# The maths on Ernie Els’ comeback

That piece of wisdom, offered after Adam Scott birdied the 14th hole yesterday and led Ernie Els by four shots, didn’t turn out so well. In truth, at this point my hastily-developed model gave Els a 1.1% chance of winning as he stood on the 17th tee. That was close enough to over for my taste. After Scott lost, I didn’t trust the voo-doo of a computer program, even if it my own voo-doo. How improbable was Ernie Els’ lifting the Claret Jug on Sunday afternoon?

It was pretty clear Els’ chances were remote after he settled for par on 16. No player in the field was able to play the last two holes in -2—only four players on Sunday recorded birdies on 17 alone. Therefore, the most likely scenario for an Els win was to go -1 over the last two holes while Scott played the last four in +3. Or Els could have played the final two in even par with Scott going +4. In either case, the result would be a playoff. Obviously, there are other scenarios involving Scott really blowing up, but going +5 or worse was more unlikely than Els going -2.

To try to determine Els’ true chances of victory at this point, we can look at how the rest of the field fared over the final holes. (Numbers under “Field” represent the players accomplishing the listed score over the given holes during Sunday’s final round.)

```17/18  Field
-1    14/81 (17.2%)
E    35/81 (43.2%)

15-18  Field
+3    10/81 (12.3%)
>+4     4/81  (4.9%)

```

The scenario of Els winning in regulation, involving Els going -1 and Scott going +4, had about a 0.9% chance of occurring based on what the rest of the field had done over those holes.

The more likely tying scenarios – E/+4 and -1/+3 – had a combined 4.2% chance of happening. Assuming Els had a 50/50 shot in a playoff, he has a 2.1% chance of winning in these two scenarios giving him a total chance of 3.0% based on the distribution of scores of the rest of the field.

This kind of analysis isn’t entirely fair to either golfer since both are better than the average player in the field. Andres Romero was hacking his way to an 82 in finishing last in the field. The fact that he went +4 over the last four holes isn’t all that relevant in predicting Adam Scott’s score over that stretch. Let’s revisit this looking at the 36 players not named Scott or Els that finished +4 or better.

```17/18  Field
-1    10/36 (27.8%)
E    13/36 (36.1%)

15-18  Field
+3     3/36 ( 8.3%)
>+4     0/36 ( 0.0%)

```

Since no players in the top 38 went +4 over the last four holes, there’s only one scenario to consider and that’s the -1/+3 option to get Els into the playoff. Based on these odds, that outcome would happen 2.3% of the time giving Els about a 1% chance of winning outright.

It’s a mistake to assume that something that has never happened isn’t possible. One might assume that Scott had a chance of cracking under the pressure that no other golfer had to experience yesterday. Although, if you were going to accuse someone of cracking, I don’t think it would be a guy that hardly shows emotion, had contended in majors before, and has the winningest caddy in golf on his bag. In addition he had just posted one of 11 birdies all day on the 14th hole. Confidence shouldn’t have been an issue.

(Not that my model deserves a pat on the back, but it gave Scott a 0.9% chance of going +4 on the closing four holes, and Els a 3.3% chance of going -2 on the final two holes despite the lack of precedent for either happening.)

Even the way Scott got to +4 was unusual. His bogeys on 15 and 17 weren’t killers. Both holes were difficult and putting up an even bigger number on either wasn’t out of the question. Because of this, my model barely changed Els’ chances after Scott’s bogey on 15 and Els’ par on 17. Scott was the only player in the field that scored over par on both of the relatively easy 16th and 18th holes on Sunday.

Whether it was 1% or 3%, Ernie Els’ chances of winning the Open were clearly very small after the par on 16, especially doing so without needing a playoff. After the conclusion of the round, ESPN’s cameras caught Els chatting with Scott and describing his missed birdie putt on 16. We weren’t privy to the rest of the conversation, but it seemed like Els was leading to an admission that he felt the tournament was over when that happened. If only the R&A would allow players to tweet during a round!

Concluding matters, let’s look what my model spit out for Els’ chances after each event on the closing stretch. Keep in mind “chance of winning” does not mean “chance of making it interesting”. Ernie’s 1.1% chance after the par on 16 included cases where he would get within one or even get into a playoff, and still lose.

```Event           Els WP
Els pars 16      1.1%
Scott bogeys 15  1.8%
Els pars 17      1.2%
Scott bogeys 16  5.7%
Els birdies 18  15.2%
Scott bogeys 17 46.6%
Scott bogeys 18  100%

```

One thing lost in the Scott collapse was that it’s not even clear that the walk from 16 to 17 was Els’ worst predicament. As he went to 18, he was down three, and while Scott had three holes left, two of them figured to be relatively easy. Earlier in the round, Els was six down as he headed to the tenth, and he was seven down when he teed off on the fourth hole. In both of those cases, he had multiple other golfers ahead of or tied with him on the leaderboard, each of whom was ranked higher than Els in the Official World Golf Rankings.

Paul Lawrie will always own the gold standard for major championship comebacks. In the ‘99 Open Championship, he had to leapfrog 11 golfers on Sunday just to get into a three-way playoff after Jean Van De Velde’s 18th hole disaster. But Els’ story in 2012 is rather incredible as major championship comebacks go. So congrats to Ernie Els. And congrats to the long putter. It may have saved his career, too.