS could have be off by 20 as well, so the cache could be 40 feet away". Works pretty good; the newbie will now start looking for places where the cache might be hidden that are as much as 40 feet from where the GPS took them; and they start finding caches. I suspect that most of us who have been at awhile intuitively know that the cache is sometimes (but rarely) 40 ft away and is most often within about 10 feet. We've accepted that there is a certain amount of error and don't put corrected coordinates in our log except if we find the cache with the distance we've come to accept as acceptable.

Only the reason that a cache may be as much as 40 feet from where we zero out isn't exactly the story we tell newbies. The math is a little more complicated. As fizzy showed the probability that both the hider and finder are off as much as 20 feet and in the same direction is usually very small. In fizzy's example only a little over 1 in 1000 times would this be the case (if 20 feet were the "maximum"* error that both GPSs could give). I suspect that story uses 40 feet because a 40 foot error is more common - perhaps 1 in 100 caches. If this is the case then either the hider's GPS, or the finder's GPS, or both are giving errors closer to 40 than 20 feet.

*For those who insist on the more correct term, the 20 ft wouldn't be the maximum error by the 90% confidence distance.

So other than academic trivia, what are we really learning here?

Well, I like to understand how my equipment works and what to expect from it, but that's likely just my thing.

I can usually do a pretty good job estimating what the hider's EPE should have been given the view of the sky and some other factors. If the cache is in a canyon with lots of trees, I tend to search farther form my zero point than I do in a situation where the cache is out in the open. I can also estimate the hider's accuracy by my previous experience with their caches. Alamogul, for example, always seems to have spot-on coordinates on his hides, so I am usually quite confident that I will find the cache close to my GZ.

It's extremely helpful for high-difficulty hides to know where to concentrate your search. The area covered by a 40-foot circle is 4 times that of a 20-foot circle. Many times when I have been out with other cachers, somebody decides that the coords must have been off and looks 30 or 40 feet away. I'd say 90% of the time that happens, when we find the cache everybody's GPS reads less than 20 feet from GZ, and the people who spent the time looking away from GZ were wasting their time.

Now, you and I have been caching a long time; you almost 10 years, me almost 9. We have a pretty good intuition for where a cache is likely to be, and if we see a spot 30 feet away that tickles our geo-sense we will most certainly go look there. But for a needle-in-a-haystack hide, knowing a reasonable area in which to concentrate the search is very useful.

In fact, I recently was at a needle-in-a-pile-of-trash hide in Tracy where the owner proudly proclaimed that the coords were "soft" to the tune of 40 feet or so. After a quick 5-minute search, we left. It just wasn't worth wasting our time. Understanding how accuracy works made it easy for me to know that the situation was hopeless.

Only the reason that a cache may be as much as 40 feet from where we zero out isn't exactly the story we tell newbies. The math is a little more complicated.

Absolutely right. Wow, it's kind of fun to agree!

The story we tell newbies is done to get them to quit expecting that the GPS will lead them to the cache every time. It's intended to stop them from complaining, not to actually explain how error works.

I find it interesting that the same people who consistently use this line of argument are the ones who claim that they take a single measurement and never get complaints about their coordinates. I don't attribute any motive to that, but I do find it interesting.

I wish we could come up with a better, more accurate way to tell new cachers not to expect perfect coords.

In my experience, about 90% of the times that I find a cache farther from my GZ than the EPE I would expect (which is often not what my device is telling me!) the fault is with the hider, who didn't get good coords. I almost never complain or post corrected coords unless the error is sufficiently bad that it will cause other finders serious problems or will contribute to having the area torn up by seekers.

I have definitely noticed that hiders' coordinates have gotten better in the last few years as more devices use high-sensitivity chips and WAAS. The overall trend, I think, is in the right direction.

That's my experience; YMMV.

Edited by fizzymagic

If you have a GPSr that indicates an "EPE" in feet, that number is actually an 80% confidence number.

First, I think most companies make the EPE a 90% confidence level; that is, 90% of the time the true coordinates are within the EPE of the point your GPS zeroes at. But I could easily be wrong about that.

I'm curious about where people are getting this information. My understanding is that Garmin, at least, doesn't actually publicize a confidence level for their EPE measurements, but conventional wisdom seems to peg it at 50 percent (as in this example). Perhaps that figure has changed over time, however.

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So the "worst case" scenario can happen, but it is quite rare.

Well, I do find the rest of the discussion interesting, but I was hoping you would add this. Most of the statistics I understand apply to poker. One of the misconceptions that costs people a lot of money is they think that if something is statistically unlikely, it will *never* happen. In reality, it definitely *will* happen, if given enough trials. That's why you see pros "run it twice" in headsup situations where they are a big favorite. They are guarding against the times when the unlikely becomes reality.

(Oh, yeah... I like that regression toward the mean stuff, too )

I wish we could come up with a better, more accurate way to tell new cachers not to expect perfect coords.

That works for me! Attention Newbie: Do NOT expect perfect coordinates!

Doug 7rxc

This is a fun topic. I like the math and tech discussions. I also like:

The story we tell newbies is done to get them to quit expecting that the GPS will lead them to the cache every time.

Yes, indeed.

If you have a GPSr that indicates an "EPE" in feet, that number is actually an 80% confidence number.

First, I think most companies make the EPE a 90% confidence level; that is, 90% of the time the true coordinates are within the EPE of the point your GPS zeroes at. But I could easily be wrong about that.

I'm curious about where people are getting this information. My understanding is that Garmin, at least, doesn't actually publicize a confidence level for their EPE measurements, but conventional wisdom seems to peg it at 50 percent (as in this example). Perhaps that figure has changed over time, however.

I don't know when Joe wrote his treatise, but I remember reading some similar data in 1999.

At that time, I had been using a \$5000 GPSr for 2 years. After SA got turned off and the 2 satellites in geosynch orbit went into service, things got much better.

The confidence level may well be at 90+% now. People expect instant results now. I used to sit on a spot for 10 minutes collecting waypoints and then using Differential Correction for a GIS map.

In that case I blame the misunderstanding on my lack of communication skills. I just meant that if the GPS was off by 20 feet, not that the EPE displayed value of approximate error was 20 feet.

That's exactly what I took your post to mean. I don't see where the EPE comes into it at all. It's not a discussion about what might happen in most cases, or what's likely to happen. We're assuming before we start, that the cache placer has used a GPS position 20 feet out in one direction and the seeker 20 feet out in the other direction. So whatever might happen in the real world, for our little academic debate it's 20 feet west versus 20 east.

Say there is a post, and its exact position is B (as calculated over several years using the best equipment possible). The cache hider comes along and places the cache 20 feet due west of the post at point A. The reading he takes is the same as the coordinates of the post ( B ), but for the moment it's 20 feet out.

Then the cache seeker arrives, and, because his GPSr is leading him here he checks for the cache at point C; twenty feet due east of the post.

Now it all might be highly unlikely. But it could happen; it's simply the worst case using our assumptions.

But it's been most enlightening as far as other questions go!

Edited by Happy Humphrey

If you have a GPSr that indicates an "EPE" in feet, that number is actually an 80% confidence number.

First, I think most companies make the EPE a 90% confidence level; that is, 90% of the time the true coordinates are within the EPE of the point your GPS zeroes at. But I could easily be wrong about that.

I'm curious about where people are getting this information. My understanding is that Garmin, at least, doesn't actually publicize a confidence level for their EPE measurements, but conventional wisdom seems to peg it at 50 percent (as in this example). Perhaps that figure has changed over time, however.

I don't know when Joe wrote his treatise, but I remember reading some similar data in 1999.

At that time, I had been using a \$5000 GPSr for 2 years. After SA got turned off and the 2 satellites in geosynch orbit went into service, things got much better.

The confidence level may well be at 90+% now.

I'm not sure when Joe's web page was published either, but the 50% figure pops up in several places when I Google the subject. I also found it in this 2008 Groundspeak forums thread.

I'm not disputing the 80% or 90% figures. I'm just wondering where they came from.

That's exactly what I took your post to mean. I don't see where the EPE comes into it at all. It's not a discussion about what might happen in most cases, or what's likely to happen. We're assuming before we start, that the cache placer has used a GPS position 20 feet out in one direction and the seeker 20 feet out in the other direction. So whatever might happen in the real world, for our little academic debate it's 20 feet west versus 20 east.

....

Now it all might be highly unlikely. But it could happen; it's simply the worst case using our assumptions.

But that's exactly the point. How does either of them know how far off they might be? The EPE is what tells them. So yes, it can happen, but if both GPSrs showed an EPE of 20 feet, then it's not likely to happen and so you shouldn't expect it to happen. Since you don't know for sure how far off either of them are and in what direction, that's all the information you have. It's also not the worst case scenario, as with an EPE of 20 feet your coordinates can also be out 40 feet, 60 feet, 100 feet, 300 feet or even more, it's just even less likely to happen. The worst case scenario is that you're out by ~20,000 km, but the chances for that to happen are so low that you probably won't ever see it in real life.

All this is also true if both EPEs were showing 10 feet. You can still be out 40 feet, it's just less likely to happen.

Edited by dfx
That's exactly what I took your post to mean. I don't see where the EPE comes into it at all. It's not a discussion about what might happen in most cases, or what's likely to happen. We're assuming before we start, that the cache placer has used a GPS position 20 feet out in one direction and the seeker 20 feet out in the other direction. So whatever might happen in the real world, for our little academic debate it's 20 feet west versus 20 east.

....

Now it all might be highly unlikely. But it could happen; it's simply the worst case using our assumptions.

But that's exactly the point. How does either of them know how far off they might be? The EPE is what tells them. So yes, it can happen, but if both GPSrs showed an EPE of 20 feet, then it's not likely to happen and so you shouldn't expect it to happen. Since you don't know for sure how far off either of them are and in what direction, that's all the information you have. It's also not the worst case scenario, as with an EPE of 20 feet your coordinates can also be out 40 feet, 60 feet, 100 feet, 300 feet or even more, it's just even less likely to happen. The worst case scenario is that you're out by ~20,000 km, but the chances for that to happen are so low that you probably won't ever see it in real life.

All this is also true if both EPEs were showing 10 feet. You can still be out 40 feet, it's just less likely to happen.

No, it's not the point at all. An error exists in a reading, and it's not important that anyone know that they're X number of feet off in order to ask the question. 20 feet was just a nice average round number to use in the example. But the question can be asked even without numbers.

The question sets up the assumption that the error is exactly 20 feet in order to remove several variables from the discussion, so that the point of the question can be focused on. And the point was, do the two errors (whatever they may be) add together, or is there some other factor unknown to this poster that enters into it?

Bringing up EPE is answering a question that wasn't asked. For instance:

Q: If a car drives 40 miles and it takes 20 minutes, how fast is the average rate of speed?

A: Often a car's odometer isn't very accurate, so if he's showing that he's driven 40 miles he may only have driven 39.5 or as much as 40.5. And without knowing how the time was measured (Atomic clock, hourglass, etc) the 20 minutes might also be off an unknown amount. The chance that he went exactly 40 miles in exactly 20 minutes is about 1 in 1000, so I wish we could tell noob drivers to stop expecting to get places on time.

The question sets up the assumption that the error is exactly 20 feet in order to remove several variables from the discussion, so that the point of the question can be focused on. And the point was, do the two errors (whatever they may be) add together, or is there some other factor unknown to this poster that enters into it?

In that case: yes, if both errors are exactly 20 feet, then the furthest off the finder can be from the cache is 40 feet.

But that misses the point that both errors are not exactly 20 feet, and even if they are, then the chances the finder will be 40 feet off are slim to none.

The original question included the words "worst case scenario." Well, the worst case scenario could have the finder looking in the wrong county -- but that would be so rare as to not be worth mentioning. As a rule of thumb, get fairly close to GZ as indicated on your GPS and look around for hiding places within a 20 to 30 foot radius.

If you really want to understand the science, go read the above items in the thread about expected error. If you don't care about the science, use the rule of thumb I just posted. But that whole "if he's 20 feet off and I'm 20 feet off, we could be as much as 40 feet apart" is true, but not useful.

The question sets up the assumption that the error is exactly 20 feet in order to remove several variables from the discussion, so that the point of the question can be focused on. And the point was, do the two errors (whatever they may be) add together, or is there some other factor unknown to this poster that enters into it?
In that case: yes, if both errors are exactly 20 feet, then the furthest off the finder can be from the cache is 40 feet.
That's what I've taken from the discussion as well. It's possible for both hider and finder's errors to be in opposite directions and which would have the finder looking further away than if the errors were both in the same direction. The errors apparently do simply add together. No other factors enter into it.

But that misses the point that both errors are not exactly 20 feet,
Who's point are you talking about? The point in the example given in the OP is that the errors ARE exactly 20 feet.

and even if they are, then the chances the finder will be 40 feet off are slim to none.
Correct. But that too was specified in the question using the phrase "worst case", as in the errors are exactly 180 degrees from each other.

The original question included the words "worst case scenario." Well, the worst case scenario could have the finder looking in the wrong county -- but that would be so rare as to not be worth mentioning.
Not if the errors were 20 feet, which is one of the givens in the OP. Unless, of course, you're within 40 feet of the county line.

As a rule of thumb, get fairly close to GZ as indicated on your GPS and look around for hiding places within a 20 to 30 foot radius.
That is a great rule of thumb, and I've told that to a lot of people I've taken caching. But it's completely off topic to the thread. Thanks anyway.

If you really want to understand the science, go read the above items in the thread about expected error.
If I really want to understand the science of EPE I would (and did. The additional information was definitely educational, even if it didn't address the question asked). But the science of EPE isn't what was asked.

If you don't care about the science, use the rule of thumb I just posted. But that whole "if he's 20 feet off and I'm 20 feet off, we could be as much as 40 feet apart" is true, but not useful.
If you don't care about science, you should hide the largest cache container that an area will support instead of the container you want to hide. But that rule of thumb is also irrelevant to the conversation.