If you compare the actual electoral map with his forecast, they seem to match in every state. Why is the number different? Obama got 303 electoral votes but his prediction was 313.

It’s uncanny that as advanced an art/science as statistics is, Nate appears to be the one who has mastered election forecasting. I am very impressed by him.

I am sure there are statistics professors all over the country saying, well if I had wanted to I could have done that analysis. Maybe the Republicans should hire a few.

@Simon. The reason for the difference is that the 313 EVs in Nate’s model is an average of multiple runs of different scenarios. So, it basically means that Obama was fairly certain to get the 303 he got without Florida, and Florida was probably leaning toward Romney, meaning that its 29 EVs would show up for Obama in some model runs and for Romney in more runs.

It’s the same thing with the percentage prediction of an Obama victory (like 90%?). Obviously if he won all the states he was forecast to win based on polling averages (and he ultimately did), he has a 100% chance of winning. But given polling uncertainties and margins of error, when Nate runs his model multiple times it sometimes shows a Romney win.

Fortunately for all of us, the real vote last night turned into a strong Obama win. So the models can take a rest and look ahead to 2014 and the Dems’ hopes to hold onto the Senate.

As a reply to Simon’s comment, “If you compare the actual electoral map with his forecast, they seem to match in every state. Why is the number different? Obama got 303 electoral votes but his prediction was 313.”

The 303 number does not include Florida, and the results for Florida are current not certain, If Obama wins Florida, he’ll gain another 29 electoral votes. Since it’s so close, it would add an average value of around 15 votes to a model that gave equal weight to each possible outcome. That puts the best guess between 303 and
332 given the results that are currently in.

BTW, Obama is slightly ahead in Florida in the vote count as of a short time ago, but it will take a while to be certain.

Regarding Fahd’s comment: almost anyone familiar with statistics and the theory of probability can easily do the sort of analysis that Nate Silver did, although tracking down all the polls (state by state) could be a bit tedious. The one advantage that Nate Silver has is that, with lots of people paying attention to him and reading his blog, he can call Gallop or Pew and actually get to talk to someone who can provide details that would normally not be publicized – it is in the polling company’s interest to cooperate with him so they get listed in his blog.

He’s also done a good job in packaging the results in a form that the general public can digest. But, the analysis is more or less straightforward – and I might add that he seemed to say that in one of the TV interviews. It’s just that most journalists/pundits, at least in the U.S., have a very poor grasp of mathematics.

Thank Luke and Bill for the explanation. I still think it would be more realistic to put into the model the assumption that the electoral votes can’t be split between both candidates. In other words, if the poll average of a candidate in the state is over 50%, he will get all the votes. That would be easy. You just look at the predicted electoral map and add up the votes for the blue states.

As a follow up to Simon’s comment (11:29:15 PM), the assumption is that electoral votes (for Florida) cannot be split between two candidates. So, Obama had about a 50/50 chance of getting either 0 or 29 electoral votes for Florida. If the probability of 0 votes is p and 29 votes is q, then the mean is 0p + 29q. The error is the square root of [(0-x)(0-x)p + (29-x)(29-x)q] and it turns out that this is a minimum when x is the mean value, 14.5 when p and q are both 1/2. You do better by being slightly off in both cases than by being way off half the time.

Summing electoral votes for all the states works similarly – after summing, the result is close to a normal distribution (the bell-shaped curve you’ll see in statistics books) centered on the sum of the mean values for each state.

For those who are curious, if each state gives all its electoral votes to the winner in that state and the polls show no advantage for either candidate in either state, the following shows the number of elections out of a total of 1 million in which a candidate gets a particular number of electoral votes (just including the range 200 to 340). You’ll see the peak at about 270. It took under 30 minutes to put it together, including collecting the number of electoral votes per state, writing a program, and running it.

it makes my heart sing that there are people so dedicated like Nate who CARE about truth and accuracy. The icing on the cake is that he shares my gayness! Gay geeks will inherit the earth and have the best sex!

Diogenes Arktos:
Can you tell which state doesn’t have the “winner takes all” system? Certainly not Florida. If it is true, we won’t have the Bush vs Gore legal battle when there were 25 votes at stake instead of just one vote.
The wiki says:
While laws vary, most states, including Florida, award all electoral votes to the candidate for either office who receives a plurality of the state’s popular vote.
It doesn’t say which states are the exceptions.
Anyway, no matter what the rules are, Nate Silver should have got the number right if his model is 100% accurate.
Luke and Bill here seem to imply that the Florida’s result is still pending and the media assigned only a fraction of the votes to make up the 303 number which obviously is not going to happen.

As an answer to Simon’s question, Maine and Nebraska assign two electoral votes to the state-wide winner and the rest depend on who won the election in each congressional district in those states. It seems that in both states, the same candidate won in all of a given stete’s districts, so a split has not been seen in practice.
Source: http://archive.fairvote.org/e_college/me_ne.htm

Simon’s statement that “Luke and Bill here seem to imply that the Florida’s result is still pending and the media assigned only a fraction of the votes to make up the 303 number which obviously is not going to happen,” indicates a misunderstanding as to what we were saying. The 303 number is without Florida (the Florida vote is still pending although Romney has apparently conceded that Obama will win Florida). Until the vote is official or the outcome certain, the media is not assigning Florida’s votes to either candidate. The sort of pre-election analysis that Nate Silver did, however, would formally split the vote, but purely for mathematical reasons. Basically, he’s computing the distribution function for the vote – the probability of the electoral vote having some specific value – and that function is to a good approximation a normal distribution (a “bell-shaped curve”) whose peak value is the sum of the means for each state. For Florida, because it is so close to a tie, the mean is approximate 14.5 (i.e., 29/2). If you want to see in detail why it works this way, do a google search for “central limit theorem” and “law of large numbers”, but keep in mind that you will be lost if you haven’t had a few years of college-level calculus so that, for example, you know what a Fourier transform is.

Alex Parrish says

Well, it looks like Nate-boy gets laid this year!

endo says

Gay nerd power!

Byron St. James says

And all the creaky old network idiots are sitting around saying: What the F just happened?

chasmader says

Is Nate one of us? I hope so.

Frank O'File says

Gay geek poster boy. Love him.

io says

ii love my geeks!

J. Alan says

Funny how math and science work.

Rafael says

Nate is great. I can’t have enough of FiveThirtyEight

Nathan says

@chasmader – Yep, Nate is openly gay.

simon says

If you compare the actual electoral map with his forecast, they seem to match in every state. Why is the number different? Obama got 303 electoral votes but his prediction was 313.

Diogenes Arktos says

@J Alan: So that’s why Romney didn’t write a concession speech – his pollster’s use of dowsing rods didn’t work;-)

Fahd says

It’s uncanny that as advanced an art/science as statistics is, Nate appears to be the one who has mastered election forecasting. I am very impressed by him.

I am sure there are statistics professors all over the country saying, well if I had wanted to I could have done that analysis. Maybe the Republicans should hire a few.

Profe Sancho Panza says

I’m adding Nate Silver to my “Future Ex-Husbands List”.

DeeVee says

I want John Turturro to play him in the movie.

jamal49 says

Read his book. Fascinating read! Congrats, Nate.

Luke says

@Simon. The reason for the difference is that the 313 EVs in Nate’s model is an average of multiple runs of different scenarios. So, it basically means that Obama was fairly certain to get the 303 he got without Florida, and Florida was probably leaning toward Romney, meaning that its 29 EVs would show up for Obama in some model runs and for Romney in more runs.

It’s the same thing with the percentage prediction of an Obama victory (like 90%?). Obviously if he won all the states he was forecast to win based on polling averages (and he ultimately did), he has a 100% chance of winning. But given polling uncertainties and margins of error, when Nate runs his model multiple times it sometimes shows a Romney win.

Fortunately for all of us, the real vote last night turned into a strong Obama win. So the models can take a rest and look ahead to 2014 and the Dems’ hopes to hold onto the Senate.

Bill says

As a reply to Simon’s comment, “If you compare the actual electoral map with his forecast, they seem to match in every state. Why is the number different? Obama got 303 electoral votes but his prediction was 313.”

The 303 number does not include Florida, and the results for Florida are current not certain, If Obama wins Florida, he’ll gain another 29 electoral votes. Since it’s so close, it would add an average value of around 15 votes to a model that gave equal weight to each possible outcome. That puts the best guess between 303 and

332 given the results that are currently in.

BTW, Obama is slightly ahead in Florida in the vote count as of a short time ago, but it will take a while to be certain.

Bill says

Regarding Fahd’s comment: almost anyone familiar with statistics and the theory of probability can easily do the sort of analysis that Nate Silver did, although tracking down all the polls (state by state) could be a bit tedious. The one advantage that Nate Silver has is that, with lots of people paying attention to him and reading his blog, he can call Gallop or Pew and actually get to talk to someone who can provide details that would normally not be publicized – it is in the polling company’s interest to cooperate with him so they get listed in his blog.

He’s also done a good job in packaging the results in a form that the general public can digest. But, the analysis is more or less straightforward – and I might add that he seemed to say that in one of the TV interviews. It’s just that most journalists/pundits, at least in the U.S., have a very poor grasp of mathematics.

simon says

Thank Luke and Bill for the explanation. I still think it would be more realistic to put into the model the assumption that the electoral votes can’t be split between both candidates. In other words, if the poll average of a candidate in the state is over 50%, he will get all the votes. That would be easy. You just look at the predicted electoral map and add up the votes for the blue states.

Bill says

As a follow up to Simon’s comment (11:29:15 PM), the assumption is that electoral votes (for Florida) cannot be split between two candidates. So, Obama had about a 50/50 chance of getting either 0 or 29 electoral votes for Florida. If the probability of 0 votes is p and 29 votes is q, then the mean is 0p + 29q. The error is the square root of [(0-x)(0-x)p + (29-x)(29-x)q] and it turns out that this is a minimum when x is the mean value, 14.5 when p and q are both 1/2. You do better by being slightly off in both cases than by being way off half the time.

Summing electoral votes for all the states works similarly – after summing, the result is close to a normal distribution (the bell-shaped curve you’ll see in statistics books) centered on the sum of the mean values for each state.

Bill says

For those who are curious, if each state gives all its electoral votes to the winner in that state and the polls show no advantage for either candidate in either state, the following shows the number of elections out of a total of 1 million in which a candidate gets a particular number of electoral votes (just including the range 200 to 340). You’ll see the peak at about 270. It took under 30 minutes to put it together, including collecting the number of electoral votes per state, writing a program, and running it.

200 3337

201 3353

202 3442

203 3607

204 3599

205 3776

206 3848

207 3850

208 3976

209 4093

210 4187

211 4351

212 4359

213 4545

214 4502

215 4592

216 4745

217 4770

218 4868

219 4936

220 4977

221 5252

222 5217

223 5275

224 5445

225 5471

226 5640

227 5643

228 5719

229 5674

230 5807

231 5920

232 6146

233 6160

234 6131

235 6259

236 6222

237 6405

238 6361

239 6603

240 6567

241 6631

242 6915

243 6713

244 6791

245 6903

246 6792

247 6847

248 7109

249 7087

250 7071

251 7238

252 7188

253 7303

254 7394

255 7380

256 7328

257 7426

258 7424

259 7265

260 7309

261 7356

262 7464

263 7552

264 7495

265 7660

266 7508

267 7634

268 7603

269 7654

270 7507

271 7655

272 7526

273 7421

274 7539

275 7511

276 7422

277 7511

278 7427

279 7290

280 7314

281 7265

282 7309

283 7203

284 7277

285 7267

286 7307

287 7156

288 7145

289 6925

290 6934

291 7174

292 6883

293 6795

294 6798

295 6806

296 6616

297 6833

298 6600

299 6469

300 6397

301 6352

302 6307

303 6244

304 6166

305 5961

306 6134

307 5860

308 5946

309 5811

310 5716

311 5682

312 5535

313 5387

314 5399

315 5414

316 5140

317 5203

318 4988

319 4876

320 4926

321 4724

322 4692

323 4625

324 4486

325 4382

326 4314

327 4209

328 4079

329 4056

330 3963

331 3816

332 3788

333 3746

334 3718

335 3471

336 3481

337 3453

338 3384

339 3258

340 3225

Diogenes Arktos says

@Simon: There are states where the electoral votes do not all go to the winner. I remember seeing that on the live TR blog election night.

BrokebackBob says

it makes my heart sing that there are people so dedicated like Nate who CARE about truth and accuracy. The icing on the cake is that he shares my gayness! Gay geeks will inherit the earth and have the best sex!

simon says

Diogenes Arktos:

Can you tell which state doesn’t have the “winner takes all” system? Certainly not Florida. If it is true, we won’t have the Bush vs Gore legal battle when there were 25 votes at stake instead of just one vote.

The wiki says:

While laws vary, most states, including Florida, award all electoral votes to the candidate for either office who receives a plurality of the state’s popular vote.

It doesn’t say which states are the exceptions.

Anyway, no matter what the rules are, Nate Silver should have got the number right if his model is 100% accurate.

Luke and Bill here seem to imply that the Florida’s result is still pending and the media assigned only a fraction of the votes to make up the 303 number which obviously is not going to happen.

Bill says

As an answer to Simon’s question, Maine and Nebraska assign two electoral votes to the state-wide winner and the rest depend on who won the election in each congressional district in those states. It seems that in both states, the same candidate won in all of a given stete’s districts, so a split has not been seen in practice.

Source: http://archive.fairvote.org/e_college/me_ne.htm

Simon’s statement that “Luke and Bill here seem to imply that the Florida’s result is still pending and the media assigned only a fraction of the votes to make up the 303 number which obviously is not going to happen,” indicates a misunderstanding as to what we were saying. The 303 number is without Florida (the Florida vote is still pending although Romney has apparently conceded that Obama will win Florida). Until the vote is official or the outcome certain, the media is not assigning Florida’s votes to either candidate. The sort of pre-election analysis that Nate Silver did, however, would formally split the vote, but purely for mathematical reasons. Basically, he’s computing the distribution function for the vote – the probability of the electoral vote having some specific value – and that function is to a good approximation a normal distribution (a “bell-shaped curve”) whose peak value is the sum of the means for each state. For Florida, because it is so close to a tie, the mean is approximate 14.5 (i.e., 29/2). If you want to see in detail why it works this way, do a google search for “central limit theorem” and “law of large numbers”, but keep in mind that you will be lost if you haven’t had a few years of college-level calculus so that, for example, you know what a Fourier transform is.