Math Trix: So, exactly how lucky is Hillary?

I know that this doesn’t matter from a political perspective… Bernie stands zero chance of winning the nomination.

But I think that the math is interesting … made me dust off my recollections of combinatorial probabilities.

Just in case you’ve been asleep for the past couple of days (or get all of your news from the NY Times), Hillary squeaked by Bernie in Iowa … I mean, really squeaked.

The ending tally was that Hillary got credit for 701 delegates and Bernie got credit for 697.

How those final totals were concocted is very interesting.

image

Here’s the scoop … and the stats.

 

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Based on the raw vote tallies Bernie got 697 delegates, Hillary scored 695 and there were 6 ties.

Might have expected that the ties would have been split evenly with 3 delegates going to each of the candidates.

If that were the case, Bernie would have ended with 700 and Hillary with 698 … Bernie wins.

But, the Iowa Democratic Party had a different idea: flip a coin for each of the tied delegates individually and give the ‘whole delegate’ to the candidate winning the toss.

So, they flipped 6 times and Hillary won all 6 coin flips.

How lucky is that?

Easy … two possible outcomes (heads or tails)  … 6 tries … just multiply 2 x 2 x 2 x 2 x 2 x2 = 64 … odds are 1 in 64 … probability of 1.6%.

Hmmm

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Let’s cut the data another way ….

Given that Bernie had a 2 delegate lead before the tosses, what were the statistical probabilities that he’d prevail.

Here’s the stats recap, below is the explanation.

Clinton coin toss luck

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Bernie would have won

  • 703 to 695 if Hillary had lost all tosses (1.6% – the same as her winning all 6 tosses)
  • 702 to 696 if Hillary had only won 1 of the tosses (9.4%)
  • 701 to 697 if Hillary had only won 2 of the tosses (23.4%)
  • 700 to 698 if Hillary had only won 3 of the tosses (31.3%)

Sum up those probabilities and Bernie stood a 65.5% chance of winning.

The was a 23.4% chance that Bernie would win 2 and Hillary would win 4 … resulting in a 699 tie.

So, Hillary’s probability of winning was 10.9% (100% less 65.5% Bernie wins and 23.4% tie).

In other words, Hillary got very lucky on Monday night.

No data re: whether Bill also got luck Monday night

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P.S. Does anybody find it curious the the Iowa Democratic is “unable” to release the raw vote totals?

Since I love conspiracy theories, gotta believe that Bernie won the popular vote.

Oh well, we’ll never know … info has probably been deleted.

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Stats example: probability of Hillary winning 2 tosses out of 6 = (6-factorial) divided by (2 factorial times 4 factorial) …. which is:

(6 x 5 x 4 x 3 x 2) = 720

… divided by [(4 x 3 x 2) times 2] = 48

…. 720 divided by 48 = 15 occurrences out of 64 possible outcomes = 23.4%

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#HomaFiles

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