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

[mainbutter]

@ 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"

[bdpicha]

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.

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...

[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?

[rabernet]

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?

Gotta come to Atlanta for that!

[wolfy-hound]

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.

[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.

[OhhWatALoser]

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.

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.

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.

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.

[OhhWatALoser]

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

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

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.

[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

[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.