Why do we say "per egg" instead of "per clutch"

This is said over and over and I have no idea why, I just saw it in a recent thread again so riddle me this...

I breed a lesser to a normal, I tell someone statistically they will be 50% lesser/50% normal. Then for some reason, people want to say its not per clutch, its per egg....why?

Say I have a 4 egg clutch
L = Lesser
N = Normal

0 Lesser - 1 way
NNNN

1 Lesser - 4 ways
LNNN
NLNN
NNLN
NNNL

2 Lesser - 6 ways (the 50/50...)
LLNN
LNLN
LNNL
NLLN
NLNL
NNLL

3 Lesser - 4 ways
LLLN
LLNL
LNLL
NLLL

4 Lesser - 1 ways
LLLL

so it looks like you have the best chance of getting 2 Lessers out of 4 eggs, so how the heck can you deny statistically the clutch will be 50/50?

Because you can still get all lessers or no lessers. Each egg has a 50/50 percent chance. So while in a mathematical sense that means the clutch should be 50/50 in the real world it just doesn't always work out that way. If each egg ends up being normal you do not have a clutch that matches the odds, but it still makes sense per egg

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Originally Posted by purplemuffin

Because you can still get all lessers or no lessers. Each egg has a 50/50 percent chance. So while in a mathematical sense that means the clutch should be 50/50 in the real world it just doesn't always work out that way. If each egg ends up being normal you do not have a clutch that matches the odds, but it still makes sense per egg

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Your missing the word statistically

Statistically it should be that. But the problem is it's the real world, so it's just more realistic to say per egg. Each egg DOES have a chance at being any of those things. Statistically it should make sense, but the problem is it just doesn't end up that way in the real world. In math world, yes.

Compare it to flipping a coin. If I flipped heads 10 times in a row that has no effect on the 11th flip. The 11th flip is still a 50/50 shot.

So, if you have a six egg clutch from lesser x normal you would expect three lessers and three normals; however, if the first three are lessers you still have 50/50 odds on the last three eggs.

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Originally Posted by purplemuffin

Statistically it should be that. But the problem is it's the real world, so it's just more realistic to say per egg. Each egg DOES have a chance at being any of those things. Statistically it should make sense, but the problem is it just doesn't end up that way in the real world. In math world, yes.

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How does saying statically not account for the real world, it doesn't mean concrete thats whats going to happen.

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Originally Posted by Dave Green

Compare it to flipping a coin. If I flipped heads 10 times in a row that has no effect on the 11th flip. The 11th flip is still a 50/50 shot.

So, if you have a six egg clutch from lesser x normal you would expect three lessers and three normals; however, if the first three are lessers you still have 50/50 odds on the last three eggs.

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That's a much better way of explaining it, I couldn't figure out the words to use. :D

Your math goes wrong when you add more genes. You can't average an average. You have to apply that to each egg and it changes your number drastically when more genes are involved. That's why mutligene animals are more expensive than adding two genes prices together.

Regards,

B

Because the Egg Gods and the Odds Gods prefer to hear the "per egg". It makes them more merciful to us breeders when the tiny heads start poking out of each egg.

That's my excuse.

The coin flip explanation is a good one too. And it's true that it 'seems' like the 50/50 clutch would be true in the 'real world' but using the same math to figure a multiple gene clutch will lead you to possible disappointment, since if each egg has only a 1/16 chance of being your golden combo, just because you have 16 eggs doesn't mean that you'll automatically expect at least one of the golden combo. Since each EGG has a very small chance of nabbing all the genes it needs, it's a less likely outcome than just needing to produce 16 possibilities/eggs.

On the surface, it seems the same thing egg vs clutch. But it really does make sense once you delve deeply into it.

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Originally Posted by Dave Green

Compare it to flipping a coin. If I flipped heads 10 times in a row that has no effect on the 11th flip. The 11th flip is still a 50/50 shot.

So, if you have a six egg clutch from lesser x normal you would expect three lessers and three normals; however, if the first three are lessers you still have 50/50 odds on the last three eggs.

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It still never changes the clutch's statistics, despite what actually hatches. Real world doesn't change statistics

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Originally Posted by Simple Man

Your math goes wrong when you add more genes. You can't average an average. You have to apply that to each egg and it changes your number drastically when more genes are involved. That's why mutligene animals are more expensive than adding two genes prices together.

Regards,

B

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I don't understand how my math went wrong when I didn't do any. I just listed every possible outcome. Multiple genes will make it more complicated but I don't see how it would effect anything.

Why does everyone want to keep saying real world? It seems no one is reading the word statistically. I'm not asking what happens in the real world. I'm not saying per egg is wrong. I'm asking how can statistically per clutch be wrong because it is always "corrected" when there is nothing wrong with it.

The only thing about real world and statistics being related is the law of averages, which has nothing to do with what i'm talking about.

Well, per clutch just sounds bad! It sort've makes it sound (to newcomers) like you only have a 50% chance of getting "A SINGLE" spider in a clutch of spider x normal babies. If you say every egg has a 50/50 shot it sounds better, at least that's my story and I am sticking to it! LOL

You get what you get.

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Originally Posted by OhhWatALoser

It still never changes the clutch's statistics, despite what actually hatches. Real world doesn't change statistics

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I never mentioned real world vs. statistics. The genetics/odds work per individual snake/egg. Of course you can apply it to a clutch, or 100 eggs, or 1000 eggs, etc. But at the end of the day it all comes down to the fact that each egg has a 50/50 shot of being a lesser or normal (using your example).

I used the coin flip example as it helps explain the odds. If I had 100 lesser x normal eggs incubating we can all guess that I would get close to 50 lessers and 50 normals but odds are only odds. If the first clutch hatches and I had 8 lessers and 0 normals it may change the results but it only means I beat the odds and it has no effect on future egg or clutch results.

I don't think it's a big deal either way...

Dave is explaining the same thing as myself but I'm going to give this a crack to help you out. I don't mean to offend you if you don't understand probability. I loved this stuff in school. So here goes...

Probability doesn't work the way you're thinking. I will just use your 1/2 or 50/50 for this explanation but you can follow along with the chart if that's easier. Probability means that the more eggs you have the higher percentage you have to hit your probability (50/50). That is because your odds are applied to each egg (not clutch). For smaller clutches your chances of hitting (50/50) probability are lower. The more eggs you have, the higher the (50/50) probability is that you will hit the expected number. That's why the odds are applied per egg. Even with 100 eggs you never will hit the 100% 50/50 probability just because of the way probability works and the fact that the odds are applied per egg. This is posted online @ www.cornguide.com by Serpwidgets to help breeders understand the chances of successfully hitting based on the amount of genes.I don't know any other way to help you understand it besides reading up on probability yourself. I don't mean this offensively.

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Originally Posted by Serpwidgets

Since the predictors give odds per egg, I though it might be useful to show the odds in a different way: expressed in terms of "probability of success."

What do I mean by that? Well, say your desired morph has a 1 in 16 chance according to the predictor. How likely are you to hatch one or more in a clutch of 4, or a clutch of 17? If you have a 1/64 chance per egg of some new triple morph from triple hets, what are your odds of hatching one or more if you've got 47 eggs to hatch?

In these charts "success" is defined as hatching any number of the desired morph... not just one, but one or more. All of the charts are the same thing, just "zoomed" to show finer detail for smaller numbers, and zoomed out to show the odds for up to 150 eggs. They include 1 in 2, 4, 8, 16, 32, 64, 128, and 256 "odds per egg" which will cover any combination of hets/homos for up to 4 recessive traits at a time.

First is for 16 eggs:
http://cornguide.com/odds/Eggs016.gif

So, to demonstrate how to read this, if your odds are 1/2 per egg you use the top green area. Follow the line up from the bottom depending on how many eggs you have. If you have 1 egg, your chance of success is 50%. With 2 eggs, it goes up to 75%. With 3 eggs you've got an 87.5% chance. And with 4 eggs, the odds go up to 94%.

Notice that the curve never reaches 100%... probabilities are not guarantees. Which probability equates to saying you "should" succeed? Well, it's up to you to decide what level of "risk" you are comfortable with in your own projects. But these make more sense of the predictions because it's not often that you plan on hatching a single egg at a time. ;)

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http://cornguide.com/odds/Eggs016.gif

Regards,

B

Well to me, if you have say a 1 in 64 chance at a morph, no ball python I know is going to have 64 eggs at one time! :O

So, by saying the chance is per egg, it seems easier to wrap your head around, at least to me. To me, saying per clutch means my ball MUST have 64 eggs and then I get the morph I want. By saying per egg, that to me means I could get that morph in my first 4 eggs, or not get it at all no matter how many eggs I get. This is more realistic to me. Does that make sense ? :confused:

Gale

You know what? I don't really care which way people say it. As long as I can understand what they mean it's all good to me.

LOL, I didn't imagine when I posted earlier today in a thread about the probability being per egg, that it would spark this conversation, but it's turned out to be a pretty interesting thread. :)

I don't think I really need to add much in way of explanation, because I don't think I could explain it any better than it has already been, by prior posters. :bow:

Ok ill start with can you guys please stop repeating yourselves about the per egg. We all understand that and its not what im trying to discuss, im trying to understand why saying "statistically you should get 50% lesser 50% normal" is wrong, why does it need "correcting". I understand the odds are per egg. an odd number egg clutch its obviously impossible to have a 50/50. but again, statistically what should you get?

ok ill try this fill in the blank "statistically you should get _______ per clutch"

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Originally Posted by Dave Green

I never mentioned real world vs. statistics. The genetics/odds work per individual snake/egg. Of course you can apply it to a clutch, or 100 eggs, or 1000 eggs, etc. But at the end of the day it all comes down to the fact that each egg has a 50/50 shot of being a lesser or normal (using your example).

I used the coin flip example as it helps explain the odds. If I had 100 lesser x normal eggs incubating we can all guess that I would get close to 50 lessers and 50 normals but odds are only odds. If the first clutch hatches and I had 8 lessers and 0 normals it may change the results but it only means I beat the odds and it has no effect on future egg or clutch results.

I don't think it's a big deal either way...

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Big deal not really, but If no one cared, no one would keep "correcting" others.

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Originally Posted by rabernet

LOL, I didn't imagine when I posted earlier today in a thread about the probability being per egg, that it would spark this conversation, but it's turned out to be a pretty interesting thread. :)

I don't think I really need to add much in way of explanation, because I don't think I could explain it any better than it has already been, by prior posters. :bow:

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It's posted in a lot of threads, I was going to respond in the thread, but figured it be better as its own topic

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Originally Posted by Dave Green

Compare it to flipping a coin. If I flipped heads 10 times in a row that has no effect on the 11th flip. The 11th flip is still a 50/50 shot.

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This is the perfect answer. A+ ;)

Statistically - using a large enough sample - they should tie out.

To respond to Ohwhatloser. People say per egg because a typical clutch is statistically not a large enough sample for the odds to work out. I'm too many decades out of my statistics 401 class to remember the formula, but there is calculation that will determine a statistically accurate sample size...and its a boatload bigger than the biggest clutch size...hence - per egg.

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Originally Posted by OhhWatALoser

Ok ill start with can you guys please stop repeating yourselves about the per egg. We all understand that and its not what im trying to discuss, im trying to understand why saying "statistically you should get 50% lesser 50% normal" is wrong, why does it need "correcting". I understand the odds are per egg. an odd number egg clutch its obviously impossible to have a 50/50. but again, statistically what should you get?

ok ill try this fill in the blank "statistically you should get _______ per clutch"

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I get what you're saying.....and here's my take on the answer:

It's actually pretty rare that someone says "Statistically you should get ____ per clutch." And even that statement isn't really correct. There is no "should" in statistics. It would more accurately read "Statistically you could get...." But again...people rarely ever actually express it that way.

More often you'll hear, "You'll get 50% lessers in a lesser x normal clutch" ...or something along those lines. The ways it is most commonly expressed leaves the impression to a newbie that they WILL get half lessers and half normals in their clutch.

And the simplest way to fix that misunderstanding is to explain that the genetic statistics are calculated PER EGG. Each egg is its own little formula, independent of the whole clutch.

If you have a lesser x normal clutch that has 12 eggs in it....what are the odds that you'll actually hatch out 6 lessers and 6 normals? I don't know the formulas, but I'll bet the odds of that outcome are not 50/50. ;)

This is a great thread! :gj:

Couldnt agree more with JLC..if there is a fill in the blank question in the examination like this:
"statistically you should get _______ per clutch"

I should get free marks because the question itself is wrong.

The reason people keep "focusing on" the per-egg instead of addressing the 'statistically' is because that's the issue. You're asking a circular argument in my opinion.

If you have a clutch of ten eggs, and it's a co-dom x normal breeding, you "could" say "Well, half the eggs will hatch as the co-dom".

But by the math, is that correct? Since each egg has a 50/50 shot, you have to actually calculate what the odds are that half of the eggs will fall on the one side and the other half will fall on the other side of the gene payout.

So.... what are the odds that 5 seperate eggs will get the co-dom gene and 5 eggs will get the normal gene? That's a completely different calulation in math than just saying '50/50'. It CAN work out that way, but it's not a simple "Well, half will get the co-dom gene" because you are calulating a whole different equation. You have several possibilities at this point. You could have 9 co-doms and 1 normal... 8 co-doms and 2 normals.... etc etc. If my poor abused brain is right, you have 11 possibilities in a 10 egg clutch.

0 co-dom - 10 normal
1 co-dom - 9 normal
2 co-dom - 8 normal
3 co-dom - 7 normal
4 co-dom - 6 normal
5 co-dom - 5 normal
6 co-dom - 4 normal
7 co-dom - 3 normal
8 co-dom - 2 normal
9 co-dom - 1 normal
10 co-dom - 0 normal

So technically at this point, you only have a 1 in 11 shot of producing 50/50. I think that's a 9% chance of hitting the 50/50 split exactly.

But now, what if you don't have 10 eggs? That changes the odds for the clutch. Fewer eggs/more eggs either way it changes the odds for hitting a 50/50 clutch split. So if you used 'per clutch' then you'd have to actually do math to figure out what your odds are for hitting the 50/50 split and THEN figure in the odds vs the genetics odds.

Or... you can say it's a 50/50 chance per egg, and let the brain stop churning with math and odds and numbers.

Someone can correct me if this is all bogus, but it's how I understand the odds and math.

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Originally Posted by wolfy-hound

So technically at this point, you only have a 1 in 11 shot of producing 50/50. I think that's a 9% chance of hitting the 50/50 split exactly.

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DING, DING, DING........winner, winner, chicken dinner! That's EXACTLY why it's far more accurate to explain that the odds are PER EGG, not per clutch.

Another example is when people commonly confuse the odds with winning the lottery. People think that by buying MORE tickets, they'll increase their odds of winning. If you have a 1:1,000,000,000 chance of winning, buying 100 tickets gives you the same odds of winning as buying 1 ticket. No matter what, the odds of winning always stay at 1,000,000,000. So, buying 1 ticket gives you 1:1,000,000,000 chance of winning, buying 100 tickets gives you 100:1,000,000,000 chance of winning.

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Originally Posted by wolfy-hound

The reason people keep "focusing on" the per-egg instead of addressing the 'statistically' is because that's the issue. You're asking a circular argument in my opinion.

If you have a clutch of ten eggs, and it's a co-dom x normal breeding, you "could" say "Well, half the eggs will hatch as the co-dom".

But by the math, is that correct? Since each egg has a 50/50 shot, you have to actually calculate what the odds are that half of the eggs will fall on the one side and the other half will fall on the other side of the gene payout.

So.... what are the odds that 5 seperate eggs will get the co-dom gene and 5 eggs will get the normal gene? That's a completely different calulation in math than just saying '50/50'. It CAN work out that way, but it's not a simple "Well, half will get the co-dom gene" because you are calulating a whole different equation. You have several possibilities at this point. You could have 9 co-doms and 1 normal... 8 co-doms and 2 normals.... etc etc. If my poor abused brain is right, you have 11 possibilities in a 10 egg clutch.

0 co-dom - 10 normal
1 co-dom - 9 normal
2 co-dom - 8 normal
3 co-dom - 7 normal
4 co-dom - 6 normal
5 co-dom - 5 normal
6 co-dom - 4 normal
7 co-dom - 3 normal
8 co-dom - 2 normal
9 co-dom - 1 normal
10 co-dom - 0 normal

So technically at this point, you only have a 1 in 11 shot of producing 50/50. I think that's a 9% chance of hitting the 50/50 split exactly.

But now, what if you don't have 10 eggs? That changes the odds for the clutch. Fewer eggs/more eggs either way it changes the odds for hitting a 50/50 clutch split. So if you used 'per clutch' then you'd have to actually do math to figure out what your odds are for hitting the 50/50 split and THEN figure in the odds vs the genetics odds.

Or... you can say it's a 50/50 chance per egg, and let the brain stop churning with math and odds and numbers.

Someone can correct me if this is all bogus, but it's how I understand the odds and math.

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^^This

The trouble with your understanding is 50/50, so lets look at 1 in 4 chance. 25/75 per clutch 16 eggs would always give you an average of 4 of the what ever it is. The real world doesn't work that way, a 1 in 4 chance of ___ means per egg, so in 16 egg clutch you would be lucky to get 4. It is simply not per clutch it is on an egg to egg basis.

I felt the need to jump in on this, even though it appears to me that this has been explained really well already. However, I haven't seen anyone really touch on what I was thinking when I read the original post.

The reason the chance is applied per egg is because that is what a Punnet Square defines. When you build a punnet square, what you are doing is showing what genes each parent has available to pass on the the offspring. One side shows the mother possible genes, and the other side shows the fathers possible genes. Each square within the entire process is showing the possible combinations. Therefore each square shows the outcome of what the sperm was carrying and contributed to the egg (which was carrying the other side). The punnet square is a visual way to look at what can happen to each egg.

As others have said, my description above is exactly why I just hatched 6 normals from a Sugar bred to a Normal. In the long run, as Dave stated, with a large enough sampling size, why will come very close to the statistics, but the punnet square still only applies to each egg.

I hope that wasn't too confusing.

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.....im trying to understand why saying "statistically you should get 50% lesser 50% normal" is wrong.....

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How does that work with a 5 egg clutch??

How about if we add in the male female possibility?

Per egg.:rolleyes:

@ The OP, here's the situation as it comes up multiple times a year:

Someone tried to describe statistics to someone new. Person 1 tells person 2 "if you breed a lesser to a normal, half the clutch will be lessers".

Person 3 jumps in and, in the interest of full disclosure, feels it is necessary to tell person 2 that "actually, you aren't guaranteed that half the clutch will be lessers. In fact, each egg has a 50/50 chance of being either, so you CAN end up with all normals, all lessers, or a mix. Statistically, half the clutch should be lessers, but it can swing either way"

Do whatever you want with statistics, but the above example is where you often hear someone saying that "each egg has X% chance of being Y"

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Originally Posted by rabernet

DING, DING, DING........winner, winner, chicken dinner! That's EXACTLY why it's far more accurate to explain that the odds are PER EGG, not per clutch.

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Blackjack!

no really though... this is a very good thread. I'm no breeder but remembering my stats classes. Each egg is an "independent trial". Meaning, one egg's outcome doesn't effect any of the other outcomes, or eggs. Therefore the %'s have to be about each individual egg, and not the clutch as a whole, like most people have stated already. Just wanted to get in on the stats discussion. :)

It's like roulette. Just because the ball landed on black 4 times in a row, doesn't mean there is a higher chance of it falling on red the next time. They're all independent trials and past trials in no way effect the outcome of the next trial.

phew... this is fun! Please correct, add or whatever if I'm off...

It's an excellant thread. Very much enjoying reading/discussing it, even though it's math. I used to be quite good at math.

And where do I pick up my chicken dinner?

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Originally Posted by wolfy-hound

It's an excellant thread. Very much enjoying reading/discussing it, even though it's math. I used to be quite good at math.

And where do I pick up my chicken dinner?

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Gotta come to Atlanta for that!:D

I'm sure I'll end up in Atlanta at some point.

I did actually brag today about managing to engage my brain and figure out the math that lurked in the back of my head since I read this thread the first time.

Statistically, I would expect half the clutch from a lesser x normal to be lesser and the other half to be normal.

Therefore, a one-egg clutch would be expected to produce half lesser and half normal. Is the lesser half of the baby the front half or the rear half? :)

The binomial theorem covers distribution of results in a given set of trials. Briefly, the larger the clutch, the lower the probability of getting a exact 50:50 split. A 50:50 split is the most likely single result, though.

The 16 possible results from a 4 egg clutch:
lesser - lesser - lesser - lesser = 4 lesser
lesser - lesser - lesser - normal = 3 lesser
lesser - lesser - normal - lesser = 3 lesser
lesser - lesser - normal - normal = 2 lesser
lesser - normal - lesser - lesser = 3 lesser
lesser - normal - lesser - normal = 2 lesser
lesser - normal - normal - lesser = 2 lesser
lesser - normal - normal - normal = 1 lesser
normal - lesser - lesser - lesser = 3 lesser
normal - lesser - lesser - normal = 2 lesser
normal - lesser - normal - lesser = 2 lesser
normal - lesser - normal - normal = 1 lesser
normal - normal - lesser - lesser = 2 lesser
normal - normal - lesser - normal = 1 lesser
normal - normal - normal - lesser = 1 lesser
normal - normal - normal - normal = 0 lesser

Probability of a 4 lesser clutch = 1/16
Probability of a 3 lesser clutch = 4/16
Probability of a 2 lesser clutch = 6/16
Probability of a 1 lesser clutch = 4/16
Probability of a 0 lesser clutch = 1/16

This shows that while the probability of a lesser from one egg is 1/2, the probability of 2 lessers from a four egg clutch is less than 1/2. This is why the odds are on a per egg basis rather than a per clutch basis.

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Originally Posted by JLC

I get what you're saying.....and here's my take on the answer:

It's actually pretty rare that someone says "Statistically you should get ____ per clutch." And even that statement isn't really correct. There is no "should" in statistics. It would more accurately read "Statistically you could get...." But again...people rarely ever actually express it that way.

More often you'll hear, "You'll get 50% lessers in a lesser x normal clutch" ...or something along those lines. The ways it is most commonly expressed leaves the impression to a newbie that they WILL get half lessers and half normals in their clutch.

And the simplest way to fix that misunderstanding is to explain that the genetic statistics are calculated PER EGG. Each egg is its own little formula, independent of the whole clutch.

If you have a lesser x normal clutch that has 12 eggs in it....what are the odds that you'll actually hatch out 6 lessers and 6 normals? I don't know the formulas, but I'll bet the odds of that outcome are not 50/50. ;)

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Well maybe there in lies my problem. When I hear some say statistically you should/will/could/can/ect. it all means the same thing to me. there are almost never any 100%'s or 0%'s in statistics and if someone is using the word, i assume no certainties automatically, just probability. If you tell me statistically you will get X. I'm going to take that as X is my most likely scenario.

I was going to say maybe I need to relook my definition of statistically and google gave me the most helpful definition ever...."with respect to statistics." So with that as no help. I'm still going to assume im the screwed up one.

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Originally Posted by paulh

Statistically, I would expect half the clutch from a lesser x normal to be lesser and the other half to be normal.

Therefore, a one-egg clutch would be expected to produce half lesser and half normal. Is the lesser half of the baby the front half or the rear half? :)

The binomial theorem covers distribution of results in a given set of trials. Briefly, the larger the clutch, the lower the probability of getting a exact 50:50 split. A 50:50 split is the most likely single result, though.

The 16 possible results from a 4 egg clutch:
lesser - lesser - lesser - lesser = 4 lesser
lesser - lesser - lesser - normal = 3 lesser
lesser - lesser - normal - lesser = 3 lesser
lesser - lesser - normal - normal = 2 lesser
lesser - normal - lesser - lesser = 3 lesser
lesser - normal - lesser - normal = 2 lesser
lesser - normal - normal - lesser = 2 lesser
lesser - normal - normal - normal = 1 lesser
normal - lesser - lesser - lesser = 3 lesser
normal - lesser - lesser - normal = 2 lesser
normal - lesser - normal - lesser = 2 lesser
normal - lesser - normal - normal = 1 lesser
normal - normal - lesser - lesser = 2 lesser
normal - normal - lesser - normal = 1 lesser
normal - normal - normal - lesser = 1 lesser
normal - normal - normal - normal = 0 lesser

Probability of a 4 lesser clutch = 1/16
Probability of a 3 lesser clutch = 4/16
Probability of a 2 lesser clutch = 6/16
Probability of a 1 lesser clutch = 4/16
Probability of a 0 lesser clutch = 1/16

This shows that while the probability of a lesser from one egg is 1/2, the probability of 2 lessers from a four egg clutch is less than 1/2. This is why the odds are on a per egg basis rather than a per clutch basis.

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Makes sense, I was just looking at no matter how many eggs you have your either going to have the best chance at the 50/50 spilt with even number of eggs and with odd number of eggs its going to be the same for 2 between the 50/50 split, 5 eggs, you got the same chances for 2 lessers as you do for 3 lesser.

I think I was looking for more of an English lesson than a math lesson, I understand the math.

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Originally Posted by wolfy-hound

Someone can correct me if this is all bogus, but it's how I understand the odds and math.

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you need to take into account there are more than one way to have 1 lesser, 2 lesser, ect.

0 Lesser 1 way
1 Lesser 10 ways
2 Lessers 45 ways
3 Lessers 120 ways
4 Lessers 210 ways
5 Lessers 252 ways
6 Lessers 210 ways
7 Lessers 120 ways
8 Lessers 45 ways
9 Lessers 10 ways
10 Lessers 1 way
total of 1024

so i guess it would be 252/1024 near 25%. which you still have a better chance of the 50/50 split than anything else. but no its not 50% chance over all.

Probability is what people should be saying. Not statistically... The probability of this happening is ____. That might clear things up a bit?

Regards,

B

Well, if you are counting which egg will be which in a clutch(instead of just 11 possibilities) aren't you counting 'per egg' rather than 'per clutch'? Since it doesn't matter which egg was lesser and which was normal, if you are just counting numbers?

Just wondering on that.

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Originally Posted by Simple Man

Probability is what people should be saying. Not statistically... The probability of this happening is ____. That might clear things up a bit?

Regards,

B

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then i guess my question is, how do you use the word statistically correctly?

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Originally Posted by wolfy-hound

Well, if you are counting which egg will be which in a clutch(instead of just 11 possibilities) aren't you counting 'per egg' rather than 'per clutch'? Since it doesn't matter which egg was lesser and which was normal, if you are just counting numbers?

Just wondering on that.

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Its all the possible outcomes of the clutch over all. it does matter which egg was lesser, because each egg is different and has the 50/50 shot. there are more ways to get the 50/50 spilt than anything else. To say you have the same chance of getting 0 Lessers (1/1024) as 5 Lesser (252/1024) isn't correct, but the chance of getting 0 lessers as 10 Lessers is. With a big enough sample size according to the law of averages, the real world data will reflect that. If You have 11x 10 egg clutches, your most likely not going to see one with 0 lesser, one with 1, one with 2 lessers,...., one with 10 lessers.

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Originally Posted by purplemuffin

Because you can still get all lessers or no lessers. Each egg has a 50/50 percent chance. So while in a mathematical sense that means the clutch should be 50/50 in the real world it just doesn't always work out that way. If each egg ends up being normal you do not have a clutch that matches the odds, but it still makes sense per egg

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This makes perfect sense to me BTW. I don't see why there is so much confusion, or a debate..

Cheers.

The probabilities that people so often use in snake genetics are based off of the probability of a certain gene being passed to an individual based off the population of potential genes. Each time the gametes are formed in a lesser, there is a 50% chance that it will contain the lesser gene and a 50% chance it will contain the normal gene. So lets say the lesser is a male. If every meiotic division is successful and leads to 4 sperm cells, then we'd expect 2 sperm to carry the lesser gene and 2 sperm to carry the normal gene. Now do this thousands of times and you have a large number of both. This is your population of gametes that can be passed to the next generation. 50% are normal and 50% are lesser. Now this male is paired with a female. She is a normal so every egg she develops carries that normal gene. Now if every sperm went to a single egg, there were no other factors (though there can be!), and every egg went full term, then you'd could expect a 50/50 ration in the clutch as you're stating. Instead, out of those thousands or millions of sperm, only 4-12 make it to eggs so instead of 4 eggs being fertilized by four sperm, 2 carrying the lesser gene and 2 carrying the normal gene, the eggs are fertilized by a "random" sampling of all the possible sperm.


Here is another way to recreate what I was saying above:
Get two colors of M&M's and take 100 of each color and mix them in a container. Pour out 10 and see how often you get 5 of each color. Try this and I doubt you'll get 5 of each color each trial even though there is a 50/50 chance of pulling either one.

Each egg has a 50% chance of getting the lesser gene. If you hatch 10000, or more eggs, then you may expect to see ratios similar to 50/50. Until that time, your numbers are based on the probability of a gene being inherited by a particular individual from the total possible combination of genes.

The "per clutch" statements don't take into account the random sampling (think M&Ms). Just because there are equal amounts of both colors in the vat, it doesn't mean that equal proportions will be drawn when a very small sample is pulled from the population.

If the M&Ms don't do it, you can take a coin toss too. Each flip of a fair coin has a 50/50 shot of being either side. Flip it once and the next flip is not guaranteed to be the other side. Even "statistically speaking". If each flip is independent, then each flip has a 50/50 shot of being either heads or tails. Just like if you have four eggs from a lesser and normal pairing, just because you have 2 normals, you're not guaranteed 2 lessers (the statistics are based on a much larger population of gametes, and not the finite number of eggs in the clutch). The inheritance of the lesser gene is still a 50/50 shot regardless of what the siblings inherited.


As a final thought using the coin example:
If you were to flip the coin for the rest of your life. As you near infinity (much more than the number of eggs in a BP clutch), the totals will look more like the 50/50 ratio you expect from each flip. Likewise take every lesser X normal cross that ever has been and ever will be done. Plus a few more for good measure and you may notice a 50/50 ratio of normals and lessers in the offspring even though the numbers don't hold per clutch. A single clutch is very finite sample drawn from an independent "random" population of possible outcomes. Because of this the ratios are per egg and not per clutch or sample.

I've really simplified some genetic concepts as well as some aspects of probability so hopefully this makes some sense.

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Originally Posted by OhhWatALoser

then i guess my question is, how do you use the word statistically correctly?

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Here is the fourth definition of "probability" from http://dictionary.com:

4.
Statistics .
a. the relative possibility that an event will occur, as expressed by the ratio of the number of actual occurrences to the total number of possible occurrences.
b. the relative frequency with which an event occurs or is likely to occur.

And here is the definition of "statistically":

of, pertaining to, consisting of, or based on statistics.

And the definition of statistics is

the science that deals with the collection, classification, analysis, and interpretation of numerical facts or data, and that, by use of mathematical theories of probability, imposes order and regularity on aggregates of more or less disparate elements.

To me, statistics includes but is not limited to probability. IMO, "statistically" is acceptable useage in this thread but "probability" is more accurate. YMMV.