Pig crap - statistical problem (updated with new results)

[BackInTex]

This is so frustrating and infuriating.

There are 268 kids raising pigs for FFA this year. The way pigs are selected is as follows:

A large group of pigs are brought to the barn, usually 10-15 more than to be selected. Each student must select from that group. The order of selection is done through a random draw.

For the random draw there is a rotating barrel containing poker chips numbered 1 through 268. The kids, alphabetically with the starting point randomly picked (e.g. starting at M then M-Z and then A-L) reach in and draw a chip. The number on that chip is their order for selecting their pig. So the kid with chip 1 gets to select out of all 290 something pigs while kid with chip 268 gets to select from what’s left after the 267 kids before him have selected and taken their pig.

Pig selection is Saturday a week from now. The draw for numbers was held Wednesday.

Except that when they started the drawing not all the chips were in the barrel available to draw. The missing chips were in the 251-286 range. 12 kids drew chips before they realized the error. So those kids had an advantage that they were drawing from 1-250. When the mistake was realized they added chips 251-286 and continued the draw.

They should have stopped and then made the first twelve redraw, but they didn’t. The completed the drawing and everyone got a number they considered fairly drawn and went home with their plans for the day of pig selection, knowing about where they would be in line. Some were happy with their draws, some were disappointed, of course.

Caroline drew 12. We were extremely happy. Not only would she have practically pick of the herd, but she will be done hours before the end and be free to do what she needs to do the rest of the day.

Today though, the school district, noting the ‘irregularity’ is saying they will do a complete new redraw.

I talked to the district person in charge trying to convince her not to do a complete redraw explaining that while the first 12 did have an advantage, everyone else’s disadvantage was very slight. And that they will anger more people than they satisfy as most will not care and don’t want to go through the process again (it took 2 ½ hours). Half will get better numbers, half will get worse, but more people will get angrier with the redraw than if left as is.

Am I being unreasonable?

Can anyone provide me a way to determine the difference in chance to draw within a certain range due to the error?

12 people drew numbers from 1-250
274 people drew from numbers 1-286 (less the 12 previously drawn)

What are the distribution odds for folks drawing in the second group for picking a number in each of the following groups?
1 - 50
51 - 100
101 - 150
151 - 200
201 - 250
251 - 286

Its 17.4825% for each group of 50 and 12.5874% for the last group, IF it was all done properly.

For the 12 initial draws it was 25% for the first 4 groups and 0% for the last two. A definite advantage for those first 12, but what are those percentages for each group for those drawing after? How much was the disadvantage from the 17.4825%s and 12.5874%?

[jarnon]

Let's assume for simplicity that the first twelve kids' picks were evenly distributed. Then the odds for the remaining students are 17.15% for the first four groups, 18.25% for the fifth group, and 13.14% for the last group. You're right that the difference is insignificant.

Also, a higher chip number doesn't mean a better pig. I know nothing about raising pigs, but I've watched pro sports drafts over the years. Players chosen in the second or third rounds are often just as successful as first round picks. I would guess there's even less variation in a herd of swine than in a class of college athletes.

[BackInTex]

Let's assume for simplicity that the first twelve kids' picks were evenly distributed. Then the odds for the remaining students are 17.15% for the first four groups, 18.25% for the fifth group, and 13.14% for the last group. You're right that the difference is insignificant.

Also, a higher chip number doesn't mean a better pig. I know nothing about raising pigs, but I've watched pro sports drafts over the years. Players chosen in the second or third rounds are often just as successful as first round picks. I would guess there's even less variation in a herd of swine than in a class of college athletes.

Thanks for the stats work. So essentially the chance for a top 100 pick went to 34.3% from 34.9% because of the error. Not much of a disadvantage.

An earlir pick doesn't guarantee a better pig, but it helps. Pigs are judged by several physical traits, many negatives are apparent while young and cannot be corrected. A pig with a thin stance does not develop a wider stance because of better coaching or personal motivation. Its genetics. But given the 100's of pigs, you can find some nice specimens in later rounds but not likely in the 250-286 realm. Good skin color is also a genetic disposition.

Hopefully they will consider some of my alternatives. I suggested allowing kids to decide if they want to redraw. If they do, they give up their previous number and whatever the new draw number is, that is their number, even if worse. But is someone chooses not to draw, they keep their number, but must be aware that there will be folks moving in front of them. So someone with 143 may be pushed back to an effective 213 if 70 people behind him choose to redraw and draw new numbers before him.

[jaybee]

Maybe as important as the odds - By the time they get to picking pig # 250, we can assume that all of the "Payton Manning" pigs have already been chosen and what's left is is the bottom of the (pork) barrel. I mean, really, so 12 kids had no chance at those last group of pigs.......is pig pick #235 really that much better than pig pick # 257?

A redo will PO just about everyone. Everyone under #140 is probably willing to stand pat while those above are pushing for the recount. Some will do better, some will do worse - your high-number-ticked-off-people will include those who got nailed with a high number TWICE! and those who did have a low number until the redo.

If the same number will be mad no matter what, far better to just stay with what you've got rather than have some really mad people. You just can't put lipstick on that pig. <sorry, had to say it>

[ItsAMadMadMadMadSwine]

I'll take care of this problem.... let me at those piggies!

Can't have that lameass ebola virus try to outdo me in the media...

[BackInTex]

Maybe as important as the odds - By the time they get to picking pig # 250, we can assume that all of the "Payton Manning" pigs have already been chosen and what's left is is the bottom of the (pork) barrel. I mean, really, so 12 kids had no chance at those last group of pigs.......is pig pick #235 really that much better than pig pick # 257?

A redo will PO just about everyone. Everyone under #140 is probably willing to stand pat while those above are pushing for the recount. Some will do better, some will do worse - your high-number-ticked-off-people will include those who got nailed with a high number TWICE! and those who did have a low number until the redo.

If the same number will be mad no matter what, far better to just stay with what you've got rather than have some really mad people. You just can't put lipstick on that pig. <sorry, had to say it>

I wish you were in charge.

I compare the situation to this:

We're really sorry your kid got hit in the head, but we can't un-hit him. Best we can do it hit all the other kids in the head to make it fair.

[Bob78164]

Maybe as important as the odds - By the time they get to picking pig # 250, we can assume that all of the "Payton Manning" pigs have already been chosen and what's left is is the bottom of the (pork) barrel. I mean, really, so 12 kids had no chance at those last group of pigs.......is pig pick #235 really that much better than pig pick # 257?

A redo will PO just about everyone. Everyone under #140 is probably willing to stand pat while those above are pushing for the recount. Some will do better, some will do worse - your high-number-ticked-off-people will include those who got nailed with a high number TWICE! and those who did have a low number until the redo.

If the same number will be mad no matter what, far better to just stay with what you've got rather than have some really mad people. You just can't put lipstick on that pig. <sorry, had to say it>

I wish you were in charge.

I compare the situation to this:

We're really sorry your kid got hit in the head, but we can't un-hit him. Best we can do it hit all the other kids in the head to make it fair.

But in this case they can "un-hit" him or her. Redoing the entire draw is clearly the most fair way to handle this, since it didn't occur to them to restart the draw after they identified the problem in the first place. Whether the difference is enough to be worth the logistical effort is a different question. --Bob

[Bob78164]

This is so frustrating and infuriating.

There are 268 kids raising pigs for FFA this year. The way pigs are selected is as follows:

A large group of pigs are brought to the barn, usually 10-15 more than to be selected. Each student must select from that group. The order of selection is done through a random draw.

For the random draw there is a rotating barrel containing poker chips numbered 1 through 268. The kids, alphabetically with the starting point randomly picked (e.g. starting at M then M-Z and then A-L) reach in and draw a chip. The number on that chip is their order for selecting their pig. So the kid with chip 1 gets to select out of all 290 something pigs while kid with chip 268 gets to select from what’s left after the 267 kids before him have selected and taken their pig.

Pig selection is Saturday a week from now. The draw for numbers was held Wednesday.

Except that when they started the drawing not all the chips were in the barrel available to draw. The missing chips were in the 251-286 range. 12 kids drew chips before they realized the error. So those kids had an advantage that they were drawing from 1-250. When the mistake was realized they added chips 251-286 and continued the draw.

They should have stopped and then made the first twelve redraw, but they didn’t. The completed the drawing and everyone got a number they considered fairly drawn and went home with their plans for the day of pig selection, knowing about where they would be in line. Some were happy with their draws, some were disappointed, of course.

Caroline drew 12. We were extremely happy. Not only would she have practically pick of the herd, but she will be done hours before the end and be free to do what she needs to do the rest of the day.

Today though, the school district, noting the ‘irregularity’ is saying they will do a complete new redraw.

I talked to the district person in charge trying to convince her not to do a complete redraw explaining that while the first 12 did have an advantage, everyone else’s disadvantage was very slight. And that they will anger more people than they satisfy as most will not care and don’t want to go through the process again (it took 2 ½ hours). Half will get better numbers, half will get worse, but more people will get angrier with the redraw than if left as is.

Am I being unreasonable?

Can anyone provide me a way to determine the difference in chance to draw within a certain range due to the error?

12 people drew numbers from 1-250
274 people drew from numbers 1-286 (less the 12 previously drawn)

What are the distribution odds for folks drawing in the second group for picking a number in each of the following groups?
1 - 50
51 - 100
101 - 150
151 - 200
201 - 250
251 - 286

Its 17.4825% for each group of 50 and 12.5874% for the last group, IF it was all done properly.

For the 12 initial draws it was 25% for the first 4 groups and 0% for the last two. A definite advantage for those first 12, but what are those percentages for each group for those drawing after? How much was the disadvantage from the 17.4825%s and 12.5874%?

There's one other problem with this procedure, by the way, as you describe it. A kid named Maxwell has roughly 1 chance in 26 of getting to go first. A kid named Murphy has roughly 0 chance. The entire alphabet should be randomized (as is done for California ballots), not just the first letter. --Bob

[jaybee]

It seems like if you put aside the snafu that happened this time than the system double-layered to be fair. If you start out with all 286 numbers in the pot then the only advantage to having the alphabetical order thing is to have some form of order to the line. Each number has a 1:286 chance of being picked, no matter what order it's picked in. While it is very possible that many of the low numbers will be drawn early - leaving worse odds for those to follow to get low numbers, it is just as possible that more high numbers will be drawn by the first alphabet people. This would make the odds of getting a low number better as the draw goes on. In other words - there is no advantage to picking first.

Think of it this way. Everyone draws a tile in the alphabetical order system, but they hold the tile in their hand and do not look at it or show it to everyone. When all 286 have been picked - does the kid who picked last have a better chance of getting the only #1 than the kid who got to pick first? Would #286 blindly trade tiles with #1? Not for any logical reason.

They should have immediately restarted the draw as soon as they found the problem. But they didn't. Since the 'advantage' those first 12 or so who drew tiles is so slight, it makes more sense to move on. It's the difference between families being slightly ticked that a few kids had a slight percentage advantage in the draw compared to the extreme anger of those who got a #5 in the first draw and wound up with #237 in the second. Those who would get a bad deal in the second draw will be much more vocal than those whose number turns out to be lower.

[Appa23]

This is so frustrating and infuriating.


They should have stopped and then made the first twelve redraw, but they didn’t.

Today though, the school district, noting the ‘irregularity’ is saying they will do a complete new redraw.

And that they will anger more people than they satisfy as most will not care and don’t want to go through the process again (it took 2 ½ hours).

I tried to eliminate the irrelevant information to get down to what it seems you are saying is the problem. You seemed to agree that the correct response to the failure to include all of the numbers at the start of the draw would be to have everyone re-draw with all of the numbers in the pot.

If so, the correct, ethical decision always is the correct, ethical decision, even if you do not like the cost (extra time out of your (daughter's) life.)

PS It is not 2.5 hours out of everyone's life. The fictional Aaron Ma only is spending the time to get there and back to draw. If you have a last name that starts with J, K, or L, you are waiting for an hour to pass before you show up. I would say less than an hour for anyone.

[BackInTex]

This is so frustrating and infuriating.


They should have stopped and then made the first twelve redraw, but they didn’t.

You seemed to agree that the correct response to the failure to include all of the numbers at the start of the draw would be to have everyone re-draw with all of the numbers in the pot.

No, reread my post. I said they should have stopped and made the first 12 redraw. Now the game is over.

A similar sports analogy would be where after the football game is over they review the first scoring play, a 2nd and goal on the 5 where the QB threw the ball to a receiver in the end zone for a touchdown. They ended up winning by 2 points. However, after watching that play from several different angles, that receiver clearly stepped out of bounds on the way to the end zone and was ineligible to catch the ball. The touchdown should not have counted.

However, in football they have written ruled for handling this. Those rules are not to replay the game, or even the last few plays, but that once a play has begun, the books on all previous plays are closed. No changes.

It would be ethical and fair that prior to the kickoff, but even after the extra point, that the play could be called back? What's the harm? But they don't. They move on if they did not call the penalty and force a replay before the next play starts.

The same should happen here. After the touchdown, the opposing team still had almost as much chance to win as they did had it been 3rd and goal from the 15. Kids 13 through 268 had almost as much chance of getting a top 100 pick as they did had the draw been done correctly.

[mrkelley23]

This is so frustrating and infuriating.


They should have stopped and then made the first twelve redraw, but they didn’t.

You seemed to agree that the correct response to the failure to include all of the numbers at the start of the draw would be to have everyone re-draw with all of the numbers in the pot.

No, reread my post. I said they should have stopped and made the first 12 redraw. Now the game is over.

A similar sports analogy would be where after the football game is over they review the first scoring play, a 2nd and goal on the 5 where the QB threw the ball to a receiver in the end zone for a touchdown. They ended up winning by 2 points. However, after watching that play from several different angles, that receiver clearly stepped out of bounds on the way to the end zone and was ineligible to catch the ball. The touchdown should not have counted.

However, in football they have written ruled for handling this. Those rules are not to replay the game, or even the last few plays, but that once a play has begun, the books on all previous plays are closed. No changes.

It would be ethical and fair that prior to the kickoff, but even after the extra point, that the play could be called back? What's the harm? But they don't. They move on if they did not call the penalty and force a replay before the next play starts.

The same should happen here. After the touchdown, the opposing team still had almost as much chance to win as they did had it been 3rd and goal from the 15. Kids 13 through 268 had almost as much chance of getting a top 100 pick as they did had the draw been done correctly.

Actually, if you want to go to a sports analogy, the pine tar game is probably more apt.

I agree with you that there is not enough problem with fairness here to do a total redraw. But neither one of us is in charge of the decision. And in dealing with teenagers (and their parents) sometimes emotion trumps logic. But why not use it as a positive lesson for your daughter? Things are not always fair or logical in life, but you learn to cope with them, often by the example your parents set. Tell her what a great story this is going to make, when she gets a worse number (as she almost certainly will) and still does the stellar job you know she will do.

[BackInTex]

And her new number is 137. Better than average (143) but not by much. And much worse than her original 12.

[jaybee]

And how does she feel about that?

As I know next to nothing (OK, totally nothing) about this pig thing to clarify - Once the kids pick their pig, they then will raise it and enter it into competition at a future date? (Next years fair?) Is that correct?

As is seems that the whole pig picking process looks like to be set up to be as fair as possible then the next question: Is there that much difference between the pigs that the picking really makes a difference. Are all 286 pig(lets) fairly close in size etc. or is there a huge difference between what will turn out to be pig #1 and the final pig picked? From a non-pig guys viewpoint, I would think that unless there is a bunch of practically perfectly proportioned pigs up against a bunch of runts that the big difference would be in how they are cared for over time.

[SportsFan68]

And how does she feel about that?

As I know next to nothing (OK, totally nothing) about this pig thing to clarify - Once the kids pick their pig, they then will raise it and enter it into competition at a future date? (Next years fair?) Is that correct?

As is seems that the whole pig picking process looks like to be set up to be as fair as possible then the next question: Is there that much difference between the pigs that the picking really makes a difference. Are all 286 pig(lets) fairly close in size etc. or is there a huge difference between what will turn out to be pig #1 and the final pig picked? From a non-pig guys viewpoint, I would think that unless there is a bunch of practically perfectly proportioned pigs up against a bunch of runts that the big difference would be in how they are cared for over time.

I don't speak for BiT, but here's what he wrote earlier:

An earlir pick doesn't guarantee a better pig, but it helps. Pigs are judged by several physical traits, many negatives are apparent while young and cannot be corrected. A pig with a thin stance does not develop a wider stance because of better coaching or personal motivation. Its genetics. But given the 100's of pigs, you can find some nice specimens in later rounds but not likely in the 250-286 realm. Good skin color is also a genetic disposition.

I'm guessing she'll be OK with her 137, and I'm really glad she didn't end up with 250 or lower.

[BackInTex]

And how does she feel about that?

As I know next to nothing (OK, totally nothing) about this pig thing to clarify - Once the kids pick their pig, they then will raise it and enter it into competition at a future date? (Next years fair?) Is that correct?

As is seems that the whole pig picking process looks like to be set up to be as fair as possible then the next question: Is there that much difference between the pigs that the picking really makes a difference. Are all 286 pig(lets) fairly close in size etc. or is there a huge difference between what will turn out to be pig #1 and the final pig picked? From a non-pig guys viewpoint, I would think that unless there is a bunch of practically perfectly proportioned pigs up against a bunch of runts that the big difference would be in how they are cared for over time.

I don't speak for BiT, but here's what he wrote earlier:

An earlir pick doesn't guarantee a better pig, but it helps. Pigs are judged by several physical traits, many negatives are apparent while young and cannot be corrected. A pig with a thin stance does not develop a wider stance because of better coaching or personal motivation. Its genetics. But given the 100's of pigs, you can find some nice specimens in later rounds but not likely in the 250-286 realm. Good skin color is also a genetic disposition.

I'm guessing she'll be OK with her 137, and I'm really glad she didn't end up with 250 or lower.

In my experience, no pig picked beyond 100 has ever won grand or reserve champion. It is usually within the first 30 or so, but I believe an 80ish pick won last year or the year before. In the end, they will all pretty much taste the same, but what the judges look for is mostly genetic. A good pig is not guaranteed to show well, it is up to the student to do their job in feeding and working the pig. But a bad pig will never show well no matter what the student does. To a casual observer, such as me, I don't see a lot of difference between pigs 25-175. I can see a difference in the first few picked from the last few left, but the great majority, to me, I see no difference. When selecting their pigs, there is alwasy an 'expert' to help the kids evaluate the pigs. He or she will point out a number of pigs that are worthy of selection, explaining to the kids what they like and don't like about each.

In the end, most kids' pigs will not go to auction but 'freezer sale' meaning they get a flat price. The main thing for them to take away is the experience, the responsibility and discipline of raising the animal, not necessarily the prize at the end. Sort of like all the atheletes that participate, but only a few every get MVP awards.

[BackInTex]

And how does she feel about that?

As I know next to nothing (OK, totally nothing) about this pig thing to clarify - Once the kids pick their pig, they then will raise it and enter it into competition at a future date? (Next years fair?) Is that correct?

She is O.K. She understands she is in the same situation as all the other students. It is just disappointing to have a really good pick taken away on a technicality. A good friend of ours was 143 and now has 22. He is very happy. I'm sure I will hear stories of others that had really good picks and are now in the 250+ range. I'm thankful that is not us.

They get their pigs this Saturday. They will show them at the livestock show Feb. 5th or 6th. So they will have 16 1/2 weeks to work with the pigs. The pig will weigh between 25 and 45 pounds on Saturday and will weight between 150 and 275 by showtime. They will be judged in 10 weight classes. All pigs will be weighed at show time and then each clase divided up as evenly as possible by weight.

[mrkelley23]

And how does she feel about that?

As I know next to nothing (OK, totally nothing) about this pig thing to clarify - Once the kids pick their pig, they then will raise it and enter it into competition at a future date? (Next years fair?) Is that correct?

She is O.K. She understands she is in the same situation as all the other students. It is just disappointing to have a really good pick taken away on a technicality. A good friend of ours was 143 and now has 22. He is very happy. I'm sure I will hear stories of others that had really good picks and are now in the 250+ range. I'm thankful that is not us.

They get their pigs this Saturday. They will show them at the livestock show Feb. 5th or 6th. So they will have 16 1/2 weeks to work with the pigs. The pig will weigh between 25 and 45 pounds on Saturday and will weight between 150 and 275 by showtime. They will be judged in 10 weight classes. All pigs will be weighed at show time and then each clase divided up as evenly as possible by weight.

Shows my ignorance of the subject. I didn't realize the big prizes at the end were so heavily tilted toward the first 25 or so pigs. That makes a huge difference in the calculus. I understand better now why you were so upset, and I"m glad that your daughter has the sense (and the good upbringing, I bet) to be handling the disappointment so well.

[themanintheseersuckersuit]

In the end, they will all pretty much taste the same

would make a pretty good signature line

[BackInTex]

Shows my ignorance of the subject. I didn't realize the big prizes at the end were so heavily tilted toward the first 25 or so pigs.

Last year the Grand Champion pig sold for $17,000, the reserve champion for $14,500.

Freezer sale was $400.

All in all we spent about $1300 raising last year's pig. We got the $400. The prior year's pig died on us a month before show. Counting the vet bill to try and save it we spent aroung $1,600. The two pigs prior also resulted in freezer sale pricing.

My other daughter who raised two steers got last pick her first year and next to last pick the following year. We lost $4,000 - 6,000 each on those as both had health issues and spent significant amounts of time in the hospital.

Expensive learnings.

[smilergrogan]

Just introduce the pig to a literate spider and a sarcastic rat and you can recover your costs by charging admission fees to see the words in the spider's web.

[MarleysGh0st]

My other daughter who raised two steers got last pick her first year and next to last pick the following year. We lost $4,000 - 6,000 each on those as both had health issues and spent significant amounts of time in the hospital.

I remember you mentioning those stories about her bad luck with the random drawings. I didn't realize those outcomes had been so expensive for you!

[jaybee]

This is some serious pig business. Kind of helps explain all the details in the drawings if the winners are consistently in the first 10% of pigs picked.

Another question then: Are the pig pick order numbers known to the judges (in next years event)? And if so, does that slant the votes? Just wondering if it turns out to be like many judged events (Olympic ice skating comes to mind) where the select group of those expected to win prior to the event can turn in a basic performance and manage to beat out a relative unknown who does a spectacular job.

[BackInTex]

This is some serious pig business. Kind of helps explain all the details in the drawings if the winners are consistently in the first 10% of pigs picked.

Another question then: Are the pig pick order numbers known to the judges (in next years event)? And if so, does that slant the votes? Just wondering if it turns out to be like many judged events (Olympic ice skating comes to mind) where the select group of those expected to win prior to the event can turn in a basic performance and manage to beat out a relative unknown who does a spectacular job.

No. The judges have no idea of the draw order. The draw order is not published. During the actual selection some people write down the selected pig's tag number as the process goes so you know which pigs are unavailable. Then during the show may refer back to that written list. I've never done it for pigs, just got the draw numbers for the winners from others (so they are not official). I did do that for steers since there were only 65 and 47 steers, respectivelye, each year we participated and I was there the entire time. Selection day for the pigs, 286 of them, will run from 8:00 in the morning until probably 7:00 that night. I think each person is given 3 minutes to make their selection. Most do it faster so its usually between 1 and 2 minutes per selection. So between 30 and 40 an hour, plus breaks so about 11 to 12 hours.

[themanintheseersuckersuit]

Nice signature line