Orton's Arm

On average you expect the die to roll a 3.5. This is a conglomerate of six separate expectations involving the numbers 1 - 6. Obviously, a die roll of 6 is not an error. It is a die roll of 6. Your attempt to use that particular die roll to estimate the average value of an average die roll, however, will result in an error of 2.5.

How do you roll a 3.5 with a single die? I suggest you keep rolling dice until you figure it out. (That should keep him busy for a while. ) I know my die analogy seems a little strange, but it's actually the same thought process that goes into giving someone any other sort of a test. Suppose you give someone an I.Q. test. The number you're really interested in is how well this person would do, on average, if given 1000 I.Q. tests (assuming no fatigue effects or learning effects). You're using the first score on the first I.Q. test to estimate what their average score would be across those 1000 tests. With the die, you're using that first die roll to estimate what your average roll would be if you were to roll the die 1000 times. A six sided die rolled 1000 times will, on average, give you a roll of 3.5.

The word "raw" makes me very nervous. Ryan Leaf was "raw," and needed time. Peyton Manning was "polished" and was presented as someone who could make more of an immediate imact. "Raw" means "has not yet demonstrated the ability to be a consistent pocket passer in a complex offense." Maybe the reason that ability hasn't been consistently demonstrated is because it just isn't there.

Wrong: there is only one acceptable comparison QB to Losman: Drew Brees. Surely Losman is the next Drew Brees, right?

I take umbrage with the term "noodly." But yes, I, Holcomb's Arm, would have produced a lot more yardage than Losman did.

Compare this year's supporting cast to last year's. The Bills have improved on the OL and at TE. The WR situation is a little worse because of the loss of Moulds. Overall, though, this year's supporting cast, and this year's playcalling, are better than last year's. With last year's playcalling, and last year's supporting cast, Kelly Holcomb was able to achieve some pretty good things. Yet nobody wanted Holcomb as a starter. If Losman this year can't do better than Holcomb last year, why would anyone want Losman as their starter?

I read part of a book by Joe Montana. He said that everyone gives him credit for that TD drive to win that last Super Bowl. In reality, he wrote, it wasn't just him who stepped it up. It was the entire team. He talked about how great his pass protection was, how his receivers made good catches. He wrote that if John Taylor hadn't gotten open on that last play, or if he'd dropped the pass, the Super Bowl would have had a very different ending. For whatever reason, the Colts team hasn't stepped up in the postseason. Maybe some of that's not having a complete team (mediocre defense), some of it's having an offensive line that gets pushed around come postseason, and some may even be officiating. For example, I think the officials really let the Patriots' DBs mug the Colts' WRs. How much of the Colts' postseason woes are on Manning? Some, to be sure. But most of the problems have been from other players.

Certainly. Suppose you have a die, and you roll it to get some idea as to what its average roll might be. You roll it the first time, and get a six. In this case, your attempt to measure the die's true average roll resulted in an error of 2.5. What will the die yield the second time you roll it? Its expected roll is 3.5--in other words, it will, on average, regress fully toward the mean. In the above case, the expected value of the regression toward the mean was 100%, because the trial was entirely luck-based. Now suppose you're observing something that's based partly on luck, but mostly on skill--such as an I.Q. test. Someone who scores a 180 the first time around is generally going to have been a little lucky. This person's score will, on average, regress toward the mean upon taking a retest. The extent to which the regression toward the mean is expected to take place depends entirely on how luck-based that I.Q. test really was. The more luck-based the test, the greater the expected regression toward the mean.

Why am I continuing to beat my head against the brick wall of your incomprehension? I wish I knew . . . Suppose the following: there exists an I.Q. test. If an average person were to take that test 1000 times, that person's scores would vary within a 20 point range. Suppose someone got a 180 on first taking this test. Do you agree or disagree that this person's expected score upon retaking it is less than 180?

You actually managed to correctly describe the difference between probabilistic and deterministic systems! I'm impressed. I'd be even more impressed if you actually connected it with the discussion at hand, but one step at a time.

I am measuring the regression of I.Q. scores. Someone who obtains a score that's far from the mean on the first test, more often than not, will get a score that's closer to the mean upon taking a second test. This is what the article meant when it said that someone who scored a 750 on the math section the first time around will, on average, get a 725 upon taking the retest.

I seem to have a hard time understanding it? I've only been trying to communicate that exact same message for the last five or ten pages! What's next? Are you going to tell us that Ronald Reagan had a hard time understanding that communism might not always be a good thing? Or that Al Gore had a hard time understanding that he nearly won the presidency back in 2000? Please, do share.

Your post is of course incorrect, but less so than usual. If the lightbulb in your head had previously been turned off, it's now on its lowest setting. In a few more pages it will perhaps be at its brightest; and then you'll see exactly how wrong you've been. You probably won't admit it, but you'll know it. And that will be enough. My Monte Carlo simulation shows that someone who scores well on a test involving mostly intelligence, but also a little luck, will tend to do a little worse the second time around. If you want me to put this in the language you've apparently developed, the mean error for the Threshold group is positive the first time around (on average, they got lucky) and regresses toward a mean error term of zero the second time around (on average they are neither lucky nor unlucky the second time they take the test). Why was the Threshold group, on average, luckier than the non-Threshold group on that first test? Because the Threshold group was selected based on its high scores on the first test, which in part are a function of luck.

Did you also read the HyperStat article to which I linked? Its length is quite reasonable, and it's an easy read as far as stats go. I suggest you read it, and then go back through the last five pages or so of Bungee Jumper's and Ramius's posts. I want someone other than me to see how very badly those two have embarrassed themselves.

If you want me to stop calling you a follower, I suggest you stop acting like one. As for your claim that you've gone through this thread reading my posts but not any of theirs . . . um . . . yeah. Whatever dude. You actually quoted one of Bungee Jumper's posts on this very page.

And you think this because Bungee Jumper and Ramius said so. As I said, you lack self-confidence.

You lack self-confidence, which is why you're trying to ingratiate yourself with Bungee Jumper. Too bad the leader you picked doesn't know beans about regression toward the mean.

You are wrong. And not merely wrong, but wrong in a way which shows zero comprehension of, oh, I don't know, the last five pages, the Monte Carlo simulation, two or three links, and probably some other stuff I'm forgetting. This has gone far beyond ridiculous. Do you finally understand now? You are trying to measure someone's true score. But due to random chance, or luck, there may well have been a little incorrectness in measuring that person's true score. It's this inaccuracy or error in the measurement system which allows people to get "lucky" or "unlucky" on tests instead of being measured correctly. If measurement was always 100% accurate, there would be no regression toward the mean. Someone who got a 750 on the math section of the SAT the first time he took the test would get a 750 again the second time, and the third, etc. Regression toward the mean happens because someone who scored a 750 just might be a person with a true score of 725 who got lucky when taking the test. Granted, he might also be a true 775 who got unlucky, but the odds of this are less likely; because there are fewer true 775s than true 725s.

That's not a bad video.

You honestly didn't understand a single word of that article, did you? I'm dumbfounded that you and Ramius can claim to understand so much about statistics, yet display so abysmally poor an understanding of regression toward the mean. The two of you have gone on for pages about this, but not once has either of you even so much as hinted at a flicker of understanding about this concept. I feel a deep sense of pity for whichever poor fools attempted to teach either of you stats. I've tried explaining this for pages, and you still don't get it. As though lack of comprehension wasn't bad enough, the two of you actually jeered at what's been a consistent, correct, and clear explanation of regression toward the mean. In my simulation, 1000 people were assigned true I.Q.s Then each person was given an I.Q. test where the result was the person's true I.Q. modified by an error term. Those who did the best on this I.Q. test were assigned to the Threshold group. Threshold members were given a second test; again based on their true I.Q. and the same error formula as before. As a whole, the Threshold group consistently did slightly less well on the second test than on the first. If you look at the link I provided, and explore around a little, you'll find a link to a simuation. In that simulation, people are given a test of some sort, which is based partly on luck and partly on innate ability. Those who score above whichever threshold you choose are retested. They'll do a little less well the second time around. It's the exact same simulation, except that I developed mine before I learned anything at all about theirs. Not only are the simulations conceptually the same, but my explanations (using I.Q. tests where people score 200, 190, 180, etc.) have been conceptually the same as the explanations provided by the website WRT math scores on the SAT. There is not a single error in anything I've written about regression toward the mean. The fact you're still trying to find such an error only exposes your own ignorance about the issue. As you were unable to understand the explanations aimed at adults, I suggest you learn about the topic here. In particular, I want to draw your attention to the following quote:

You know, you may well be right. I'm just so used to some Losman's more, um, extreme supporters coming up with silly stuff that I saw this post as one more example of that.

My argument has remained consistent, as has your inability to comprehend it. Had you understood the relation between measurement error and regression toward the mean in the first place, the last several pages of this discussion would have been unnecessary. As it is, I had to put together a Monte Carlo simulation to demonstrate a statistical concept with which you should already be familiar.

Nice try, but wrong. If you look at the way the article used the word "chance," it involved the possibility of people getting lucky or unlucky when taking the math section of the SAT test. Please don't tell me you're trying to say that the people the article described got lucky or unlucky on the SAT due to "chance" while the people I described got lucky or unlucky on the I.Q. test due to "measurement error," and that "chance" and "measurement error" have nothing in common. You can't possibly be that desperate, can you?

I completely agree. I'd add that the Republicans haven't known what to do with it either these past six years. The prescription drug benefit? Ha! More federal spending? Who on earth within the Republican base wants that? Beyond the tax cut, it's not immediately clear the Republican Party has delivered any meaningful benefit to its base. And even the tax cut is a mirage, because it's coupled with federal spending increases. The government is consuming more than ever; we're just waiting until later to pay the bill.

The Republican Party deserved to lose control of Congress, but the Democratic Party didn't deserve to gain control.