Posts by J. Brian Adams

Two Days and Counting – But has Anything Changed?

Nov7th
2016 1 Comment J. Brian Adams Written by J. Brian Adams

We have reached the end. Early voters are already voting and by late Tuesday a new president will have been elected.

So who will that new president be?

The polls show a handful of close races, but overall the states that have supported Donald Trump six months ago are still supporting him. And the states that have supported Hillary Clinton are still supporting her.

So what do these polls say about Tuesday’s outcome?

The model used to predict the election uses a Monte Carlo method with the most current polls to simulate the vote result in each state and the district. The electoral vote of each trial is tabulated and a winner determined. This is repeated a million times to enable each combination of state wins to occur.

From the model, Secretary Clinton wins the election 94% of the time with Mr. Trump taking the electoral college majority just over 5% of the time. Not a certainty but it does give Clinton 16:1 odds for winning.

The expected number of electoral votes for Clinton is 308 to 230 for Trump. Of course this results is actually quite infrequent – happening less than 2% of the time. A more reasonable predictive value is that the interval from 261 to 355 will include the actual electoral result 95% of the time.

The median result – the value at which each candidate would expect to be above 50% of the time is also 308 for Clinton and a vote less at 229 for Trump. The middle 50% interval is 294 to 324 for Clinton – all above the critical value of 270, and 219 to 245 – all below 270 – for Trump.

Much has been said and written about the polls this election season. They are fixed. They are biased. They are just plain wrong. Could errors in the polls be forcing erroneous predictions?

To check if polling bias might change the outcome, a sensitivity analysis was run on the data with two additional simulations being run.

The first adjusted the polling data so that all of Donald Trump’s results are increased by one percentage point and Hillary Clinton’s reduced by one point. This was to test the sensitivity on the much touted shadow Trump supporter – the voter who does not want to tell a pollster that they will actually vote for Trump – or just to counter the claim that the polls are biased to the Democratic candidate.

When this reduction is made on all fifty states and the District of Columbia, the percentage of times that Trump wins does indeed increase, but not significantly. Instead of winning 5% of the time, Trump’s win percentage increases to just over 31%. This is a far better result – 1:2 odds – but still a long term losing position.

If the Trump polls are increased by 1% what about the same for Clinton? In a third run each of the fifty-one percentages were changed by 1% but this time increasing Clinton’s polls by 1% and decreasing Trump’s by 1%. This idea was to take into account the possibility of voters who while publicly supporting Trump, when they go in to vote they simply change their mind. Or – the counter to the previous bias issue – the polls are all biased but now in favor of the Republican candidate.

With the increase in the percentage for Clinton, her probability climbs to a certainty – winning 100% of the time.

The sensitivity issue appears to be moot. The probabilities change but Hillary Clinton still becomes the President-elect almost every time. To change this outcome would require a large scale drop in the results of almost all of the polls.

The model results are, of course, based on polls. And while the often repeated mantra that “the only polls that count are those on election day” is often considered the last breath of a losing campaign, election day will determine how close these predictions will be.

But at this point – forty eight hours from the final tally – the question for November 8th is still not who should win, but by how much will Clinton win?

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This Election is Many Things, But a Tie is Not One of Them

Sep11th
2016 6 Comments J. Brian Adams Written by J. Brian Adams

Labor Day is the traditional start of the fall campaign season. Hard to believe since the Presidential race has been on for two years, but the election is less than sixty days away.

This is where polls become the life’s blood of a candidate’s campaign. Based upon the most recent polls, how are Donald Trump and Hillary Clinton doing?

According to the pundits the race has pushed back into the tied region. A conclusion they make based on national polls – but the White House is not decided by a national popular vote but instead by the electoral college. This makes this conclusion interesting in terms of the two candidates’ popularity, but invalid as a harbinger of winning the election.

The second claim of a tight race is based on a misunderstanding of the margin of error. There is a misconception that says when the two candidates are polling within the margin of error of each they are tied – they are not.

With these two disclaimers, how close is the race?

An alternative to drawing conclusions from the individual state polls is to run an election simulation. The model – which uses state by state polls not a national poll – statistically simulates running the November election in each state thousands or millions of times to determine the probability that a particular candidate wins the necessary 270 electoral votes.

Using the most current polls, this model estimates that Secretary Clinton wins at least 270 electoral votes and thus the Presidency 95.7% of the time.

The magnitude of the win is often used an indicator of a mandate. The model predicts that Clinton wins an average of 322 electoral votes, fifty-two more than the needed 270.

The expected number of electoral votes may not be the most common number of electoral votes that she wins. The most common result, the mode, is 332 electoral votes, sixty-two more than 270. This occurs just a bit over 4% of the time.

Both of these values are interesting, but they are but single results – and both with low probabilities of that exact result. Instead, a more useful measure is the confidence interval. This is the centered interval which covers the middle 95% of the model’s outcomes.

At this point in the campaign, Secretary Clinton’s 95% confidence interval is 268 to 390 electoral votes. This does show a very small window in which Donald Trump wins.

The model also brings to light some interesting state wide results.

The must win state for Trump, Ohio, is virtually tied with Trump and Clinton each winning 50% of the time.

Pennsylvania, the other northern must win swing state, goes to Clinton 88% of the time. Not a guaranteed win, but not close enough to use as your base for a Republican electoral college win.

Florida is much closer than PA, but Clinton still shows a command of the probabilities with a 66% chance of winning the state’s twenty-nine electoral votes.

Similarly close races are in Nevada and Virginia with Clinton winning 61% and 62% of the time respectively.

The curious results are the reliably red Utah and Georgia. In 2012, Romney won Utah by forty-eight points, and Georgia by seven points. Today Trump still wins Utah but only 82% of the time. And Georgia is tied.

Volumes have already been written about how this year’s presidential election is unlike any that has come before. These same articles often present the election as a horse race with both candidates within striking distance of edging out the other. And while this election may be many things, a tie is not one of them.

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With five months to go, has the election already been decided?

Jun6th
2016 1 Comment J. Brian Adams Written by J. Brian Adams

The presidential election is five months away and the primaries are winding down. While not yet official, the parties have made their choices, and the race is on.

This race is not between two presumptive nominees but instead three – or even more. At this point the Republicans will be represented by Donald Trump, the Democrats by Hillary Clinton, and the wildcard, the Libertarians have nominated Gary Johnson.

With the candidates selected, polling takes on new meaning. The polls reveal the voters’ opinions, but to be useful the polling must be relevant.

A recent national poll shows Secretary Clinton with a one point lead over Mr. Trump and a thirty point lead over Governor Johnson. This appears to show a tight race that may hinge on how Johnson’s numbers change over the coming months; but the poll does little to predict the actual November outcome.

The White House is decided by the electoral college, not the popular vote. Thus the polls that matter are those in the states. Luckily the major polling firms have also started collecting state wide data.

These current statewide polls have been used in a simulation model that mimics running a national election many times. The winner of each state is determined and the appropriate electoral votes attributed to the candidate.

After one million simulated elections, Clinton wins 94.7% of the time with Trump winning 5.3%. This corresponds to an approximately 95% chance of the Democrats keeping the White House.

The most frequently occurring result is that Clinton receives 318 electoral votes – well over the 270 needed to win the election.

Further, there is a 50% chance that she receives between 296 and 334 electoral votes, and a 95% chance that she receives between 259 and 357 electoral votes.

Similarly, Trump’s most frequent electoral vote is 220 with a midrange (50%) of 204 to 242 and a 95% range of 181 to 279. While not statistically impossible, at this point a Republican win is a definite long shot.

In addition to the overall results the results of individual states may be a bit surprising. As would be expected, California is won by Clinton 99.9% of the time while Trump wins Louisiana 98.9% of the time.

But in the rustbelt states Clinton has a 69% of winning Ohio but only a 53% chance of winning Pennsylvania.

On the other side, there is a slightly better than even chance of Trump winning New Hampshire.

The real surprise is Mississippi – a state that Mitt Romney won by 11 points in 2012. In the most recent Mississippi poll Trump’s chance of winning is barely 50%. This appears to be due to the inclusion of the third party Libertarian candidate.

The election is months away; there are many undecided voters; and many states have yet to be polled. But in terms of electoral math these numbers show the Democrats with the high ground, and for the Republicans, a steep path to November.

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Republicans Moving to Regain the Senate

Aug5th
2014 3 Comments J. Brian Adams Written by J. Brian Adams

The latest chatter among the political classes is whether or not the Republican party can regain control of the Senate. There are currently fifty three Democrats and forty five Republicans in the Senate enjoined with two Independents who caucus with the Democrats. This makes the control numbers fifty five to forty five. The math is simple – a net change of five seats and the Senate will be tied while six has Nevada’s Reid relinquishing his leadership post to McConnell of Kentucky.

Can it be done? According to many pundits the polls are indicating a done deal. Probabilities of 65% to 75% and even 80% are currently be tossed around as the chance of a change. The probabilities are based on their analysts’ interpretations of the current polls.

But before you either celebrate or toss in the towel be warned – these are July polls at the beginning of the campaign season with high rates of undecided voters.

With the caveat in place we generated our own prediction by running the polls for November’s senate race through our model. This model runs sample elections a million times analyzing all of the likely or even possible outcomes.

Our results – while slightly different from those currently touted – do not bode well for President Obama and the Democrats in the Senate. If the November election were held on July 31 the Republicans would have a 54% chance of taking control of the senate while the Democrats have only a 26% of retaining control.

But 54% is only part of the story. These probabilities add to only 80%. In fact the most common outcome of the model is not a Republican takeover but a tie – fifty Republican and fifty Democratic Senators come January 2.

It is easy to argue that if the change occurs it is a result of the policies of the White House, or a change in voter attitudes, or simply Presidential fatigue in the sixth year of an administration. These are the easy conclusions to make. An alternative is to look at the individual Senate races.

November will see thirty five senate races. Of these twenty one are held by Democrats and fourteen are held by Republicans – a lopsided ratio already putting the Democrats at a disadvantage. If races were decided by a toss of a coin then the 60% to 40% ratio of races would have us expecting the Democrats to lose as many as nine seats while gaining at most one. While the idea of regression to the mean is interesting and surely has some influence, races are not decided randomly.

The second possibility is that of the thirty five races eight seats are open – seven retirements and one resignation. These eight are split five Democrats and three Republicans – another lopsided margin. Two of the Republican seats are in Oklahoma and Nebraska – both strong Republican states and thus unlikely to switch. The only open red seat that might possibly switch to blue is in Georgia where the daughter of the popular Georgia Senator, Sam Nunn, is in the race to replace Saxby Chambliss. While this opens the race up as a possible swing the polls are showing her chances presently as a long shot. Thus all three red vacancies are likely to remain red.

But of the five blue seats that have no incumbent the only safely blue seat is that being opened by Carl Levin’s retirement in Michigan. The other four are all in play. In fact recent polling has the Republican Party picking up the seats in South Dakota and West Virginia with a toss up in Iowa.

As for the rest of the class, there is one incumbent who stands to lose his reelection bid – Pryor of Arkansas. Joining him in the south are Landrieu of Louisiana and Hagans of North Carolina who while polling ahead are still in tight races. Another red state with a Democratic incumbent senator is at the other geographical extreme. Begich of Alaska is in a tight race to retain his seat. The four at risk blue seats are completed by Udall of Colorado who is currently in a dead heat.

While the Republicans have a shot at between one and all four of these seats, there is only one seat on the other side of the aisle that is at risk. It is – surprisingly – the seat of Minority Leader McConnell in Kentucky. And while polling close it is leaning for the incumbent.

What does all of this say about 2016? Little perhaps but not much. Control of the senate in the upcoming Congress will be determined by a half dozen races in a half dozen states. As for the White House in two years, these states are most likely to maintain an ideological course in voting for either a Republican or a Democrat for the next President. Instead the 2016 elections will be determined by the candidates that are running in 2016 – including an entirely different class of senators. And instead of having control be decided by six states all fifty will have the opportunity to make the choice for the White House known.

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With only three days left, Obama’s reelection chances have rebounded to 96%

Nov3rd
2012 4 Comments J. Brian Adams Written by J. Brian Adams

Despite the near tie in the latest polling of the nationwide popular vote, Obama appears poised to remain in the White House for four more years.

Running our simulation model with the last set of weekly polls before Tuesday’s election, President Obama once again has moved up to a near certain win for the electoral vote. As of November 2, our model predicts a 96% chance of reelection with Governor Romney’s chance of unseating the President falling back to 4%. While there is still buzz about the possibility of an electoral college tie – and the resulting President Romney and Vice-President Biden – that probability has also fallen to near zero.

At this point, Obama can claim 199 electoral votes as near certainties to Romney’s 159. When the likely wins are included Obama’s total rises to 226 and Romney’s to 173. If you include all of the states that are currently leaning for reelection, the President climbs well past the needed 270 to 332 electoral votes.

The challenge for Governor Romney is to retake several of the states that are leaning blue. The most likely of these is New Hampshire followed by Ohio but at a total of 22 electoral votes that only drops Obama to 310. If Romney can also win both Virginia and Florida he raises his total to 272 and a win – but even losing New Hampshire’s four votes from that mix turns his win back to a loss.

At this point our model is predicting an electoral college vote of 314 for President Obama and 224 for Governor Romney – a buffer of 45 votes. While this is the most likely outcome, the next most likely possibilities have even higher totals for the President. In fact the top fifty percent of the outcomes are all above 294 electoral votes.

A common saying by candidates is that the only poll that counts is the one on election day. And while an upset is still a possibility, that possibility currently appears to be quite unlikely.

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With A Week To Go, October Reelection Slide Reverses

Oct29th
2012 3 Comments J. Brian Adams Written by J. Brian Adams

There have been volumes written on how the presidential debates might impact the election. With their conclusion last week the polls have shown a significant impact.

Our simulation model which uses the latest state wide polls has been run each week since the beginning of summer. Its estimate of the probability of the President winning reelection peaked at 99.9% on September 28 when the electoral college math showed there was no likely way that Governor Romney could garner the necessary 270 electoral votes.

But the campaigns continued, the Benghazi attack was still making headlines, the stock market dropped, and the debates began.

With the first debate came performance critiques of the two candidates and new state polls. By the end of that week the race had tightened. Our model predicted that Governor Romney had gained in several key states primarily Florida, Virginia, and North Carolina. With this surge his probability of winning also rose – moving from 0% the week before to 11% on October 5.

The following week provided an opportunity for the Vice Presidential candidates to debate. As the debate was late in the week they could not have had significant impact on that week’s polls. Instead the new polls were more likely a continuation of the results of the first debate. On Octaber 12 our model showed a continued decline for the President with his probability of reelection dropping to 82%. At the same time Governor Romney’s probability of winning rose to 16% and for the first time in several months the probability of an electoral college tie reached significance at 2%.

The effects of the Vice Presidential debate and the third Presidential debate could be seen in the following week’s polls. As of October 19, Governor Romney’s chances continued to rise reaching a probabilty of 25%. Similarly President Obama’s probability of winning continued its slide dropping to 73%. The probability of a tie held at just under 2%.

Now the debates have been concluded and the candidates are back to the criss-crossing the country giving stump speeches in the battleground states. But with this return to the traditional campaign has also come a return to President Obama’s reelection hopes. As of last week our model shows the chance of reelection reversing, climbing from the previous week’s low back up above 92%. Similarly Romney’s chances have declined to about 7% with the probability of tie again dropping below 1%.

Why the reversal? A noticeable change has occurred in Florida. Romney had taken significant leads in the Sunshine State over the past several weeks. While still leading Florida has again tightened. Similarly Romney’s Virgninia lead has dropped to a tie. And in Ohio, a key for a Republican victory, the polls show that while Obama had been able to retain a slight lead throughout most of October, his lead has increased over the last week.

While the model does not indicate that reelection is a certainty, it does indicate good news for the President. Our model currently predicts an electoral college vote of 301 for President Obama and 237 for Governor Romney – a buffer of only 31 votes – a slim margin in electoral college math. But with only a week to go, and early voting and absentee voting already in progress, our model indcates the GOP may have a significant challenge to get those 31.

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While the campaigns move into the fall, polls show that little has changed

Sep23rd
2012 Leave a Comment J. Brian Adams Written by J. Brian Adams

The party conventions have passed and the fall campaign season is in full swing. As the campaigns prepare for the October debates the question continues to be asked; “is the current presidential race too close to call, or has one candidate already taken what is possibly an insurmountable lead?”

Polls tend to lag public opinion by about a week so any current events may not be reflected, but using the available polls and our simulation model, President Obama’s probability of reelection has dropped – but by only a small amount. He currently has near a 97% chance of winning with Governor Romney’s probability up slightly to about 3%. The chance of an electoral college tie – a serious possibility several months ago – has dropped to near zero.

The first plot shows the trend in the probabilities while the second shows the range of expected electoral votes for each of the candidates. With the exception of the Romney bounce that occurred following his selection of Paul Ryan for Vice-President in the middle of August, the trends have remained consistently strong in favor of the President.

The slight rise in Romney’s chance appears to be the result of favorable polling in Florida. While Florida has been considered a tossup throughout the campaign, the latest polls indicate a switch from leaning blue to now leaning red. This change gives Romney about a 58% of winning Florida and its 29 electoral votes.

With the possible loss of Florida, our model now gives Obama 247 likely or certain electors to Romney’s 151. That leaves only 23 votes to clinch reelection – with 46 of the remaining 140 electoral votes currently leaning in the President’s favor.

A common discussion point for polls is the margin of error. This is a measure of the uncertainty in the polling. The argument goes that if one candidate is polling within the margin of error – no matter how far from the center – then that candidate still has a chance.

The margin of error in our model is shown in the blue and red bands for each of the candidates. To be a tie these bands would have to have a significant level of overlap – more so than what even occurred in the middle of June. While they do currently overlap – explaining why the current probabilities are not at the certainty level – the overlap is so small that it is a statistical leap to argue that Romney’s true vote count is actually higher than Obama’s, and that the reason for the difference is due to the random error that occurs in all polls.

While world news, campaign announcements, and candidate debates are sure to move these lines, at the present it appears that the status quo is expected to stay.

Polling

Reelection probability rises to near certainty

Aug14th
2012 1 Comment J. Brian Adams Written by J. Brian Adams

As the summer wanes and the presidential campaign continues, a recurring question relates to electoral mathematics – what states will either President Obama or Governor Romney need to win in November? There are several that are touted as battleground states that will determine the outcome of the election. Is this true?

As any follower of presidential elections already knows, it requires 270 electoral votes to win a presidential election.

Running the current statewide polling data through our simulation model, there are currently sixteen states – including Pennsylvania – in which Obama has a greater than 95% probability of winning. These sixteen contribute a total of 205 electoral votes to his total. Governor Romney also has sixteen states in his certain win column, but because of population differences they contribute only 141 electoral votes to his total.

A second level includes those states that while not certain wins for each of the candidates a win is considered likely. This level adds three more states to the Obama tally with an additional 58 electoral votes. Romney gains a single state and only three additional electors.

Including this level the President currently has 263 electoral votes requiring only seven additional electors. Governor Romney has 144 electoral votes and still needs 126 more.

To reach 270 it might be possible for Romney to win all four of the states that are leaning in his favor – Kansas, Kentucky, South Carolina, and South Dakota. This adds thirty-two electors to his total. If he also takes all three of the true tossup states – Colorado, Missouri, and Tennessee – he gains an additional thirty electors. But that only brings him to 203 – still 67 short. To make up these additional votes he will need to take all of the states that are polling close, but still leaning Obama.

At this point the probability of an Obama reelection is at 99.8% – as close to a certainty as one might expect. But it might be possible for Romney to change the result by swaying a few of the battlegrounds. But it will take more than a single win. For example Ohio is currently a likely Obama win. But if between now and November Romney can change that outcome and take Ohio his odds barely improve with Obama’s chance of winning dropping to just under 99%.

Instead, Romney will have to sweep all of the battlegrounds. Assume that he is able to win Florida, North Carolina, Ohio, and Virginia. His probability of winning puts him back into play at 46% to the President’s 52% with a 3% chance of tie. If you add Michigan or Pennsylvania into the Romney win column his chances rise to a likely – albeit not certain – electoral college win. Of course it is important to recognize that these are all states in which Obama is currently leading, some – such as Michigan and Pennsylvania – by significant margins.

This is not to imply that the election is over; far from it. This is simply a snapshot based on the current statewide opinion polls. It remains to be seen how Romney’s choice of Paul Ryan will play out in the polls or what impact the party conventions will have. As we enter the fall campaign season we are sure to see changes in the numbers. But based on the current polls, the odds are not on a photo finish, but instead a contender who is struggling to get out of the gate.
electoral_map_08102012

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President’s Reelection Chances Rebound with a Rise to Above 96%

Jul19th
2012 1 Comment J. Brian Adams Written by J. Brian Adams

With last week’s release of eight new statewide polls the probability of President Obama being reelected has rebounded eight points to a new high of over 96%. Governor Romney’s probability of winning has similarly dropped eight points to 3%. These percentages represent the probability of each candidate receiving at least 270 electoral votes. The probability of a tie remains at less than 1%

These results are based upon a statistical model that uses currently available opinion polls for each of the fifty states and the District of Columbia. It analyzes these polls determining each possible outcome with its likelihood of occurring.

Of the eight states involved in the new polls, five – New Mexico, Virginia, Maine, North Carolina, Pennsylvania, and Wisconsin – have increased their support for the President. Two states – Florida and North Dakota – show increases for Governor Romney. Polls from Virginia and North Carolina indicate strong increases for Obama with both states moving from leaning Romney to now leaning Obama.

Florida which had been showing a fractional advantage towards Obama remains close but the slight advantage has now moved to Romney.

There are still three states, Iowa, New Hampshire, and Tennessee that are in the tossup category. Tossup states are the states in which there is not a statistically clear winner.

States that are leaning Obama are currently CO, MI, NV, NC, OH, and PA.
The states that are leaning Romney are FL, IN, KS, KY, SC, and SD.

The states that are likely wins for the President are ME, NM, OR, VA, and WI.
MO, and MT are likely wins for Governor Romney.

The final category are those states that would be considered statistically certain outcomes.

For President Obama these are CA, CT, DE, DC, HI, IL, MD, MA, MN, NJ, NY, RI, VT, and WA.
For Governor Romney the certain win states are AL, AK, AZ, AR, GA, ID, LA, MS, NE, ND, OK, TX, UT, WV, and WY.

The box plots show the distribution of predicted electoral votes for each candidate over the past seven weeks. The center rectangle includes the middle 50% of the outcomes while the whiskers cover the most likely 99.5% of outcomes. The green line marks the 270 electoral vote cutoff needed to win the election.

The time series plot tracks the trend in the probability of winning since the middle of May.

Box Whisker Plots for Possible Electoral Votes

Comparison of Predicted Electoral Vote Outcomes for President Obama and Governor Romney

Trend of Probabilities of Receiving 270 or More Electoral Votes

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Latest Polls Indicate Probability of Reelection Down But Still Strong

Jul9th
2012 1 Comment J. Brian Adams Written by J. Brian Adams

With the release of the latest statewide polls President Obama has an 88% chance of winning reelection as compared to Gov. Romney’s 11% with a 1% chance of a tie.

These results are based upon an analysis of the combinations of possible results using Monte Carlo techniques. This simulation model combines the estimated percentage of votes that each candidate is expected to receive while further taking into account the percentage of the electorate that may still be undecided.

With each run a number of electoral votes is predicted for each of the fifty states and the District of Columbia. A simulated winner of the election is thus determined. By running the model millions of times, the technique estimates the percentage of the simulated elections that each candidate wins and thus the probability of winning the election.

The input data for the simulation model is collected from the most current public opinion polls that are available for each state. Since new polls are conducted almost daily, the probabilities frequently change.

Of course the polls only reflect the electoral vote outcome for a single state so while the results do vary, the magnitude a particular change is dependent upon the size of the state. For example, a change in the public polls for Florida with its twenty-nine electoral votes has a far larger impact on the outcome of the national election than does a change in Delaware with its three electoral votes.

The model has been run weekly since the middle of May. With the latest set of polls President Obama’s probability of winning has dropped slightly from 93% in the previous week to 88% this week. With this drop for the President, Governor Romney’s probability of winning the election has risen from 6% the previous week to just over 11%. The probability of a tie – both candidates receiving 269 electoral votes – has also risen to just under 1%.

As events unfold over the next five months the polls will reflect the opinions of the electorate to those events. With the changing polls the probability of a particular candidate winning the election can change as well. If a third party candidate enters the race and is included in the polls then that candidate’s impact can also be modeled.

While polls provide a snapshot of the opinion of the electorate, this statistical modeling technique can use these opinions to make quantitative predictions about the November outcome.

Comparison of Predicted Electoral Vote Outcomes

Trend of Probabilities for Winning the November Presidential Election

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