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Saltface

Accuracy and Precision

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Dear All,

 

I found a wonderful post on our forum. Krupp and Sigma explained. (link at the end of this post)

The author @Fat_Maniac made a wonderful job. I suggest this as basic reading for all.

I will, based on this post, try to present it in a different way. Why? Because we don't all understand in the same way. In this respect presenting one subject in more than one ways will increase the audience that will understand it.

You will note that I have a difference with the post that I am referring to but this is a matter of terminology. We define accuracy differently. 

 

Accuracy vs Precision

Accuracy is the description of systematic error, a measure of statistical bias.

Precision is a measure of statistical variability.


Accuracy refers to the closeness of a measured value to a standard or known value. For example, if in lab you obtain a weight measurement of 3.2 kg for a given substance, but the actual or known weight is 10 kg, then your measurement is not accurate. In this case, your measurement is not close to the known value.

So, if you aim at the x and your shell lands far away it is not accurate.

 

Precision refers to the closeness of two or more measurements to each other. Using the example above, if you weigh a given substance five times, and get 3.2 kg each time, then your measurement is very precise. Same for our aim. If we aim at the x and most of our shells land close to one spot (not the x) then your guns are precise.

 

Precision is independent of accuracy. You can be very precise but inaccurate, as described above. You can also be accurate but imprecise.

 

For example, if on average, your shells land close to the point you aim at, but they land far from each other (all around the point you aim), then you have accuracy without precision.

 

A good analogy for understanding accuracy and precision is to imagine a basketball player shooting baskets. If the player shoots with accuracy, his aim will always take the ball close to or into the basket. If the player shoots with precision, his aim will always take the ball to the same location which may or may not be close to the basket. A good player will be both accurate and precise by shooting the ball the same way each time and each time making it in the basket. 

 

How are these two notions expressed in the game?

 

In brief Accuracy is the area of the dispersion ellipse. Imagine, referring to the basketball example, an ellipse drawn around the basket. It is given to us as the Horizontal Dispersion (HD) in metres [m] and in Vertical Dispersion (VD) in metres [m]. The dispersion ellipse is the area (expressed in [m2] metres square) where your shells will land. The smaller the area of the ellipse the more accurate the guns are. Or we could say that Accuracy is inversely analogous to the area of the dispersion ellipse. Another way to express this is that our guns are accurate by HD/2 [m] on the horizontal axis and by VD/2 [m] on the vertical axis. It is the description of the systematic error.

 

Precision is the tightness of the shells in the ellipse. Actually, the tighter the grouping is around the point where we intended the shells to land the more precise the guns are. So if we measure the distance of where each shell landed from where we actually intended the shell to land and (oversimplifying) calculate the average we have a metric of precision. This is expressed in the game with the Sigma value. Bigger Sigma better precision.Bigger Sigma more tight grouping of shells. Precision is directly analogous to the Sigma value. It is the measure of the statistical variability. The good thing about the game is that our shells tend to group around the "centre" of the ellipse. We don't have to deal with "offset"

 

As we defined both accuracy and precision as statistical measures it should be clear that we are not talking about one salvo. We are talking about many salvos. For any statistical measure you need a big sample.

 

Read both values together. You want guns that are both accurate and precise. And if I was to chose one of the two I would go for precision.

 

As we saw above, the smaller the ellipse the more accurate are the guns. So, this should be the first indication of the quality of our guns. If the ellipse is very small we can ignore the sigma value. In other words if the guns are very accurate we don't care if they are precise. Alas, this is not the case in the game. The ellipse generally is rather big. Hence our guns are not all that accurate. This is when Sigma value becomes significant. Precision becomes important.

 

In conclusion, dispersion tells us how much bonkers our shells can land (accuracy of the guns) and sigma tells us how often they will land bonkers (precision of the guns). 

And to quote from the wonderful post of @Fat_Maniac "All sigma does is guarantee that OVER TIME a ship with higher sigma will more likely land shots in the middle of its dispersion area" 

 

So these two values Dispersion and Sigma should be evaluated together. And in my humble opinion Sigma is more important.

 

The post of @Fat_Maniac Read it it is wonderful 

 

 

 

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Based on that definition: Precision is the dispersion and accuracy is your point of aim.

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Accuracy is the area (which is an ellipse in the game) in which the dispersed shells will fall and precision is how close to each other they will fall. Fortunately, the shells fall around the centre of the ellipse. In geometry an ellipse has two centres but lets not get pedantic now.

or

Accuracy is how close they fall to where you aim

Precision is how well grouped they are

 

Told you we need to say everything in as many different ways as possible.

 

From the basketball example an accurate player shoots the ball in or close to the basket

A precise player shoots the balls to the same spot every time.

 

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20 minutes ago, Saltface said:

From the basketball example an accurate player shoots the ball in or close to the basket

A precise player shoots the balls to the same spot every time.

As I said, Accuracy is the aim, precision is the deviation from that aim.

 

20 minutes ago, Saltface said:

Accuracy is how close they fall to where you aim

Precision is how well grouped they are

You are aware that according to your words the aiming of the player would have no influence on accuracy?

Nobody can influence the closeness of fall of the shells to your aimpoint.

And it would not matter where you aimed. You could aim at some island, the map border or the bow of a ship. That would make no difference on accuracy, according to your words, since that would have no influence on the closeness of fall of the shells.

 

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Dear @ColonelPete I hope the following graphic will clarify

Presentation1.thumb.jpg.5890f9c4a0045704b5df9e98ca746173.jpg

Not accurate not precise = big dispersion low sigma

Accurate not precise = small dispersion low sigma

Accurate precise = small dispersion big sigma

 

Not accurate but precise doesent exist in our game because we don't have an offset.

Edited by Saltface
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3 minutes ago, Saltface said:

Dear @ColonelPete I hope the following graphic will clarify

Presentation1.thumb.jpg.5890f9c4a0045704b5df9e98ca746173.jpg

The target circle is not the dispersion elipse.

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2 minutes ago, ColonelPete said:

The target circle is not the dispersion elipse.

Dear @ColonelPete,

 

You aim at the centre. Your shells are the red dots.

Why it is not the dispersion ellipse? Because it is not drawn as one?

Actually in geometry a circle is an ellipse who's two centres coincide. 

 

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56 minutes ago, Saltface said:

Dear All,

 

I found a wonderful post on our forum. Krupp and Sigma explained. (link at the end of this post)

The author @Fat_Maniac made a wonderful job. I suggest this as basic reading for all.

I will, based on this post, try to present it in a different way. Why? Because we don't all understand in the same way. In this respect presenting one subject in more than one ways will increase the audience that will understand it.

You will note that I have a difference with the post that I am referring to but this is a matter of terminology. We define accuracy differently. 

 

Accuracy vs Precision

Accuracy is the description of systematic error, a measure of statistical bias.

Precision is a measure of statistical variability.


Accuracy refers to the closeness of a measured value to a standard or known value. For example, if in lab you obtain a weight measurement of 3.2 kg for a given substance, but the actual or known weight is 10 kg, then your measurement is not accurate. In this case, your measurement is not close to the known value.

So, if you aim at the x and your shell lands far away it is not accurate.

 

Precision refers to the closeness of two or more measurements to each other. Using the example above, if you weigh a given substance five times, and get 3.2 kg each time, then your measurement is very precise. Same for our aim. If we aim at the x and most of our shells land close to one spot (not the x) then your guns are precise.

(...)

In conclusion, dispersion tells us how much bonkers our shells can land (accuracy of the guns) and sigma tells us how often they will land bonkers (precision of the guns). 

And to quote from the wonderful post of @Fat_Maniac "All sigma does is guarantee that OVER TIME a ship with higher sigma will more likely land shots in the middle of its dispersion area" 

 

No.

Sorry, but according to the explanation of "precision" and "accuracy" you yourself provided, both dispersion and sigma deal with precision.

The only thing that affects accuracy is the player's ability to aim.

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Dear @Saltface 

All I can take credit for is cutting and pasting, from LWM on shipcomrade. 

But I thought it explained things so well we should all see it here.

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1 minute ago, eliastion said:

No.

Sorry, but according to the explanation of "precision" and "accuracy" you yourself provided, both dispersion and sigma deal with precision.

The only thing that affects accuracy is the player's ability to aim.

 

You aim at the point where the reticle is. 

Aiming is the players job.

 

Your guns are accurate and or precise. Not you. You aim where the reticle is.

Your aim may be good or bad. Not accurate or precise. Those are qualities of the guns.

 

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Just now, Saltface said:

 

You aim at the point where the reticle is. 

Aiming is the players job.

 

Your guns are accurate and or precise. Not you. You aim where the reticle is.

Your aim may be good or bad. Not accurate or precise. Those are qualities of the guns.

 

Yes, aiming is player's job. Accuracy is determined by the player. Precision is determined by dispersion and sigma. If all your shells fall in one place that's farr off what you wanted to hit then it's you who screwed up, not your guns being inaccurate. There is no mechanic in WoWs that would introduce systematic error into your gun performance.

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Dear @Fat_Maniac

 

Thank you for giving credit where it is due. I was absorbed by your article and I failed to recognize the source. I stand corrected.

All credit for the original to LWM. Gratitude to you for enlightening us.

 

Regards

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The problem with using this accuracy/precision model is that dispersion is influenced by the dispersion pattern, dispersion value, and sigma.

This model is useful for real life examples of weapons or measuring equipment with a specific pattern to their behaviour, not digital guns that use an RNG model to determine their spread.

Dispersion deals entirely in gun accuracy, while sigma is a function of both accuracy and precision.

 

Also, regarding aiming and accuracy. Gun accuracy =/= player accuracy. When a player fires his guns, the gun accuracy is based on where the shots land compared to where the player was aiming. The player's accuracy is where he's aiming compared to where his target is. What the person behind the gun intends to hit is entirely irrelevant to how accurate the guns are.

The guns will fire, and the projectile will leave the barrel. The spread of the gun is completely irrelevant to what the person behind the gun is actually intending to hit, as the gun will only fire where it is pointed.

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22 minutes ago, Saltface said:

Dear @ColonelPete,

 

You aim at the centre. Your shells are the red dots.

Why it is not the dispersion ellipse? Because it is not drawn as one?

Actually in geometry a circle is an ellipse who's two centres coincide. 

 

Because the target circle is much bigger than the dispersion elipse, except in the upper left target. The dispersion is much smaller on the lower targets.

And as you said yourself, we do not have an offset in the game. Therefore the upper right target does not apply either.

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3 minutes ago, eliastion said:

Yes, aiming is player's job. Accuracy is determined by the player. Precision is determined by dispersion and sigma. If all your shells fall in one place that's farr off what you wanted to hit then it's you who screwed up, not your guns being inaccurate. There is no mechanic in WoWs that would introduce systematic error into your gun performance

 

Player aims - Aim can be good or bad - The player aims well or not

Accuracy is how far from where you aim the shells will land - They will land in the dispersion ellipse - This depends on the gun - The gun is inaccurate or accurate.

Precision is how close to each other (on average) your shells will land - This is Sigma - This also depends on the gun - The gun is imprecise or precise.

The confusion about these two qualities of the gun - accuracy and precision - come because they do not offset - lets say to the left or the right of further or shorter. They group around the centre of the dispersion area.

 

Anyway, so long you manage to hit the ship you are aiming for who cares what is accuracy and what is dispersion.

Read more  here

Source: https://nptel.ac.in/courses/102103044/module1/lec1/2.html

 

Accurate and precise determination of analytes

It is hardly necessary to explain how critical an accurate determination of an analyte is. If a breath alcohol detector is not accurate, a drunk driver may be let off risking the life of others while a sober one may be detained. Unless the concentration of analyte is determined accurately and precisely, it is difficult to make meaningful conclusions. So, what exactly do the accuracy and precision mean? Accuracy is the measure of how closely the measured values match the true values. Precision tells about the reproducibility of the measurement i.e. how closely the measured values are if repeated measurements are made on the sample (Figure 1.1).

01.png.54d4d0e132a7477b7ae5e43408dd3ef2.png

Figure 1.1 Schematic representations of accuracy and precision. Consider the centre of the concentric circles as the true value; the measured values are represented as the black dots. The measured values shown in panel A are close to the true value (accurate) as well as to each other (precise). The measured values in panel B are close to each other (precise) but far from the true value (inaccurate). The individual values in panel C are far away from the true value but randomly distributed about the true value; the average value lies close to the true value (accurate but imprecise). Panel D represents inaccurate and imprecise measurements.

It is easy to imagine the consequences of using an inaccurate equipment; it would give inaccurate results. Imprecise equipments, even if accurate, are problematic as a large number of measurements are required to arrive close to the true value which may take considerable amount of time. An analytical tool therefore has to be both accurate and precise to be used reliably and for faster analysis.

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3 minutes ago, Ubrael said:

The problem with using this accuracy/precision model is that dispersion is influenced by the dispersion pattern, dispersion value, and sigma.

This model is useful for real life examples of weapons or measuring equipment with a specific pattern to their behaviour, not digital guns that use an RNG model to determine their spread.

Dispersion deals entirely in gun accuracy, while sigma is a function of both accuracy and precision.

 

Also, regarding aiming and accuracy. Gun accuracy =/= player accuracy. When a player fires his guns, the gun accuracy is based on where the shots land compared to where the player was aiming. The player's accuracy is where he's aiming compared to where his target is. What the person behind the gun intends to hit is entirely irrelevant to how accurate the guns are.

The guns will fire, and the projectile will leave the barrel. The spread of the gun is completely irrelevant to what the person behind the gun is actually intending to hit, as the gun will only fire where it is pointed.

Thank you for the input.

In my understanding (and from LWM text) it seems that Sigma defines the repeatability of a good grouped shot. It is closer to the definition of precision. But I am willing to accept also your interpretation that it is a function of both.

Either way, guns have accuracy and precision.

Dispersion defines accuracy

Sigma defines accuracy and precision.

Could be. I wish I had the hard data from WG. Then this debate would be over in a flash.

 

Thank you again for the input.

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6 minutes ago, Saltface said:

Precision is how close to each other (on average) your shells will land - This is Sigma -

No.

If you have dispersion elipse of 1m in the game, you sigma can be 0.1 and you will still have BY FAR the most precise gun in the game.

That is the reason WG gave different ship types have different dispersion sizes.

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1 minute ago, Saltface said:

Then this debate would be over in a flash.

 

This debate has been over since you started it, as in, there is no debate.

 

You are trying to make it fit, but it does not, as CP already pointed.

 

Not to mention, this has no real goal, you will not have WGs data, and real world has no sigma value...

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Dear @ColonelPete,

3 minutes ago, ColonelPete said:

No.

If you have dispersion elipse of 1m in the game, you sigma can be 0.1 and you will still have BY FAR the most precise gun in the game.

That is the reason WG gave different ship types have different dispersion sizes.

 

I quote from my OP

1 hour ago, Saltface said:

As we saw above, the smaller the ellipse the more accurate are the guns. So, this should be the first indication of the quality of our guns. If the ellipse is very small we can ignore the sigma value. In other words if the guns are very accurate we don't care if they are precise. Alas, this is not the case in the game. The ellipse generally is rather big. Hence our guns are not all that accurate. This is when Sigma value becomes significant. Precision becomes important.

 

 

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Precision being based on the average placement of each shot gives rise to the following corny joke:

 

Three statisticians go clay pigeon shooting.  The first one misses five metres left of the target, while the second misses five metres right of it.  The third one yells "We got it!"

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12 minutes ago, Saltface said:

Dear @ColonelPete,

 

I quote from my OP

 

 

And if you aim at the border, you still do not hit a thing --> inaccurate.

 

You still do not get that the dispersion elipse is:

Quote

... a measure of statistical variability. 

 

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33 minutes ago, ColonelPete said:

Because the target circle is much bigger than the dispersion elipse, except in the upper left target. The dispersion is much smaller on the lower targets.

And as you said yourself, we do not have an offset in the game. Therefore the upper right target does not apply either.

This is correct, I should have drawn the ellipses for clarity.

 

I also noted that the upper right does not apply.

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@ColonelPete

 

It seems our difference is that you consider the player as being accurate.

I see the player as having good aim and the guns being accurate and precise.

 

Lets agree that I am not referring to the player's aim at all.

I am only discussing guns attributes as they are expressed by dispersion and sigma.

 

And I shall correct my graphic. Your observation was correct. It lacks clarity.

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@ColonelPete

 

As promised 

 

Shaded blue ellipse is dispersion - aim point is centre of target

 

Big ellipse = large dispersion = not accurate gun (inaccurate)

Small ellipse = small dispersion = accurate guns

Well grouped shells = high sigma value = precise guns

not well grouped shells = low sigma value = not precise guns (imprecise)

 

222.thumb.jpg.7c1573b26dcf8ac20687bcbf7607e6b4.jpg

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