Orton's Arm

I watched Peyton Manning in his game against the Patriots. There's no way you can tell me that Losman and Manning are the same except for the quality of their supporting casts.

On the contrary, the Hyperstat example I found is exactly what I've been trying to explain for the last untold number of pages. Look again at my I.Q. test examples (which I wrote before I found that page I linked to). I described how someone who scored a zero on an I.Q. test would, upon retaking it, be expected to score a 10 the second time around. Likewise, I wrote about how someone who scored a 200 the first time would likely score a 190 the second time. You surely remember that example. Well, how is that different from the logic below? Next time, don't call me a moron unless you can back it up.

Big Ben looked like a real quarterback last year. Did he suffer permanent brain damage from that motorcycle accident? Will he ever be what he once was? I don't know. If he does come back 100%, the JP/Big Ben question is a no brainer.

I suggest you reread the bolded sentence in the quote from my above post. The element of chance--that is, of measurement error--causes scores to seem more widely distributed than they really are. Thus, someone who scored a 750 on the math section of the SAT is expected to get a 725 upon retaking that test.

I believe the original post referenced the Springsteen song "Born in the USA." Springsteen himself has said that if you listen closely to the lyrics, they're not about praising the USA. They're about exploring what Springsteen sees as this country's flaws. Look at the some of the song's lyrics: What you're looking at is an anti-war song which some people mistakenly think is a patriotism song based on the chorus. I believe this is the point the original poster was making.

You're really going out on a limb with that one, buddy. Okay, I admit a declining Brett Favre put up 287 yards against our defense. A few weeks earlier, Jon Kitna put up 278 yards. Brad Johnson had 267 yards. But Peyton Manning? Peyton Manning! Ha! There's no way he puts up more than 50. Points, that is, not yards. But maybe the Bills will score a point themselves.

I've tried explaining it every way I can. Since you still won't believe me, I suggest you go here. Also:

Perhaps I need to be more specific about what my hypothesis actually is. (Although it's not really "my" hypothesis since I read about it elsewhere.) Someone who gets an extremely high score on an I.Q. test is likely to get a somewhat lower score if that person is retested. Someone who gets a very low score on an I.Q. test is likely to get a slightly higher score if retested. This is because people who did very well on the first I.Q. test tend to be disproportionately lucky; while those who did very poorly on the first I.Q. test tend to be disproportionately unlucky. This phenomenon would disappear if there was no measurement error associated with the I.Q. test.

The point I'm making here is simple. Suppose someone who'd previously scored a 200 on an I.Q. test walks into a room to take a retest. The second time around, this person's expected score is 190. Likewise, suppose someone who'd earlier scored a zero on an I.Q. test shows up for a retest. This second person's expected score the second time around is 10. In both cases, the people who got extreme scores on the test will tend to regress toward the mean when given a retest. Nor does regression toward the mean end there. Someone who scored a 190 the first time they took the test will, on average, get a score in the low 180s the second time around. Someone who scored a 10 on the I.Q. test will, on average, get a score in the high teens the second time they take the test.

Let's look at the other end of the scale. In this example, there are 10 people with an I.Q. of 10, 100 people with an I.Q. of 20, 1000 people with an I.Q. of 30. They're taking the same error-prone I.Q. test. Of the ten people with an I.Q. of ten, two will get unlucky and score a zero on the I.Q. test. Another six will get the correct score of 10. The remaining two will get lucky and score a 20 on the test. If you look at those who scored a zero on the test, you're looking at only people who got unlucky. Were those two people to retake the test, they would, on average, get a score of ten. Now consider those who scored a 10 on the test. There are the six 10s who were scored correctly; as well as 20 20s who got unlucky on the test. The true average I.Q. for the 26 people who scored 10 is actually a lot closer to 20 than to 10. Were those who scored a 10 the first time around to retake the test, their average score the second time would be in the high teens. It would regress toward the mean value of the distribution.

Acting like a three year old doesn't make you one. What my example illustrates is that people who get unusually high scores on I.Q. tests, on average, tend to do a little less well the second time they take the test. Whether you set the Threshold at 200, 190, 180, or some other number greater than the mean, you're looking at a group of people that's not only intelligent, but also disproportionately lucky. In my example, the average person who scored a 200 on the I.Q. test had an I.Q. of 190. The average person who scored a 190 on the I.Q. test had an I.Q. in the low 180s. If you knew that a man scored a 200 on an I.Q. test, and knew that he was sitting down to retake the test, you'd expect him to get a 190 on that second test. If you knew that a woman had scored a 190 on the I.Q. test and she was sitting down to retake the test, you'd expect her score the second time around to be in the low 180s; because a low 180s score is the average true I.Q. for those who scored 190 on the test.

This post is a continuation of my last post. You have the same 10 people with an I.Q. of 190; the same 100 people with an I.Q. of 180, the same error-prone I.Q. test, etc. If you were to test the whole population a second time, you'd get the same results as you got the first time. There'd be two people who scored 200 on the test, 26 who scored 190, etc. But look more closely at what happens when you retest subgroups. Consider the two people who scored a 200 on the test. That subgroup contains only lucky test-takers. In order to score a 200 on the test, you have to have an I.Q. of 190, and you have to get lucky on that first test. Now consider the subgroup of people who scored 190 or better on the test. That group contains all the lucky or correctly tested 190s, as well as the 20 lucky 180s. In order to form a subgroup that includes anyone who got unlucky on the first test, you have to set your threshold to 180 or lower. The 180 threshold gives you 2 unlucky 190s--as well as the rest of the 190 population for that matter. It gives you the lucky and correctly tested 180s, and it gives you 200 lucky 170s. Even here, lucky people outnumber unlucky by 200+20+2=222 to 2. What happened to the odd 220 unlucky people whose bad luck should be balancing out all those lucky people's? Those 220 were excluded from the Threshold group based on their bad luck. Being assigned to the Threshold group is largely a function of I.Q., but also a function of getting lucky on that first I.Q. test. Suppose you were to set the Threshold at 180, and ask everyone to take the test a second time. All ten people with an I.Q. of 190 would still be part of the Threshold group, and their results would be the same as before--two 200s, six 190s, two 180s. 20 of the 100 180s were excluded from the Threshold group based on getting unlucky on that first test. Of the 80 180s assigned to the Threshold, 16 will get unlucky on the retest, 48 will score appropriately, and 16 will get lucky and score a 190. In addition, 200 170s were assigned to the Threshold group based on getting lucky the first time they took the test. Of those 200; 40 will get unlucky on the retest and score a 160; 120 will score an appropriate 170, and 40 will get lucky and score 180. The appropriate size for the Threshold group appeared to get smaller. This is because non-Threshold members weren't allowed to take the retest. Consider the 20 180s who got unlucky on the first test. These people weren't retested; and so weren't available to take the places of the 16 180s who appeared to exit the Threshold group on the second test. Or consider the 800 170s who scored appropriately or got unlucky on the first test. Because those 170s weren't retested, they weren't available to take the places of the 160 170s who got lucky on the first test but unlucky or neutral the second time around. By retesting only people who did very well on the first I.Q. test, you're retesting a subgroup of people who got disproportionately lucky on that first test. The retest reveals the fact that Threshold members had been selected mostly based on intelligence, but also partly based on their good luck the first time they took the test.

Thanks for addressing GG's objection. Now for my response to your post. To show how measurement error can affect your perception of a population, consider a population group that contains the following people: 10 people with I.Q.s of 190, 100 people with I.Q.s of 180, 1000 people with I.Q.s of 170, etc. A population like this looks vaguely like the right hand tail of that bell curve--enough like it to illustrate my point. Suppose you were to give each person an I.Q. test. A person taking the test has a 60% chance of getting the right score, a 20% chance of getting lucky with a score that's 10 points too high, and a 20% chance of getting unlucky with a score that's 10 points too low. How will the measured I.Q. scores compare to the true I.Q. values? First, let's look at the 190s: 2 will get lucky and score 200 on the test. Another 6 will score 190, and the remaining 2 will be unlucky and score 180. Based on measured I.Q.s, one would conclude that there are two people in this population group with I.Q.s of 200. In fact there are zero. Of the 100 people with an I.Q. of 180, 20 will get lucky and score a 190. Add those 20 to the six 190s who actually scored a 190, and there are 26 people with a measured I.Q. of 190. The true population only has ten such people; so once again measurement error has led to an overestimate of the number of people in the far right tail. The group with a measured I.Q. of 200 has a real I.Q. of only 190. The people who scored a 190 on the test, on average, have real I.Q.s that aren't much above 180. If you were to ask the people who scored a 200 on the test to retake it, their true I.Q. of 190 would manifest itself. Likewise, if those who scored a 190 were asked to retake the test, their scores the second time around would, on average, be closer to 180 than 190. My simulation modeled this same phenomenon using a normally distributed population and a normally distributed error term for both test takings.

Thanks for the inside scoop. But even though those researchers ran into trouble, I'd hate to see others be unable to try something just because of a lack of funding. There are many cases where something was presumed impossible only to later be achieved--heavier than air flight, traveling faster than the speed of sound, etc.

I'm not quite sure what you're getting at here. If you're trying to say that the running game needs to get better to take pressure off the passing game, I'd completely disagree. Teams are already ganging up to stop the run. It's time for a more effective passing game to open up the ground game.

I agree completely WRT Krugman. That said, even a broken clock tells the right time twice a day. In this case, Krugman's article is probably more or less true. And I say that not out of trust for Krugman, but out of distrust for a president who has abandoned nearly every single value Calvin Coolidge held dear. This isn't your grandfather's Republican Party, and that's a bad thing.

A reasonable post, and there was good information in the post you linked to. However, you can't just consider those percentages in a vacuum. Let's say you're deciding between taking a QB and an DT with a pick between 2 - 5. Based on what's happened in the past, you're guessing the QB has a 38% chance of succeeding. That seems low, but maybe the success rate for defensive linemen is equally bad. Even if it wasn't, a 38% chance of getting the next Peyton Manning could be considered better than a 45% chance of getting the next Sam Adams.

An excellent post, though I wouldn't read too much into the QB/OL Super Bowl comparison. Suppose you had nine dice, rolled them, and one of them came up with a six. Then you gathered five dice, rolled them, and two came up with a six. Can you really conclude that the second group of dice is weighted to give you sixes more often than the first group? If you're going to win the Super Bowl, it really helps to have a Hall of Fame-style QB--or at least someone close. Yeah, the Ravens did it without a very good QB, but they had one of the three best defenses in NFL history, good special teams, a solid offensive line anchored by Jonathan Ogden, and a Jamal Lewis-style running game. If you have that as your supporting cast, you don't need Joe Montana as your QB to win the Super Bowl. But if your supporting cast is less good, you do need a Joe Montana or at least a Tom Brady. One possible source for a Pro Bowl-style QB is early in the draft. But no matter how you do it, it will be really, really tough to win a Super Bowl unless you have a real QB.

I really wouldn't mind seeing him in a Bills uniform. Don't see that in the cards though.

I don't know that there are grounds for this much confidence. One aspect of cancer cells is that they're not subject to natural aging. The telomeres on cancer cells stay the same length. If your normal cells worked the same way, you wouldn't age either. I've heard of research involving telomeres--both to cure cancer by attacking telomeres, and to cure aging by improving the telomere situation on your normal cells. Will this research lead anywhere? I don't know. But I certainly don't want these types of projects to go unfunded simply because the government was too busy wasting money elsewhere to spend it usefully here.

Your post commands respect.

My problem with the Swedish system is that they taxed away this woman's food money. I don't want that here.

Wow! You managed to take a break from insulting me to ask a legitimate question! That's better than your usual level of self-control. Look at the group who scored 115 or better the first time they took the test. That group was selected mostly based on true intelligence, but also partly based on their luck when they first took the test. While lucky and unlucky members presumably balanced each other overall, the Threshold group contained a disproportionate number of lucky (on the first test) members, while the non-Threshold group contained a disproportionate number of people who got unlucky on the test. When the Threshold group was asked to take the test a second time, its average score was a little lower than it had been the first time. This second score was more indicative of the group's true I.Q. This example illustrates that those who obtain exceptionally high scores on I.Q. tests are, on average, a little less intelligent than their scores would indicate. Conversely, those who obtain exceptionally poor scores on I.Q. tests are a little smarter than their scores make them seem. Measurement error causes the population to appear to be more spread out than it really is.

You're wrong. But if we do too much more thread hijacking, we'll be elected honorary members of Al Qaeda. You'll be elected first, based on your comments about celebrating terrorist attacks and killing Americans.