# Statistics question about Nate Silver's predictions **URL:** \ **Category:** Factual Questions\ **Created:** [November 12, 2012, 3:24am UTC](https://boards.straightdope.com/t/statistics-question-about-nate-silvers-predictions/640745 "2012-11-12T03:24:13Z")\ **Posts on this page:** 8\ **Page:** 2
**Author:** ![ftg](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ftg/32/2801_2.png) [@ftg](https://boards.straightdope.com/u/ftg)\ **Post date:** [November 12, 2012, 2:21pm UTC](https://boards.straightdope.com/t/statistics-question-about-nate-silvers-predictions/640745/21 "2012-11-12T14:21:58Z")
Just to make very, very explicit a basic error the OP made, Nate Silver’s 90.9% odds was _not_ that every single state would go the way he said it would. It was the odds that _enough_ electoral votes total would go Obama’s way. There are a _lot_ of ways the latter could have happened. So trying to compound probabilities for each state going one particular way does give a very small chance. But that particular scenario is _only one_ of many, many ways the totals could have added up for an Obama win. There were a lot of scenarios where Obama could win, a lot where Romney could win. The Obama scenarios totaled up in statistical terms to be substantially more likely. One of the real tricks that Silver and other similar predictors used is not having to calculate the odds for every single scenario and then add them up. There are far too many scenarios to do each individual calculation. (Think of a scale of 2[sup]51[/sup] starting cases.) So various tricks are used to collapse the computational tree, each person having their own bag of tricks. ---
**Author:** ![El\_Zagna](https://avatars.discourse-cdn.com/v4/letter/e/d2c977/32.png) [@El\_Zagna](https://boards.straightdope.com/u/El_Zagna)\ **Post date:** [November 12, 2012, 2:59pm UTC](https://boards.straightdope.com/t/statistics-question-about-nate-silvers-predictions/640745/22 "2012-11-12T14:59:50Z")
> [@ftg](#): > > Just to make very, very explicit a basic error the OP made, Nate Silver’s 90.9% odds was _not_ that every single state would go the way he said it would. It was the odds that _enough_ electoral votes total would go Obama’s way. That wasn’t what I said, or at least that wasn’t what I meant to say. I was just using the 90% probability across all states as a shortcut. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [November 12, 2012, 5:50pm UTC](https://boards.straightdope.com/t/statistics-question-about-nate-silvers-predictions/640745/23 "2012-11-12T17:50:41Z")
On the [page **MikeS** linked to](http://fivethirtyeight.blogs.nytimes.com/2012/11/02/nov-1-the-simple-case-for-saying-obama-is-the-favorite/), there’s a graph titled **Tipping Point States** , which is “The probability that a state provides the decisive electoral vote.” Is that just defined by what time the Networks call the state, with the first state called that put the victor over 270 (when added to all the states already called)? So it’s partly a function of how quickly a state counts its votes. Or is there some more technical definition? (As an example of a different definition, multiply Obama’s votes by (1-x) and multiply Romney’s by (1+x), with x slowly increasing from 0, and see which state changes the election outcome when it flips.) ---
**Author:** ![AlsoNamedBort](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/alsonamedbort/32/3213_2.png) [@AlsoNamedBort](https://boards.straightdope.com/u/AlsoNamedBort)\ **Post date:** [November 12, 2012, 6:33pm UTC](https://boards.straightdope.com/t/statistics-question-about-nate-silvers-predictions/640745/24 "2012-11-12T18:33:18Z")
> [@ZenBeam](#): > > On the [page **MikeS** linked to](http://fivethirtyeight.blogs.nytimes.com/2012/11/02/nov-1-the-simple-case-for-saying-obama-is-the-favorite/), there’s a graph titled **Tipping Point States** , which is “The probability that a state provides the decisive electoral vote.” > > Is that just defined by what time the Networks call the state, with the first state called that put the victor over 270 (when added to all the states already called)? So it’s partly a function of how quickly a state counts its votes. Or is there some more technical definition? > > (As an example of a different definition, multiply Obama’s votes by (1-x) and multiply Romney’s by (1+x), with x slowly increasing from 0, and see which state changes the election outcome when it flips.) No it has to do with what would happen if the race really were close, and one state decided the election: > [@](#): > > The most rigorous way to define this is to sort the states in order of the most Democratic to the least Democratic, or most Republican to least Republican. Then count up the number of votes the candidate accumulates as he wins successively more difficult states. The state that provides him with the 270th electoral vote, clinching an Electoral College majority, is the swingiest state — the specific term I use for it is the “tipping point state.” In this election, Colorado, ended up being the tipping point. If Romney had done better across the board, and won Virgina, Ohio, and Florida, then it would’ve been Colorado that won Obama the election. See the graph here: [http://fivethirtyeight.blogs.nytimes.com/2012/11/08/as-nation-and-parties-change-republicans-are-at-an-electoral-college-disadvantage/](http://fivethirtyeight.blogs.nytimes.com/2012/11/08/as-nation-and-parties-change-republicans-are-at-an-electoral-college-disadvantage/) ---
**Author:** ![Paranoid\_Randroid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/paranoid_randroid/32/18_2.png) [@Paranoid\_Randroid](https://boards.straightdope.com/u/Paranoid_Randroid)\ **Post date:** [November 12, 2012, 6:46pm UTC](https://boards.straightdope.com/t/statistics-question-about-nate-silvers-predictions/640745/25 "2012-11-12T18:46:07Z")
> [@OldGuy](#): > > “Moderately independent” is technically impossible. Independent is an absolute. Things are either independent or not. “Correlated” however is a scale running from -1 to 1. So you can be moderately correlated. Although you’re right as far as it goes, I’m not sure you’re drawing the salient distinction. Two random variables are either independent or not, yes, but they’re also either uncorrelated or not — the problem seems less that “independence is absolute” but rather that we lack one preferred objective measure of dependence. > [@Evil\_Economist](#): > > E.g., the classic example is y=x^2. y and x have a correlation of zero, but y is completely determined by x. At the risk of complicating the discussion, I want to note that’s only true in particular circumstances. E.g. if x ~ Uniform(0, 1) then Cov(x, x^2) = 1/12 != 0. Of course you’re right that in general uncorrelated does not imply independent. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [November 12, 2012, 6:49pm UTC](https://boards.straightdope.com/t/statistics-question-about-nate-silvers-predictions/640745/26 "2012-11-12T18:49:37Z")
> [@AlsoNamedBort](#): > > No it has to do with what would happen if the race really were close, and one state decided the election: > > In this election, Colorado, ended up being the tipping point. If Romney had done better across the board, and won Virgina, Ohio, and Florida, then it would’ve been Colorado that won Obama the election. > > See the graph here: > [As Nation and Parties Change, Republicans Are at an Electoral College Disadvantage - The New York Times](http://fivethirtyeight.blogs.nytimes.com/2012/11/08/as-nation-and-parties-change-republicans-are-at-an-electoral-college-disadvantage/) Thanks. I searched for “Tipping Point” on that page, but didn’t see any link to a definition. That does look to be equivalent to the definition I gave in my last paragraph. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [November 12, 2012, 7:13pm UTC](https://boards.straightdope.com/t/statistics-question-about-nate-silvers-predictions/640745/27 "2012-11-12T19:13:55Z")
> [@Paranoid\_Randroid](#): > > …we lack one preferred objective measure of dependence. No, that’s [mutual information](http://en.wikipedia.org/wiki/Mutual_information). ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [November 12, 2012, 8:08pm UTC](https://boards.straightdope.com/t/statistics-question-about-nate-silvers-predictions/640745/28 "2012-11-12T20:08:44Z")
> [@Paranoid\_Randroid](#): > > Of course you’re right that in general uncorrelated does not imply independent. For what it’s worth, X and Y are independent just in case f(X) and g(Y) are uncorrelated for _every_ function f and g. [Previous page](https://boards.straightdope.com/t/statistics-question-about-nate-silvers-predictions/640745.md?page=1)