Cumulative Odds on Senate Polls (Reality Calibration) [UPDATED]

Pollster.com has a great article today about how likely a candidate is to win, given a particular poll spread before the race. We are pinning our hopes on a great many coin flips landing the way we would like. To understand this quantitatively, I did a little calculation.

• Probability that the dems control the senate: 0.03
• Probability that there is a 50/50 split: 0.11
• Probability that the republicans hold: 0.86

UPDATE: As several alert readers have pointed out, this assumes that the results are statistically independent, which is probably not the case. However, it does suggest that our optimism may be fueled by enthusiasm as much as by history and science. The independent odds are 3%, the rest is a wave.

Take the jump for the details.

First, I looked at the odds of a victory 13 races based on their current, average point spreads and eyeballing the graph on pollster.com. These gave me the following figures:

State	Current Poll Margin (+dem/-rep)	Probability of Dem Victory
AZ	-7.3	.2
MD	3.8	.65
MI	10.4	0.9
MO	1.6	.55
MT	3.2	.6
NJ	6	.75
NV	-15	.05
OH	11.2	.9
PA	10.2	.9
RI	6.2	.7
TN	-7.4	.3
VA	1.4	.55
WA	10.8	.9

Then I wrote a computer program that went through the probability of every potential outcome of the race. For example,

• Odds of Dems winning MO MT NV OH RI TN VA WA =

  LoseAZ*LoseMD*LoseMI*WinMO*...*WinWA =

  .8*.35*.1*.55*...*.9 = 1.08056 *10e-6

• Odds of Dems winning MD MI MT NJ OH PA RI TN VA WA =

  LoseAZ*WinMD*winMI*...*WinWA =

  .8*.65*.9*...*.9 = 0.00758061

Then I tallied all of these up, based on whether or not the dems won more than 10 of the races (giving them control), 10 races exactly (a tie) or less than ten (republican control).

• Probability that the dems control the senate: 0.03
• Probability that there is a 50/50 split: 0.11
• Probability that the republicans hold: 0.86