# The Miracle at Medinah

The Ryder Cup was about as exciting as golf can get. Down 10-6 going into the last day, the European team eked out a 14.5-13.5 victory.

The headline in USA Today reads “Europe Rallies for Miraculous Ryder Cup Win.” The Ryder Cup website calls it the “Miracle at Medinah.”

So how miraculous was the outcome from a statistical perspective?

Europe needed to win eight of twelve matches for a victory.  (If the teams tied, Europe got to keep the trophy, so it is considered a European win.)  Let’s assume that each of the pairings was an even match.  Then the likelihood that Europe wins after being down 10-6 after two days is given by the binomial distribution: what is the likelihood of at least 8 heads coming up if you flip a fair coin 12 times.

Not exactly the stuff of miracles, but fun nonetheless.

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1. Boris says:

assuming of course, that all matches were 50/50 – big assumption. Historically, USA do better than Europe in the singles and the tie was an option in all of them. Betting odds were a touch more remote, about 12% for the European WIN (not including the tie). Winning and retaining the Cup are not the same thing, although the end result of USA not winning would be the same.

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2. Chris says:

It’s not binomial though – if each of the pairings was assumed to be an equal match, then they would all have been halved, no?

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• RGJ says:

??? Why was this hidden due to dislikes? It hits the nail on the head.

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3. Chris H says:

This is a fun comparison, but doesn’t account for the possibility for each hole can be halved.

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4. Joe in GA says:

Steven,

Your calculation does not factor in things other than the golfers. You need to consider historical results, that the golf course had been modified to favor the US, that the Europeans were doing this in the US (on the road) and you can see why were feeling pretty good about our chances on Saturday night. It is a fun exercise but more accurate when applied to flipping a coin or rolling a die.

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5. Richard Van Noorden says:

‘Let’s assume that each of the pairings was an even match.’

And that’s your problem. Average US world ranking in Ryder Cup team: 12. Average Europe world ranking: 19. And the US were at home, with raucous crowd – giving extra advantage. That’s explains a little more why the result was unexpected.

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6. David Gonzales says:

We can also (especially to make miracles more miraculous), infer a player strength score according to maximum likelihood, or a Bayesian model considering the score at the end of Day 2 as evidence. Then, the probability of the come-back on Day 3 becomes even more remote.

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7. GB says:

There were three possible results for each match, not two. I demand a recalculation!

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8. Ken says:

given that the Europeans only won 6/16 points in the first two days of the competition, what were the chances that they would win 8/12 points in the final day?

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