Kerry-Bush Polls: their MOE and baseball!

Your team is batting: you feel a lot better when the hitter's batting average is .317 than when it is .134!  The same psychology is operating when you look at a Kerry-Bush poll.  Here's the skinny:

First a hypothetical example.  If 625 people are polled the MOE is 4%  (Simply the square root of 625 divided by 625 equals 25/625=.04=4%.  (A statistician calls this twice the standard deviation.)  Let's say the poll shows a Bush lead 47% to 43%.  Thus, pundits will say, the lead is "within (barely) the margin of error".  How sure can we be hat Bush is actually ahead of Kerry?  If the electorate of 100 million people really were tied at 45-45, then we would expect statistically to find 3 out of every 10 groups of 625 voters to show Bush at 47-43,or more.  Thus, the Kerry supporter consoles him/herself much like the fan watching the .300 hitter: the hitter may well get a hit.  Bush may well not be ahead!

On the other hand, if in the poll the Bush lead were 48% to 42% then we're watching a .130 hitter: only 1 (occasionally 2) out of every 10 groups of 625 voters can be expected to show Bush ahead by that margin if the electorate as a whole is 45-45.  Not something we can count on!  We have to strategize as if Bush really is ahead; 45-45 ain't likely!

Now, consider today's NY Times/CBS poll which has Bush ahead 48% to 45% with 1206 people polled.  Thus the MOE equals the square root of 1206 divided by 1206=35/1206=.030=3.0%.  (Agreeing with the stated figure 3 in the Times.)  Thus, like our initial hypothetical above, the poll margin is equal to the margin of error.  Kerry people relax: the "chances" are 3in 10 that Bush is not ahead!