Friday, February 17, 2012

Expected Score, Variance and Golf Strategy

A little while ago I made a blog post stating that Kyle Stanley’s conservative play on #18 at Torrey Pines cost him the Farmers Championship.


I still steadfastly believe that. In fact, as this was discussed more I started tor realize the folly in the ‘lay up’ crowds belief.

They never quite considered the rewards between the 2 decisions.

Meaning, if Stanley had hit a pretty good shot for him, he would have cleared the water and won the tournament in regulation. However, he could have hit the greatest layup shot he could have ever hit in his life….and he still has to cross over the water on the next shot.

With that, I’ve had a few readers bring up a valid point about ‘expected score’ and ‘score variance’ when it comes to golf strategy.

‘Expected Score’ means the average score a golfer would take from a certain spot given their skill level. Thus, if one golfer blasts their drive on #18 at Pebble Beach to 240 yards away, their ‘expected score’ into the hole may be 3.2 strokes. But, if they find the rough and are 280 yards away, their ‘expected score’ might be something like 4.5 strokes.

‘Score Variance’ is the range of scores a golfer may take from certain positions into the cup and what strategy they take. A golfer may try to drive a par-4 and their variance my go from 2 strokes to 6 strokes, thus a variance of 4 strokes.

So what we wind up with is the debate of going for ‘expected score’ or ‘lowering your variance.’ For instance, a golfer could go for a par-4 on the driver and have a variance of 4 strokes (2 – 6 strokes), but an expected score of 4.1 strokes by adopting that strategy. While the golfer who hits a 4-iron off the tee may have a variance of 2 strokes (3 – 5 strokes), but the same expected score of 4.1 strokes by adopting the more conservative strategy.

The question has come down to what strategy should a golfer take, less variance or lower expected score?

My feeling is that the golfer should pretty much always lean towards a lower expected score. My belief is that when it comes to strategy on the golf course, there is usually a bigger discrepancy in expected scores than there is a difference in score variance.

Let’s use the par-4 where we can possibly drive the green or lay-up. My belief is that it’s much more likely that 1 of the strategies will have a distinctly better expected score. Like we could say 3.9 strokes going for the green on the drive versus 4.5 strokes laying-up.

However, the score variance would probably be something like 4.0 strokes going for it on the driver versus 3.8 strokes laying-up.

Unfortunately, I have no way to measure this so I am theorizing. But, I think the differences in score variance is likely going to be minimal because of the human element involved.

Stanley’s 8 on #18 at Torrey Pines was a bit of an aberration for a Tour player. The likelihood that he would end up in the water, particularly for his Birdie Zone skill (top-50 player from the BZ) was very unlikely. And then for him to knock it on with a wedge and 3-putt was very unlikely.

But, the human element and something like the pressure to win his first tournament probably caused him to take an 8 on a hole he never should have taken an 8. I honestly believe…without question…that his expected score is noticeably lower if he goes for the green in 2 shots. But, I believe the variance was so similar that laying-up to reduce the variance was an illogical decision.

However, that does not mean that there are never instances where playing for score variance is a good idea.

In fact, I discuss this for a bit in the 2011 Pro Golf Synopsis. I call it ‘playing for your average swing.’

The problem that most amateurs have is that they do the opposite. They will either play for a poor swing or play for the greatest swing that they can make. Meaning, you have to be able to accurately gauge the results if you take your ‘average swing’ at the ball and play the shot based on that. For instance, an ‘average’ swing with the driver for me will send the ball about 280-290 yards and will find the fairway about 80% of the time and should go no worse than the first cut of rough about 90% of the time and should fade a little. I also know that when I take an average swing but still ‘miss it’, the miss is usually off to the right a bit and I have a pretty good gauge how much to the right I will miss the shot.

Thus, if I get on a hole like #3 at North Shore, I have to play for the results of my ‘average swing.’

For me, the average swing has me aim at the bunker where the 127 yard marker is (I cannot reach that bunker, it’s just an aiming point for me). This gives me enough room so that if I take an average swing and it fades, I should find the fairway. If I take an average swing and miss to the right like I typically do on my average swing ‘misses’, I should still be okay. And if I hit it straight, I’m still down the middle.

But most amateurs will either aim too far left (playing for a bad swing) or try to hug the water too close (playing for a great swing).

Brandt Snedeker played for ‘variance’ on #18 at Torrey Pines. He hit a driver in the left rough and he had a *chance* to make it over the water in two shots. However, that would mean he would have to take a great swing and still get some fortune his way. Instead, he played for his ‘average swing’, laid-up, and put it close and made birdie and put the pressure on Stanley to come in with at least a double bogey to win outright.

That being said, I believe that Snedeker also was playing for the lowest expected score as well. He just happened to have the lowest variance as well.

In other words, play for your average swing and you will likely play to the lowest expected value and over time that will allow you to lower your scores.


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