The real SUSA numbers

SUSA did a fantastic job polling all 50 states with the Clinton-McCain and Obama-McCain matchups.  But then they dropped the ball in the analysis of their results.  Assigning winner-take-all for the electoral votes is lousy way to predict a likely election outcome, and it obscures some real information that is in their polling data.

SUSA's quoted results:

Obama 280 - McCain 258

Clinton 276 - McCain 262

A more reasonable analysis of their data gives:

Obama 294 - McCain 244

Clinton 278 - McCain 260

SUSA's polling found, in fact, that Obama has a significant advantage over Clinton in the McCain matchup!  

So how does one make the more reasonable analysis?  This and state-by-state results below....

To understand the issue, imagine a game where you toss a die, and if you roll a 1 or 2 you lose, but roll a 3 through 6 and you win.   With a fair die, you have a 2/3 chance of winning on each toss.  If you were to "play" this game 30 times, you'd typically win 20 times, so that's the best projection you can make.  The SUSA analysis amounts to projecting that since you are favored to win each toss, you are projected to win 30 out of 30 times.

What do dice have to do with polling results?  The 600 people called in each state give an estimate of the result you would obtain from calling everyone.  But they aren't going to nail the result.  A different group of 600 will give slightly different results.   So if SUSA finds a candidate to have a really slim lead in their sample of 600, it's not wise to simply award all the e-votes to the leader.  Better to acknowledge that this particular state is really close and find some reasonable way to partition the votes.

Adding up all the 50 states (and DC) with these partitioned electoral votes will give a much better prediction for the national total.  It's like adding up the 2/3 chance of winning the die game 30 times.

So how to do the partitioning?  The simplest sensible way is to model the probabilities with normal distributions...I'll gloss over the math details, but I will quote the exact result I'm using so that experts can weigh in on the method.  If A is the number who selected one candidate in the poll, and B is the number who selected the other, out of N respondants (in general, N > A + B), the fraction of electoral votes that should go to A are

0.5 ( 1 + erf(z) )       where  z = (A-B)/sqrt(N)

With this method, here's what comes:

State	      Clinton  McCain	   Obama  McCain
------------------------------------------------
Alabama 	  0.0	9.0	     0.0   9.0
Alaska		  0.0	3.0	     0.1   2.9
Arizona 	  0.0  10.0	     0.0  10.0
Arkansas	  6.0	0.0	     0.0   6.0
California	 55.0	0.0	    55.0   0.0
Colorado	  0.2	8.8	     9.0   0.0
Connecticut	  7.0	0.0	     7.0   0.0
Delaware	  2.9	0.1	     3.0   0.0
Florida 	 27.0	0.0	     5.4  21.6
Georgia 	  0.0  15.0	     0.0  15.0
Hawaii		  3.6	0.4	     4.0   0.0
Idaho		  0.0	4.0	     0.0   4.0
Illinois	 21.0	0.0	    21.0   0.0
Indiana 	  0.0  11.0	     0.0  11.0
Iowa		  0.3	6.7	     7.0   0.0
Kansas		  0.0	6.0	     0.0   6.0
Kentucky	  0.0	8.0	     0.0   8.0
Louisiana	  0.0	9.0	     0.0   9.0
Maine		  1.9	0.1	     2.0   0.0
Maine1		  1.0	0.0	     1.0   0.0
Maine2		  0.9	0.1	     1.0   0.0
Maryland	 10.0	0.0	    10.0   0.0
Massachusetts	 12.0	0.0	    11.9   0.1
Michigan	  8.1	8.9	    12.1   4.9
Minnesota	  9.2	0.8	     9.9   0.1
Mississippi	  0.0	6.0	     0.0   6.0
Missouri	  0.8  10.2	     0.1  10.9
Montana 	  0.0	3.0	     0.0   3.0
Nebraska	  0.0	2.0	     0.3   1.7
Nebraska1	  0.0	1.0	     0.7   0.3
Nebraska2	  0.0	1.0	     0.7   0.3
Nebraska3	  0.0	1.0	     0.0   1.0
Nevada		  0.0	5.0	     4.7   0.3
New Hampshire	  0.0	4.0	     2.7   1.3
New Jersey	 14.6	0.4	     6.5   8.5
New Mexico	  3.0	2.0	     5.0   0.0
New York	 31.0	0.0	    31.0   0.0
North Carolina	  0.1  14.9	     4.3  10.7
North Dakota	  0.0	3.0	     2.8   0.2
Ohio		 20.0	0.0	    20.0   0.0
Oklahoma	  0.0	7.0	     0.0   7.0
Oregon		  0.1	6.9	     7.0   0.0
Pennsylvania	 11.0  10.0	     0.9  20.1
Rhode Island	  4.0	0.0	     4.0   0.0
South Carolina	  0.2	7.8	     1.2   6.8
South Dakota	  0.0	3.0	     0.3   2.7
Tennessee	  4.3	6.7	     0.0  11.0
Texas		  0.5  33.5	     8.3  25.7
Utah		  0.0	5.0	     0.0   5.0
Vermont 	  3.0	0.0	     3.0   0.0
Virginia	  0.0  13.0	     6.8   6.2
Washington	  3.0	8.0	    11.0   0.0
West Virginia	  4.7	0.3	     0.0   5.0
Wisconsin	  9.0	1.0	    10.0   0.0
Wyoming 	  0.0	3.0	     0.0   3.0
DC		  3.0	0.0	     3.0   0.0
----------------------------------------------
Total		  278	260	     294   244

So, Obama really does have a big advantage in the McCain matchup.  As for disclosure:  I'm truly excited about both candidates and still on the fence.  I just hate seeing real information going to waste by bad analysis, so I had to speak up.