syhuang

The statement is completely wrong. Even the average is 140, you can not score 140 in this test. You can only score 135 or 145 here. If a person gets 145 and then retakes the test, he won't get a score closer to the mean. You won't regress toward anywhere even if you keep retaking the test. Do you call a score sequence like following as "regression toward the mean"? 135, 135, 145, 135, 145,145,135,145,.... As you can see, it doesn't regress toward any value. ------ EDIT: HA, I've a feeling that you may use "average score" to reason that "regression toward the mean" still applies here. Thus, before you do that, please make sure you don't change your definition of "regression toward the mean" in past 50+ pages. If you want to use "average score of a group of people", please make sure you're not saying that "regression toward the mean" doesn't apply to individuals and only applies to the average score of a group. Please don't say that if a person's real IQ is 140 (known by other more accurate tests) and scores a 160 or 120 in a test with zero-mean normally-distributed error, he is NOT likely to get a score closer to the mean when retaking the test. If you want to use "average of all past scores", please make sure you're not changing your definition of "regression toward the mean" from "...... the next score is likely closer to the mean upon retaking the test" to "...... the average of the next score and all past scores is likely closer to the mean". Last, please don't say that a person can score 140 in a test which only has two outcomes, 135 and 145.

It's a valid assumption, but may not be a good assumption to explain what you said above. To explain the difference to him, I think one of the better ways is to show him the case where mean of error is not zero. With the assumption of normally distributed error with mean of zero, it's kind of hard to explain the difference of the two.

(HA, let me rephase the questions to see if they're more clear to you) HA, please answer the following two simplified questions: (1) Regression toward the mean I see you agree with me on this case, so I don't repeat the question here. Can we conclude the "mean" in "regression toward the mean" is "the mean of error"? (2) abnormally distributed error Assume the real IQ is 140 and the test has an abnormally distributed error as following: (Again, the real IQ is known by other more accurate tests. We then take another test with an abnormally distributed error. I change the error distribution again to make it extremely abnormal. ) 135: 50% 145: 50% Will "regression toward the mean" happen? (A) Yes (B) No My answers are (B) for both questions , what are you answers?

HA, please answer the following two simplified questions: (1) Regression toward the mean If the real IQ is 140 and the error is normally distributed with mean of +5, what will the regression toward to? (A) 140 (B) 145 (2) abnormally distributed error Assume the real IQ is 140 and the test has an abnormally distributed error as following: 137-: 10% 138: 20% 139: 15% 140: 10% 141: 15% 142: 20% 143+: 10% Will "regression toward the mean" happen? (A) Yes (B) No My answers are (B) for both questions , what are you answers?

Correct. And I notice that in HA's post, he uses assumptions like "Assume measurement error is normally distributed with a mean of zero" to ignore that the "mean" in "regression toward the mean" is "the mean of error" and "regression toward the mean (of error)" may not occur when error is not normally distributed.

You're right, Vince Young did get a 16 on that wonderlic test when he took the exactly same test the second time. Although wonderlic score may mean nothing on his on-field performance, you still need to get the fact right.

"Regression toward the mean" is caused by error being normally distributed. If error is not normally distributed, there's no guarantee that "regression toward the mean" will happen. In other words, if error exists but is not normally distributed, "regression toward the mean" may not happen.

Instead of looking at the completion % alone, you also need to look at the opponents. One of the reasons that Young had better completion percentage in last 4 games is that he faced bad pass defenses. Young's completion % of last 4 games are: JAC: 53.3% HOU: 65.5% IND: 60% NYG: 68.6% The numbers look good. However, if I add the "average completion percentage against" of these four defenses, you'll be able to find out that Young actually only had one excellent game (NYG) on completion %. This game happened to be the only game Young has QB rating over 100, his ratings on the other three games are between 70.1 and 73.6. JAC: 53.3% (54.5%) HOU: 65.5% (63.7%) IND: 60% (65.2%) NYG: 68.6% (59.2%) Just for fun, I also list Young's completion % before the NYG game: PHI: 36.4% (59.0%) BAL: 52% (55.6%)

If I understand the post right, the 50% conclusion doesn't include two Bills games. Thus, assume Bills have 50% chance to win each of their next two games, the overall percetange of making playoff should be around 12.5% (50% * 25%).

Don't we still get a chance if Broncos lose to 49ers in week 17 and KC finishes at 9-7?

You're making things up again. I never complain which period compares to which period. What I complained is that you can't only use your method on JP and never test your method on other quarterbacks to see if your results are meaningful in all cases. Again, you're wrong. It's not about these drives, some may think these drives should count, some may not. Get the point, it's about how you massage data by using "personal judgements" to keep the stats which should be ommitted by different threshold based on your own rules. You never bring in "personal judgements" on other drives. You need to be reminded again: Everyone can create any numbers he likes by (1) Create his own rules to omit the stats he doesn't want (2) Pick the threshold to favor him most (3) Use personal judgement to retain the stats which should be ommitted by different thresholds based on his rules (4) Simplify the whole system to favor his argument (5) Get the manufactured numbers benefit his opinion These manufactured numbers are useless and show nothing more than "I think".

Tom Brady ???....... move back 1 position ..... ??? Say it ain't so!!! This should not be allowed. They can not move Brady back. Don't they know who Brady is? Sky is falling.

Do you care to show any proof that winning percentage is significantly improved with 200+ passing yards? or you just don't care about winning and only like fancy stats? For your information, the weekly passing yard leaders this season are Week 14: Weinke 423 yards Week 13: Manning 351 yards Week 12: Leinart 405 yards Week 11: Brees 510 yards Week 10: Palmer 440 yards Week 9: Roethlisberger 433 yards Week 8: Brees 383 yards Week 7: Harrington 414 yards Week 6: Delhomme 365 yards Week 5: McNabb 354 yards Week 4: Brees 349 yards Week 3: Kitna 342 yards Week 2: Manning 400 yards Week 1: Pennington 319 yards And the final scores of these games are: Week 14: Weinke 423 yards (L, 13-27) Week 13: Manning 351 yards (L, 17-20) Week 12: Leinart 405 yards (L, 26-31) Week 11: Brees 510 yards (L, 16-31) Week 10: Palmer 440 yards (L, 41-49) Week 9: Roethlisberger 433 yards (L, 20-31) Week 8: Brees 383 yards (L, 22-35) Week 7: Harrington 414 yards (L, 24-34) Week 6: Delhomme 365 yards (W, 23-21) Week 5: McNabb 354 yards (W, 38-24) Week 4: Brees 349 yards (L, 18-21) Week 3: Kitna 342 yards (L, 24-31) Week 2: Manning 400 yards (W, 43-24) Week 1: Pennington 319 yards (W, 23-16) Overall: 4W 10L

Just one thing to add, Denver doesn't need to lose two of last three games. If Denver and Kansas City tied at 9-7, Denver is eliminated.

I didn't read TheWindySwedishSix post carefully. He has Cin and Jax going 10-6 and thus, winning the two wild cards. All the 9-7 teams miss playoff.

Maybe I understand the playoff tiebreak wrong, but isn't this one of the scenarios that Bills go to playoff? In this case, Bills beat Jets based on better conference record and KC beat DEN because of better division record. Then, Bills wins wild card over KC because of better conference record. Chris Brown playoff breakdown

Didn't you get the memo from JP bashers that no matter how Vince plays on field, Vince has "it"?

Then how come you failed to notice Leinart's QB rating was 76.0 yesterday and Losman had a 101.6 rating against Vikings earlier this season?

Don't need to be sorry, nobody cares if you're impressed or not.

No, they didn't win the super bowl. You're the one saying this and thank god you finally realize it's not a superbowl. People are just happy their team had a come-from-behind win last week. And no, nobody cares if you're impressed or not.

Yes, every Raiders game has been on TV this year. However, I could find ticket available at ticketmaster.com on Saturday before several home games, but still, none of Raiders game was blacked out.

will never?? Wow, even NFL coaches still need time to see how JP develops and don't make this kind of statement now. However, you already know it. This is amazing, you must either have more football knowledge than NFL coaches or just run your mouth too much, I take latter.

Is it you, Mrs. Holcomb?

Funny, you're the only one saying to put JP into HOF. No one even says JP will be great. He played a good game and showed he "could be" a good franchise quarterback.

<JP bashers> Losman still doesn't have "it", a comeback drive against Texans doesn't count. Any win against a sub .500 team will be put a '*' next to W </JP bashers>