Any Detectorist Mathematicians out there? Probability math

[Monkworks]

I am not good at math.
But i have been thinking about a way to come up with a probability formula that could be used to rate your hunting location via some conditions like
Age of the location
size of the location
Population around the location
Income of the population around the location
ground condition (soil type / canopy type)
Location activeness ( beach, or some reason why people came there/go there)
Pre-hunted ( known detectorist already have hunted)

I think a % chance of finding Gold, silver (old coins) could be discerned...

The formula could be used to find out a particular locations percentage of discovery over other areas... or even if just seeking gold for example...

The probability of finding said item...

Example:
Gold probability:
Silver probability:
relic probability:

I was inspired by “ search theory “ used in WW2 to find Uboats...
But where do you start to build a formula like this? and its not like we have scientific testing to see-

If 10 people go to a park for one hour and all have 10 coins in their pockets, how many coins return?

How would one start to figure out a formula for search probability in metal detecting terms?

 

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[Skippy SH13]

I've got lots of work in advanced statistics (Quality Engineering), and am happy to chime in.

What you're suggesting is a fun way to really get people's heads in a tizzy. Basically, these types of "formulas' attempt to take quantitative data and provide a probability of occurrence. This issue you're going to find is in a few points:
1) Unless you can guarantee the data is accurate, you can't properly predict outcomes. For example, how will you determine if something has been "detected?" and to what extent with what equipment, and what coverage?
2) Variation in underlying statistical probabilities. Basically, variation in #s around things like "location activeness" doesn't account for things like seasonality, activities which cause specific losses (like removal of gloves, or application of sunscreen/lotions for rings). Attempting to apply a single number or categories of numbers only increases the variation in the data (decreasing the probability of accuracy)
3) How will you determine probabilities? With a large enough sample population over a long enough time, you'll eventually get a nice Gaussian distribution (normal bell curve) for drops. This is how insurance companies can create actuary tables over population distributions... What you're talking about though is a single isolated point in what is very likely a SHORT time frame. The result is a drastic decrease in predictability, as the possibility of a normal chance occurrence is anywhere within 3 standard deviations of the mean average. (Speaking in lay terms, you can't predict a short term event probability in a very small sample size with any degree of accuracy. You might get lucky, but that's it.) This is why attempting to create a simple formula based on 10 people (or even 1000 people) won't work. You might pull it off (if you had the data) for 10,000, but even then drops don't equal finds!

Just the three above points make it darn near impossible to create a prediction rule with any degree of accuracy. The only thing you're going to get is the information you already know. Things like
- "lots of people in an area in a short amount of time increases the probability of drops."
- "A few people continually visiting in an area over a long amount of time increases the probability of drops."
- "Detectorists in an area reduce the amount of drops available"
- "Demographics (wealth, displays of wealth) of an area increase/decrease the likelihood of valuable drops"
- "Previously unsearched areas increase the likelihood of finds."

All of these things can only be qualified, rather than quantified (not enough long term data collected). As a result, if you were to put all of this together, you'll likely end up with the same list of places that are already qualified, namely:
Parks, beaches, schoolyards, tot-lots and whatnot are great locations.
Parking lot strips, sidewalk strips, skilifts, etc... are all also higher probability locations. Is it a guarantee? nope.

Even a field that gets used as a fair for a short period is likely to have drops... but not guaranteed. Drops are great... how much of it gets picked BACK up is beyond me. Those are the numbers that we can't get! Being able to determine when someone loses something and doesn't look for it, is really tough!

In the end, you can put together a quantitative formula, but it will be no more or less accurate than other qualitative evaluations, simply because the data isn't that accurate.

AND... there's the basic "eyeball" of a situation. I find 2 to 3 times the volume of what my buddies do when we go detecting, because I've learned to simply ask "where would people lose stuff?" A small hill there, a light post here, an open field where lots of things get thrown around... Those target areas become the mines... but I've only found HALF of my best finds searching expected locations. the other half typically comes because I'm walking in the middle of nowhere, and swinging the coil and BEEP! I get a strong signal. There's no reason that gold ring should be THERE... but it is. Go figure.

Basically, it comes down to the fact that your inputs aren't going to be any more accurate than simple comparisons would already give you (you already know a beach populated by sun-bathers is more likely to have jewelry drops than a beach that's filled with fishermen, do you need a number?)

Better, Better yet, and Even Better than that... Qualitative analysis works, but it's the weird crap like "I found the sapphire ring in my front yard, it's worth $15K, and I live in a neighborhood that makes $50K a year"that doesn't make any sense. I always chuckle when I read someone's post that says "eventually if you dig enough pop-tops you will find a gold ring." Uh... nope. That's just statistically not true. Does your probability increase? YES... is it a guarantee? NO.

Just ask me... I've found four gold rings, and probably have dug no more than 500 bottle tops. Why can I get so lucky? Because I'm swinging the coil in an area that someone dropped something. That's simply chance working both ways (that someone dropped something, and I happened to swing my coil over it). By the time I'd found my third gold ring, my son had swung about a half of the hours I had, and he was actually on EVERY hunt, just hunting in an area that was also "looking good" but didn't have a gold ring in it. Poor kid. Just unlucky!

Probability is not a guarantee..> Correlation is not causation, and being lucky is better than being good, sometimes!

Skippy

I am not good at math.
But i have been thinking about a way to come up with a probability formula that could be used to rate your hunting location via some conditions like
Age of the location
size of the location
Population around the location
Income of the population around the location
ground condition (soil type / canopy type)
Location activeness ( beach, or some reason why people came there/go there)
Pre-hunted ( known detectorist already have hunted)

I think a % chance of finding Gold, silver (old coins) could be discerned...

The formula could be used to find out a particular locations percentage of discovery over other areas... or even if just seeking gold for example...

The probability of finding said item...

Example:
Gold probability:
Silver probability:
relic probability:

I was inspired by “ search theory “ used in WW2 to find Uboats...
But where do you start to build a formula like this? and its not like we have scientific testing to see-

If 10 people go to a park for one hour and all have 10 coins in their pockets, how many coins return?

How would one start to figure out a formula for search probability in metal detecting terms?

 

[atomicscott]

I've got lots of work in advanced statistics (Quality Engineering), and am happy to chime in.

What you're suggesting is a fun way to really get people's heads in a tizzy. Basically, these types of "formulas' attempt to take quantitative data and provide a probability of occurrence. This issue you're going to find is in a few points:
1) Unless you can guarantee the data is accurate, you can't properly predict outcomes. For example, how will you determine if something has been "detected?" and to what extent with what equipment, and what coverage?
2) Variation in underlying statistical probabilities. Basically, variation in #s around things like "location activeness" doesn't account for things like seasonality, activities which cause specific losses (like removal of gloves, or application of sunscreen/lotions for rings). Attempting to apply a single number or categories of numbers only increases the variation in the data (decreasing the probability of accuracy)
3) How will you determine probabilities? With a large enough sample population over a long enough time, you'll eventually get a nice Gaussian distribution (normal bell curve) for drops. This is how insurance companies can create actuary tables over population distributions... What you're talking about though is a single isolated point in what is very likely a SHORT time frame. The result is a drastic decrease in predictability, as the possibility of a normal chance occurrence is anywhere within 3 standard deviations of the mean average. (Speaking in lay terms, you can't predict a short term event probability in a very small sample size with any degree of accuracy. You might get lucky, but that's it.) This is why attempting to create a simple formula based on 10 people (or even 1000 people) won't work. You might pull it off (if you had the data) for 10,000, but even then drops don't equal finds!

Just the three above points make it darn near impossible to create a prediction rule with any degree of accuracy. The only thing you're going to get is the information you already know. Things like
- "lots of people in an area in a short amount of time increases the probability of drops."
- "A few people continually visiting in an area over a long amount of time increases the probability of drops."
- "Detectorists in an area reduce the amount of drops available"
- "Demographics (wealth, displays of wealth) of an area increase/decrease the likelihood of valuable drops"
- "Previously unsearched areas increase the likelihood of finds."

All of these things can only be qualified, rather than quantified (not enough long term data collected). As a result, if you were to put all of this together, you'll likely end up with the same list of places that are already qualified, namely:
Parks, beaches, schoolyards, tot-lots and whatnot are great locations.
Parking lot strips, sidewalk strips, skilifts, etc... are all also higher probability locations. Is it a guarantee? nope.

Even a field that gets used as a fair for a short period is likely to have drops... but not guaranteed. Drops are great... how much of it gets picked BACK up is beyond me. Those are the numbers that we can't get! Being able to determine when someone loses something and doesn't look for it, is really tough!

In the end, you can put together a quantitative formula, but it will be no more or less accurate than other qualitative evaluations, simply because the data isn't that accurate.

AND... there's the basic "eyeball" of a situation. I find 2 to 3 times the volume of what my buddies do when we go detecting, because I've learned to simply ask "where would people lose stuff?" A small hill there, a light post here, an open field where lots of things get thrown around... Those target areas become the mines... but I've only found HALF of my best finds searching expected locations. the other half typically comes because I'm walking in the middle of nowhere, and swinging the coil and BEEP! I get a strong signal. There's no reason that gold ring should be THERE... but it is. Go figure.

Basically, it comes down to the fact that your inputs aren't going to be any more accurate than simple comparisons would already give you (you already know a beach populated by sun-bathers is more likely to have jewelry drops than a beach that's filled with fishermen, do you need a number?)

Better, Better yet, and Even Better than that... Qualitative analysis works, but it's the weird crap like "I found the sapphire ring in my front yard, it's worth $15K, and I live in a neighborhood that makes $50K a year"that doesn't make any sense. I always chuckle when I read someone's post that says "eventually if you dig enough pop-tops you will find a gold ring." Uh... nope. That's just statistically not true. Does your probability increase? YES... is it a guarantee? NO.

Just ask me... I've found four gold rings, and probably have dug no more than 500 bottle tops. Why can I get so lucky? Because I'm swinging the coil in an area that someone dropped something. That's simply chance working both ways (that someone dropped something, and I happened to swing my coil over it). By the time I'd found my third gold ring, my son had swung about a half of the hours I had, and he was actually on EVERY hunt, just hunting in an area that was also "looking good" but didn't have a gold ring in it. Poor kid. Just unlucky!

Probability is not a guarantee..> Correlation is not causation, and being lucky is better than being good, sometimes!

Skippy

Wow skippy you sure shot that down, lol. It was not hard to do, with so many variables involved. Cool idea though!

 

[Monkworks]

Thanks so much Skippy. Great to get some feed back from someone who knows what their doing with probability math. I suspected this would be the case just too many open-ends and unknowns. I get that.

Your point about just making common sense judgement is also right and the best way to go for now.

My little group of guys spend a lot of time researching areas to hunt. Then we bang heads to see where we should go.

The obvious locations never produces as suspected, and a the luck factor seems to prevail.

Common sense would tell you a park with a beach, near an old harbor that had an old 100 year spur line down to the peer and Lots of 100 year old trees around would produce. maybe by modeling that park and look for the same type of location that have the same attributes, should produce like the first park and in generally this idea would work... so possibly i need to change from seeking a formula to asset probability, and change to Modeling known GOOD producing locations. Find what parks and locations that have produced and look for that same type of place and conditions... in another...

thanks for the insight...

 

[Skippy SH13]

All excellent ideas. Initially, I tried to do the same, but realized, it just doesn't account for what sites you're going to actually run into the winner. It's like picking which Convenience store to buy your lottery ticket from. LOL

One other thing I've noted, is that this sport is more like fishing than other sports. I know folks who will spend, literally, HOURS researching the exact fly/bait, etc... and I know other guys who spend the same hours actually fishing. Who catches bigger fish more often? Yes, the person actually doing the fishing!

The same is for the Metal Detecting. All the investigations in the world don't do any good if we're not swinging the coil. At the same time, as with fishing, the 'spot' increases the probability of catching a big one (have to go where big fish are if you want to hope to catch one!) Therefore (if we're going to go the math route again):

Success = Location X Time Spent X Lucky Underwear/Socks

Cheers!

-Skippy

Thanks so much Skippy. Great to get some feed back from someone who knows what there doing with probability math. I suspected this would be the case just to many open-ends and unknowns. I get that.

Your point about just making common sense judgement is also right and the best way to go for now.

My little group of guys spend a lot of time researching areas to hunt. Then we bang heads to see where we should go.

The obvious locations never produces as suspected, and a the luck factor seems to prevail.

Common sense would tell you a park with a beach, near an old harbor that had an old 100 year spur line down to the peer and Lots of 100 year old trees around would produce. maybe by modeling that park and look for the same type of location that have the same attributes, should produce like the first park and in generally this idea would work... so possibly i need to change from seeking a formula to asset probability, and change to Modeling known GOOD producing locations. Find what parks and locations that have produced and look for that same type of place and conditions... in another...

thanks for the insight...

 

[Monkworks]

So in clarifying my initial concept of the piece. I wanted to use math (Probability Math, Like used in WW2 Uboat location) to create a indicator, or math function to discern a place or Hunting Location Probability Value.
I will provide more verbiage so you can see my intent better.

Why do I want to use this Probability indicator?

We do our research today in Google Earth Maps. So we could/should define a method of identifying “better than the one beside it” for comparison location hunting*.

So... I end up with a group of good locations, I can hunt. But i want to stack these locations in a priority sequence...

The solution is more fun and accurate to use probability math. To define the “priority” of said location. Maybe I am not using the right math? Like i said not a Math guy. Probability seems right. How i understand probability is I have ten unique items in a bag, if i pull one out I have 1/10 chance of getting said unique item...

So you can see how using the variables around the target (the negative space) to provide a good chance of the outcome, could be used to judge one location over another...

I know location is very hard to define in granular terms. Put i think you understand where I was trying to go.

Your comments are greatly respecting and enjoyable...


Comparison Location Hunting* The act of finding more than one good place to hunt (Metal Detect). Then comparing with other places you could also hunt, and comparing to see what place is better...(I use better loosely...)