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The Monte Carlo analysis of state head-to-head polls last week showed Democratic Sen. Hillary Clinton leading Republican Donald Trump in electoral votes by an average of 325 to 213, and with Clinton having a 99.7% probability of winning an election held then.
Since then, 24 new polls have been released in 13 states. Some states have multiple polls, for example, Florida with five and New Hampshire with three.
Now, after 100,000 simulated elections, Clinton wins 99,999 times and Trump wins the single Electoral College outcome that was a tie. Clinton received (on average) 337 to Trump’s 201 electoral votes. The results suggest that, in an election held now, Clinton would have a near 100.0% probability of winning.
Here is how the race has evolved in some key states.
Florida gains five new polls that solidly favor Clinton (+3%, +6%, +1%, +5%, and +9%). The new polls move Florida from a 67.1% probability of a Clinton victory last week to a 98.2% probability now.
Georgia flips from light blue to light red. Of the seven current polls, Clinton leads in only two of polls. Last week Clinton only had a 68.6% probability of taking the state. That has now shrunk to a 24.2% probability.
Maine gets one new poll that shows Clinton up by +10% and with 100% probability of taking the state. Unfortunately, the new poll does not provide congressional district results. The last poll that did that was from June, and showed Trump with a slight lead in one district. It would be great to get some polling in ME CDs.
New Hampshire gets three new polls (and one aging out). The oldest poll shows Trump with a +9% margin, but Clinton has the lead in the last four polls by +15%, +13%, +10%, and +9%. Clinton goes from a 38% probability of taking the state last week to a 99.9% probability this week.
One new North Carolina poll pushes Clinton from a 50.1% probability of taking the state to a 90.8% probability. She leads in the most recent two of the three current polls.
Ohio loses one poll that aged out, and has shrunk Clinton’s chances from 81% to 65%. Clinton leads in three polls (+4%, +4%, +2%) and Trump leads in one (+3%). The result is a near toss-up
South Carolina finally gets a current poll, but Trump is only up by +2% in the new poll. This small lead gives him a 72.6% probability of winning the state today.
In Virginia, two new polls come in and one old one ages out. Clinton leads in the most recent three polls by double digits with Trump leading (+4%) in the oldest poll. Clinton would almost certainly win Virginia in an election now.
Washington state gets a current poll that gives Clinton a +19% lead. Needless to say, she approaches a 100% probability of winning the state right now.
Last week, the most recent Wisconsin poll was from Marquette University taken in mid-July. Clinton was up +4.1%. Marquette just released their August poll and Clinton now has a +14% lead over Trump. The results suggest she would take Wisconsin with a 99.7% probability today.
The distribution of electoral votes [FAQ] shows all possible Electoral College outcomes:
Ten most probable electoral vote outcomes for Clinton (full distribution here):
- 340 electoral votes with a 5.00% probability
- 341 electoral votes with a 4.45% probability
- 334 electoral votes with a 4.25% probability
- 335 electoral votes with a 3.59% probability
- 333 electoral votes with a 3.48% probability
- 350 electoral votes with a 3.23% probability
- 351 electoral votes with a 2.91% probability
- 349 electoral votes with a 2.83% probability
- 322 electoral votes with a 2.66% probability
- 328 electoral votes with a 2.59% probability
After 100,000 simulations:
- Clinton wins 100.0%, Trump wins 0.0%.
- Average (SE) EC votes for Clinton: 336.6 (15.3)
- Average (SE) EC votes for Trump: 201.4 (15.3)
- Median (95% CI) EC votes for Clinton: 337 (306, 366)
- Median (95% CI) EC votes for Trump: 201 (172, 232)
Each column of this table shows the electoral vote total aggregated by different criteria for the probability of winning a state (Safe=100%, Strong=90%+, Leans=60%+, Weak=50%+):
| Threshold | Safe | + Strong | + Leans | + Weak |
|---|---|---|---|---|
| Safe Clinton | 184 | |||
| Strong Clinton | 120 | 304 | ||
| Leans Clinton | 36 | 36 | 340 | |
| Weak Clinton | 0 | 0 | 0 | 340 |
| Weak Trump | 1 | 1 | 1 | 198 |
| Leans Trump | 36 | 36 | 197 | |
| Strong Trump | 107 | 161 | ||
| Safe Trump | 54 |
This table summarizes results by state. Click on the poll count to see the individual polls included for the state.
| 1 | 0 | EC | # | Total | % | % | Clinton | Trump | |
|---|---|---|---|---|---|---|---|---|---|
| 2 | 8 | Votes | polls | Votes | Clinton | Trump | % wins | % wins | |
| AL | 9 | 1 | 3690 | 36.7 | 63.3 | 0.0 | 100.0 | ||
| AK | 3 | 1* | 435 | 37.5 | 62.5 | 0.0 | 100.0 | ||
| AZ | 11 | 3 | 2419 | 49.1 | 50.9 | 26.7 | 73.3 | ||
| AR | 6 | 1* | 623 | 43.3 | 56.7 | 0.8 | 99.2 | ||
| CA | 55 | 1* | 803 | 60.5 | 39.5 | 100.0 | 0.0 | ||
| CO | 9 | 1 | 630 | 58.6 | 41.4 | 99.9 | 0.1 | ||
| CT | 7 | 1* | 1024 | 53.2 | 46.8 | 92.9 | 7.1 | ||
| DE | 3 | 1 | 529 | 56.7 | 43.3 | 98.8 | 1.2 | ||
| DC | 3 | 1* | 1131 | 76.5 | 23.5 | 100.0 | 0.0 | ||
| FL | 29 | 7 | 4728 | 52.1 | 47.9 | 98.2 | 1.8 | ||
| GA | 16 | 7 | 4989 | 49.3 | 50.7 | 24.2 | 75.8 | ||
| HI | 4 | 1* | 801 | 61.9 | 38.1 | 100.0 | 0.0 | ||
| ID | 4 | 1* | 402 | 34.3 | 65.7 | 0.0 | 100.0 | ||
| IL | 20 | 2* | 1654 | 59.4 | 40.6 | 100.0 | 0.0 | ||
| IN | 11 | 1* | 1779 | 44.9 | 55.1 | 0.1 | 99.9 | ||
| IA | 6 | 3 | 1538 | 45.6 | 54.4 | 0.7 | 99.3 | ||
| KS | 6 | 2 | 853 | 46.4 | 53.6 | 6.7 | 93.3 | ||
| KY | 8 | 1 | 425 | 42.4 | 57.6 | 1.4 | 98.6 | ||
| LA | 8 | 1* | 1285 | 39.4 | 60.6 | 0.0 | 100.0 | ||
| ME | 2 | 1 | 1555 | 56.6 | 43.4 | 100.0 | 0.0 | ||
| ME1 | 1 | 1* | 201 | 59.2 | 40.8 | 96.8 | 3.2 | ||
| ME2 | 1 | 1* | 162 | 49.4 | 50.6 | 44.2 | 55.8 | ||
| MD | 10 | 2* | 2657 | 65.2 | 34.8 | 100.0 | 0.0 | ||
| MA | 11 | 2* | 2086 | 62.1 | 37.9 | 100.0 | 0.0 | ||
| MI | 16 | 2 | 916 | 55.0 | 45.0 | 98.5 | 1.5 | ||
| MN | 10 | 1* | 1139 | 56.1 | 43.9 | 99.7 | 0.3 | ||
| MS | 6 | 2* | 1783 | 42.3 | 57.7 | 0.0 | 100.0 | ||
| MO | 10 | 3 | 3243 | 46.7 | 53.3 | 0.5 | 99.5 | ||
| MT | 3 | 1* | 1153 | 44.1 | 55.9 | 0.3 | 99.7 | ||
| NE | 2 | 1* | 1093 | 42.5 | 57.5 | 0.0 | 100.0 | ||
| NE1 | 1 | 0* | (0) | (100) | |||||
| NE2 | 1 | 0* | (0) | (100) | |||||
| NE3 | 1 | 0* | (0) | (100) | |||||
| NV | 6 | 4 | 2889 | 50.5 | 49.5 | 66.6 | 33.4 | ||
| NH | 4 | 5 | 3579 | 53.6 | 46.4 | 99.9 | 0.1 | ||
| NJ | 14 | 2* | 568 | 60.4 | 39.6 | 100.0 | 0.0 | ||
| NM | 5 | 1* | 774 | 51.8 | 48.2 | 76.3 | 23.7 | ||
| NY | 29 | 2 | 1945 | 60.8 | 39.2 | 100.0 | 0.0 | ||
| NC | 15 | 3 | 1795 | 52.3 | 47.7 | 90.8 | 9.2 | ||
| ND | 3 | 1* | 1226 | 44.6 | 55.4 | 0.4 | 99.6 | ||
| OH | 18 | 4 | 2842 | 50.6 | 49.4 | 65.4 | 34.6 | ||
| OK | 7 | 1 | 244 | 35.2 | 64.8 | 0.1 | 99.9 | ||
| OR | 7 | 1* | 580 | 52.1 | 47.9 | 75.3 | 24.7 | ||
| PA | 20 | 6 | 4087 | 54.3 | 45.7 | 100.0 | 0.0 | ||
| RI | 4 | 1* | 886 | 57.0 | 43.0 | 99.8 | 0.2 | ||
| SC | 9 | 1 | 1032 | 48.7 | 51.3 | 27.4 | 72.6 | ||
| SD | 3 | 1* | 657 | 40.9 | 59.1 | 0.1 | 99.9 | ||
| TN | 11 | 1* | 2191 | 40.5 | 59.5 | 0.0 | 100.0 | ||
| TX | 38 | 2 | 1606 | 44.8 | 55.2 | 0.2 | 99.8 | ||
| UT | 6 | 1 | 531 | 40.3 | 59.7 | 0.1 | 99.9 | ||
| VT | 3 | 1 | 356 | 69.7 | 30.3 | 100.0 | 0.0 | ||
| VA | 13 | 4 | 3048 | 55.5 | 44.5 | 100.0 | 0.0 | ||
| WA | 12 | 1 | 335 | 64.2 | 35.8 | 100.0 | 0.0 | ||
| WV | 5 | 1* | 1187 | 33.4 | 66.6 | 0.0 | 100.0 | ||
| WI | 10 | 1 | 546 | 58.4 | 41.6 | 99.7 | 0.3 | ||
| WY | 3 | 1* | 690 | 29.6 | 70.4 | 0.0 | 100.0 |
* An older poll was used (i.e. no recent polls exist).
Details of the methods are given in the FAQ.
The most recent analysis in this match-up can be found from this page.
I have a question about the methodology. I’m on mobile so I apologize if this is explained elsewhere. For the electoral vote distribution, is every state simulated with an independent Monte Carlo simulation? If Trump’s chances in Florida and New Hampshire were both 10% would his chances of winning both in your national map be 1%?
That’s my best guess for the discrepancy between your model and 538’s which put Hillary at around 90%. I think their model assumes that if Trump wins Florida, his likelihood of New Hampshire is also higher than the polls show.
Kyle,
My methodology is explained here to the extent that anyone with an elementary knowledge of probability theory should be able to duplicate what I do.
To answer you question, yes, MC simulations are done by State (plus DC and NE and ME congressional districts) and the state results are aggregated according to electoral college rules. My analyses only use state head-to-head polls, and I include no additional assumptions (economic, demographic, or correlations among states).
Nate Silver’s methods are not very well described for any of his 3 standard analyses. He probably does includes some type of correlations among states, but I have no idea what data he bases it on, or what his statistical justification is for doing so.
Finally, as I have pointed out before, Silver’s distribution of electoral outcomes is highly overdispersed. The last time I looked at his analysis (a couple of weeks ago), he had possible outcomes from nearly 0 EV for Clinton to nearly 538 EVs for Clinton. That’s absurd. There is no data-driven analysis that would result in a distribution of electoral votes that includes mass from 0 to 538.
Doesn’t look good for Drumpf. Hillary is up +6% or more in states with 273 EVs and leads in states with 341 EVs. Doesn’t look like she’ll get to 400, though. (But she doesn’t need to, hahahahaha!)