The Corner

Slate’s Fuzzy Math

From a reader:

You’re right to pick on Sullivan for latching onto to Slate’s laughable bit of spin disguised as mathematical analysis, but you’re not quite right on the reason. First off, if Bush loses both FL and OH, he’s almost surely toast. He can’t flip WI and win. He’d need to flip several states. The basic analysis goes like this. Bush needs 37 electoral votes (to tie) out of FL (27), OH (20), PA (21), MI (17), WI (10), MN (10), and IA (7). You can figure out for yourself how many combinations get Bush to 37. There are lots. But if he loses FL and OH, he needs to pull off some relatively big upsets to get there.

The problem with the dopey 70-75% chance of winning analysis is that it looks at the uncertainty of Bush winning Bush states only. (I think this is what you were getting at, but you thought it was simpler than it is.) Yes, FL and OH are toss-ups, and I’ll accept that each candidate has a 50-50 chance of winning each state. If we KNEW for SURE how every other state would go, and if we KNEW for SURE that Bush needed to win both, then Bush’s chances of winning the election would be only 25%. But we DON’T know what’s going to happen elsewhere for SURE. We know probabilities in lots of other important states, most notably those that I listed above. And it is important to note that ALL of the other states I listed — all of which are competitive to varying degrees — are all former Gore states that Kerry is essentially counting on.

Just to give you a relatively simple example, let’s assume that Bush and Kerry have an equal chance of winning FL and OH, and that Kerry has a 70% chance of winning PA. Bush needs ANY two of these. And what are his chances of winning ANY two. The math is a bit more complex (I won’t set out the calculation here) but it works out to roughly a 60% chance of Kerry winning. That’s a 15% drop that arises simply because you consider the possibility of Kerry losing a state that he is favored to win but is not impossible for Bush to win.

Add another state, even one that you can assume Bush is even less likely to win than PA, and it gets better for Bush. For example, let’s assume Kerry has an 80% chance of winning MI. Again, the calculation is somewhat more complicated (but not very — I’m sure Derb can check the numbers), then we find that Bush is actually FAVORED TO WIN!!

That’s right, if you assume (reasonably, I think) that ALL 2000 results hold except NM and NH flip, then Bush needs ANY TWO of FL, OH, MI and PA to win (OH and MI would produce a tie, which is a Bush win unless an elector is faithless). This is true even when you assume that Bush has a 50% chance of winning FL and OH, a 30% chance of winning PA and a 20% chance of winning MI. My calculation produces a Bush chance of winning of 51.5%.

We could go on. The next most likely states to flip are IA (7) and WI (10) and MN (10). The calculations above assume ALL of these break Kerry’s way. If we add in uncertainty with respect to these, the odds of Bush’s win get better. Of course, we could add in uncertainty in Bush’s states — like NM and CO — and we could go on. But I suspect that if you were to fold in ALL of the uncertainty, you’d still end up with Bush being slightly — and I mean slightly — favored to win.

Anyone who tells you they are 75% confident of an outcome either is lying or reading the data in a way that filters out uncertainty that cuts AGAINST their guess.

And from another reader:

They are in no way assuming all swing states go to Kerry or even that Kerry wins Wisconsin; this is their analysis, which doesn’t sound optimistic:

Florida moves to Kerry, giving him 299 electoral votes. But his lead is shakier than it looks. Both Florida and Ohio are on a knife’s edge. We also think Gallup has exposed Wisconsin as a Tier 2 state, winnable for Bush with the right turnout. Kerry’s consolation is that both Iowa and New Mexico now look winnable for him, and as a package, they would negate the loss of Wisconsin or Minnesota. Kerry can now afford to lose any of the following combinations: 1) Florida, Iowa, and New Mexico; 2) Florida, Wisconsin, and New Hampshire; 3) Ohio, Wisconsin, Iowa, and New Hampshire; 4) Ohio and Pennsylvania; or 5) Wisconsin, Minnesota, and Pennsylvania. The good news for Republicans is that even if Kerry wins all the other states within his reach, he can’t survive the loss of Ohio and Florida.