# 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.

#### Boris

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.

#### Chris

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?

#### Chris H

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

#### Joe in GA

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.

#### Richard Van Noorden

'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.

#### David Gonzales

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.

#### GB

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

#### Ken

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?

#### Ben

There were 24 half-points available to win which were the smallest increments, and Europe had to win at least 16 of them which would give more like 5%. Not sure that is kosher either though.

#### Mitchel Lichtman

Steve, each match can end in a tie (that happens around 14% of the time), in which case each team gets half a point. That reduces the chances of Europe winning to 14% rather than 19%. Either way, it is not a "miracle" or even an "epic comeback," as you correctly state. Interestingly, it is about the same chance as a baseball team winning a game in which they are down by 1 run in the 9th and facing the other team's ace reliever (closer). That is considered a "ho-hum" comeback of course.

#### Mitchel Lichtman

Even considering that the US team was a little better (as somewhat evidenced by the results from days 1 and 2 and the World rankings), the results of match play in golf are not particularly sensitive to the quality of each player, especially when the spread in talent among the top players in golf is so small. In other words, if Tiger Woods played Martin Kaymar (#2 and #32) in one match play game, Tiger might win 55% of the time or something like that.

So, rather than 14%, it might be 10% at worst. In fact, if the US had a 55% chance to win any non-halved match on Sunday, which I think is a stretch, Europe would still have an 8% chance of winning. Still hardly a miracle...

#### James

"The Ryder Cup was about as exciting as golf can get."

Oxymoron, I think. Now can we hear about the thrilling finish of the International Turtle Racing championships?

#### dan

The problem is they weren't even matches. The USA team (using advanced stats ) had better numbers. A more accurate split was 58%/42% average. My calculation had it around 12%
that is 1/2 as likely as The giants first win over NE super bowl 2007. One of the biggest upsets in super bowl history. So in sports terms and by the numbers it was a miracle...!First rule: bad input in bad output out :)

#### dan

Also, Justin rose putt alone on 17 was around a 3% chance of sinking. If this one shot doesn't happen Usa most likely wins. Also, context context context. In ryder cup/history it was a miracle. it is only played once every two years. so a 10 to 1 chance means every twenty years. IF teams were behind that much each time which they are not. so yes the lead and the comeback were clearly historic!

#### Dwayne

The matchups were not even though, and that's why it was legitimately miraculous. You should take the rankings of each of the players into account somehow to make a proper calculation, as well as home field advantage, etc. The single 'even matchup' analogy doesn't hold in this case so the article's conclusion doesn't hold either.

#### Akshay

Does the fact that it is possible to tie the game change this from being a binomial distribution?

#### Baltimark

Also, the matches weren't _necessarily_ independent.

Oh sure, for any ease of calculation, you need to assume so. I wouldn't want to come up with the joint distribution.

But, once the Euros started rolling, does that start swinging the later matches to their favor, slightly?

I don't think Jim Furyk has a mental breakdown on the 18th green if the USA was sitting at 14 points with a couple matches behind him in the back.

#### Nik W

Could a more "realistic" statistic be created if instead of a coin toss, you considered 3 determinants - win, halved hole and loss. Then assuming all external factors were "even" (crowd, home soil, performance, ability to handle pressure, mental strength etc) a % in single figures would be probably be created....Still not a miracle.... But an unlikely situation. A result against the odds. A result for golf....?

#### Joe Soap

Perhaps one should also mention that the miracle started on the Saturday afternoon, the USA being 10-4 up with two games still to finish. So the requirement at that point was to win 10 out of 14 games.