Why Tournament golf is often an arbitrary game

Week after week, the most frustrating aspect of life on the PGA Tour – probably for players and certainly for statisticians – is the often arbitrary nature of the results.

This past week’s Farmers Insurance Open at Torrey Pines, which required a playoff between eventual champion Luke List and Will Zalatoris to decide, is a perfect illustration of that arbitrary factor.

List won because, over the course of 72 regulation holes, plus one playoff, he hit one approach wedge on one hole – the final one – closer than Zalatoris.

Or, if you prefer, List won because Zalatoris’ eight-and-one-half foot uphill potential winning putt on the 72nd hole only flirted with the edge of the cup rather than falling. That’s two inches worth of arbitrary right there.

It is no surprise to any regular watcher of the PGA Tour that seemingly arbitrary events often became separators in the search for a champion. Only a couple of years ago Jon Rahm beat Dustin Johnson at the BMW by famously rolling in a 60-some foot putt at Olympia Fields.

On that putt, a little matter of $680,000 jumped from Johnson’s pocket into Rahm’s. Arbitrary? Granted, Rahm was and remains a great player. But for the 2020 season, he stood 35th in Strokes Gained Putting, a decent standing but hardly qualifying Rahm as Boss of the Moss.

Beyond that, any 60-some foot putt that falls has a high ‘arbitrary’ factor to it.

The first four weeks of the 2022 portion of the current season have presented abundant evidence of the arbitrary nature of PGA Tour performance week-to-week. Look hard enough and that evidence can be seen in the results.

It’s superficially a tricky process because both courses and playing conditions can change dramatically from week to week. There probably is no better illustration of that rule than this coming week’s AT&T Pebble Beach Pro-Am, which will be played on the notoriously fickle and changing Monterey Peninsula rota.

But the calendar year’s first four tournaments – the Sentry Tournament of Champions, the Sony Open, the American Express, and the Farmers Insurance Open – are played under much more predictable and generally benign Hawaii/Southern California conditions. Particularly if we compare year-to-year performance,  those four courses constitute a reasonably fair basis for measuring the extent to which arbitrary factors influence performance.

Let’s begin with a simple number. Through these first four events, 95 competitors who made the cut in one of the year’s first four PGA Tour events last season also made the cut in that same event this season. Those 95 constitute a sufficient field to make at least some basic judgments.

If golf were a predictable game, we might expect those 95 to have performed roughly in similar fashion on the same course and in essentially the same idyllic conditions from year to year. After all, they made the cut both years. Yes, there will be some variations related to age, maturity, or injury, but given the physical state of the average PGA Tour player, those should be in the vast minority.

The best tool for measuring any change in player performance is probably the absolute value of the difference in the standard deviation of each player’s performance. That’s a loaded sentence so I’ll break down the two most critical terms. Those of you who are math averse are given permission to skip the next five paragraphs. See you at “sorry about the math interruption…”

Standard deviation is a measure of relative performance. It asks how much better (or worse) did a player do compared to the full field of players competing at the same time on the same course under the same conditions?

It is a rule of statistics that in any given data set, about 70 percent of points will fall within one standard deviation of the average. As we apply standard deviation to this question, then, a decent degree of consistency would be reflected in only a small variation in the year-to-year standard deviation of a player’s performance.

In contrast, standard deviations above 1.0 would suggest that most players’ performances – at least 70 percent – vary pretty widely despite the fact that they are playing the same courses and probably under similar conditions. We could define such results as suspiciously arbitrary.

The second term requiring some definition is “absolute value.” When a statistician talks about absolute value, all he or she is doing is removing the minus signs from the data. This is a big deal in the process of answering our question because player performance from year to year may rise or fall. We do not care about the direction of that player’s movement…we are merely interested in the extent of the movement.

Whether the year-to-year change is from -1 to +1 standard deviations or its opposite, the operative total for our purposes is 2.

Sorry about the math interruption. Back to our 95 players. How did they do?

In a word, they did arbitrary. More than four in 10 – 42 percent, if you must know – saw their year-to-year performance at the same event change by at least a full standard deviation. In the cases of more than a quarter, the year-to-year change exceeded 1.5 standard deviations.

In contrast, only 29 percent performed with a reasonable degree of consistency; that is, their performances changed by less than a half standard deviation.

The group average year-to-year change? It was 1.03 standard deviations. That’s the definition of arbitrary performance.

On an individual basis, the results of the first four PGA Tour events are littered with illustrations of this trait.

• In 2021, Patrick Reed won the Farmers with a score of 274. That translated to 2.48 standard deviations better than the field average. This week he tied for 46th at 283, a nine-stroke decline and 0.29 standard deviations worse than the field average. That’s a 2.77 change in the absolute value of the standard deviation of Reed’s play.
• Harris English won the 2021 Tournament of Champions at 267, 1.82 standard deviations better than the field. Early this month he placed 30th at 278, 11 strokes, and 0.81 standard deviations worse than the field average. That’s a 2.63 swing in the absolute value of English’s standard deviation.
• At the 2021 Farmers, Pat Perez had a rough time. He finished 69th at 292, 1.14 standard deviations worse than the field average. This past weekend, Perez tied for sixth at 275, 1.30 standard deviations better than the field. Same Torrey Pines courses, generally same Southern California conditions, but swings of 17 strokes and 2.44 standard deviations.
• At the 2021 Sony Open, Hideki Matsuyama tied for 19th with a score of 265. That worked out to 0.63 standard deviations better than the field average. A couple of weeks ago Matsuyama returned to Waialae and won in a playoff at 257, 2.57 standard deviations superior to the field.

The question has to be asked, if such seemingly arbitrary swings in performance are commonplace, what causes them?

The usual suspect, when such questions are asked, is the putter. After all, on a week-to-week basis putting tends to be the skill that dictates tournament outcomes.

The problem with that approach is that – despite its often determinative role week-to-week – over the course of a full season the putting stroke is the game’s most volatile aspect. In fact, you may be surprised to know that among 2021 PGA Tour winners the average season-end rank in Strokes Gained Putting was a decidedly unspectacular 58th.

Only four members of the season-long top 20 in putting actually won a tournament. Meanwhile, that same list of 2021 winners included seven guys who ranked below 100 on the season-ending putting list, among them U.S. Open champion Jon Rahm (106), PGA champion Phil Mickelson (144), and British Open champion Collin Morikawa (114).

I examined the week-to-week change in Strokes Gained data of 13 players who have competed in consecutive weeks so far this season. While the standard deviation of Strokes Gained Putting has indeed been volatile – averaging 1.11 – it turns out not to be the most arbitrary aspect.

That honor falls to one of the most statistically reliable indicators of performance, Strokes Gained Approaching the Green.  That standard deviation averaged out to 1.23, far higher than Strokes Gained Off The Tee (0.70) or Around the Green (0.96).

It looks, then, like the built-in arbitrary nature of golf flows from an unlikely source: a player’s iron game.