I don't think there's anything special about the tails.
Take a sheet of paper, and cover up the left 9/10 of the high-correlation graph. That leaves the right tail of the X variable. The remaining datapoints have a much less linear shape.
But: take two sheets of paper, and cover up (say) the left 4/10, and the right 5/10. You get the same shape left over! It has nothing to do with the tail -- it just has to do with compressing the range of X values.
The correlation, roughly speaking, tells you what percentage of the variation is not caused by random error. When you compress the X, you compress the "real" variation, but leave the "error" variation as is. So the correlation drops.
I read the "heretical" statements as talking about truth replacing falsehood. I read the non-heretical statements as talking about truth replacing ignorance. If you reword the "truth" statements to make it clear that the alternative is not falsehood, they would sound much less heretical to me.
One factoid says that your chance of death doubles for each 5 km/h above the limit you are. Another says that speeding factors into 40% of crashes.
Suppose the average speeder's risk is equivalent to 5 km/h over the limit (which seems low). Then only 25% of drivers must be speeding. Those 25% of drivers make up 40% of deaths, and the other 75% of drivers make up 60% of deaths. This keeps the ratio at 2.0, as required.
But non-speeders die too, when hit by speeders. The "40% of deaths had speeding as a factor" includes those non-speeders. Therefore, speeders have to be fewer than 25% of drivers. Call it 20%, for the sake of argument.
It's hard for me to believe that only 20% of drivers are doing 65 or more in a 60 km/h zone. And, remember: we made the conservative assumption that the average effect is 5 km/h. If you keep in mind that some drivers do 10 km/h over the limit, and have four times the risk, and some do 15 km/h over the limit, and have eight times the risk ... well, now, you're WAY below 20% of drivers speeding.
I have occasionally done 20 km/h over the limit (80 in a 60 zone), and so my risk was 16 times. But, still, the overall incidence is only twice as high. So there can be only 6% of drivers like me -- maybe 4%, if you include innocent other drivers in the death count -- and that's if you assume that there are ZERO drivers doing 5, 10, 15, 25, 30, or any other number of km/h over the limit.
Is there something wrong with my calculations?
"The Road and Traffic Authority of New South Wales claims that “speeding… is a factor in about 40 percent of road deaths.” Data from the NHTSA puts the number at 30%."
What does this mean, "is a factor"? If it means "at least one car was speeding," then it sounds like speeding might reduce the chance of a fatality. Suppose 40% of all drivers speed. Then, if speeding has no effect, the chance that neither driver is speeding is only 36%, which means speeding would be a factor in 64% of fatalities, not 40% or 30%.
Of course, I've made some assumptions here. The linked site doesn't tell us what percentage of drivers speed, and it doesn't say what "is a factor" means. So, the factoid, as presented, is meaningless.
"Provide reasons" helps for me. Many times I think something is obviously true, and when I start writing a blog post about it, where I have to explain and justify, I realize, mid-paragraph, that what I'm writing is not quite correct, and I have to rethink it.
Despite the fact that this has happened to me several times, my gut still doesn't quite say "it may not be that obvious, and you may be somewhat wrong." Rather, my gut now says, "the argument, written down, may not be as simple as you think."
So I feel like I still have a ways to go.
Ah, OK.
That's a slightly different case, though, isn't it? The author is not saying "it's good news for Boston [fans]" because they now are right when they were wrong before, and now their map is more accurate. Rather, he's saying that it's good news for Boston [fans] because the state of the world in the "right" case means more future Boston success than the state of the world in the "wrong" case.
Suppose Bergeron was doing well instead of poorly, and the author argued that it's because the coach is playing him too much and he's going to get tired or injured. In that case, the author might argue "Is Bergeron being played on every power play when he used to be played only rarely? If the answer is yes, it's actually bad news for Boston, believe it or not."
In other words, the "good news" and "bad news" don't seem to refer to the desirability of the map matching the territory. In this particular context, they refer to the desirability of the territory itself.
The point is well-taken that there are causes other than ego, and I could have mentioned that in the post.
I'm not sure what you're getting at with the hockey example, though.
Thanks! Now changed in original.
I like the castling analogy, might be able to use it someday.
Suppose 100 chickens are produced. And, suppose 100% of the population becomes vegetarian. The number of chickens produced will drop to zero.
100 fewer chickens demanded; 100 fewer produced. So, on average, between 1 and 100, the next marginal drop in chicken demand drops production by 1.
Which elicits the question: what is the pattern from 100 down to 0?
Suppose there's suddenly only one non-vegetarian left. At today's price, he would demand 1 chicken. Clearly, prices will have to rise if only 1 is produced instead of 100. He might, then, demand only half a chicken at the new, higher price.
That means: an instant drop in demand from 100 to 1 chicken leads to an eventual drop in production of 99.5 chickens. That's 99.5 fewer produced when 99 fewer are demanded.
Also, an instant drop in demand from 0.5 to 0 leads to a drop in production from 0.5 to zero.
If the function is monotonic, it must be that a drop in demand of X units must lead to an eventual drop in production of X+f(X) units, where f(X) > 0. That's the only way the math works out.
There is a drop of X chickens produced, to match the drop in quantity demanded at price X. The extra drop of f(X) reflects the fact that even fewer chickens are demanded at the new, higher price that must result.