- Of the 10 Democratic seats in play, 7 are solid D, 1 is likely D, 1 leans D, and 1 is a tossup.
- Of the 24 Republican seats in play, 11 are solid R, 6 are likely R, 1 leans R, and 6 are tossups.
The Democrats have fewer seats in play, and the Democratic seats are generally safer. Obviously this situation favors the Democrats. Is it enough to flip the Senate? Currently, the Republican majority is 54–46 (awarding the two Independent senators to the Democrats, since that's who they caucus with).
For the sake of building a toy model, I assigned probabilities to the Cook Report's verbal ratings as follows:
- For a tossup race, I assigned both outcomes equal probability ½.
- For leaning seats, I assigned probability ⅔ to the outcome matching the lean.
- For likely seats, I assigned probability 0.85 to the likely outcome.
- For solid seats, I assigned probability 1 to the indicated outcome.
These parameters aren't based on any firsthand knowledge of the races in question, they're just ballpark figures.
With probabilities assigned, it is easy to simulate the election many times on a computer. Assuming no coding errors (I did this on my lap during jury duty today), we obtain a probability around 24% of the Senate flipping to a majority for the Democrats.
Also, the probability of a fifty-fifty split is 20%, in which case the Vice President delivers a majority for whichever party wins the Presidential election.
Here is the frequency distribution of outcomes based on a million runs of the election. The blue bars represent flipping scenarios, and you can check that their fractions add up to 24%.
Now, don't take this analysis to the bank or anything. The Cook data are bound to change as time goes on, and on top of that, the probabilities that I assigned to Cook's verbal ratings are somewhat arbitrary. For example, if "likely" means probability 0.75 (instead of 0.85), then the chances of a flip increase from 24% to 34%. Intuitively, more volatility is bad for Republicans because they have more seats in play. Conversely, less volatility favors them; if "likely" is 0.95 and "lean" is 0.9, then the chances of a flip are only 12%.