You would think playing with a five- or six-stroke lead entering the final round of a tournament would be pretty easy. You\u2019re playing extremely well, so just take advantage of that cushion to coast home and collect the winner\u2019s check, thank you very much. <\/p>\n
Watching Kyle Stanley and Spencer Levin the last two weeks, you would think playing with a five- or six-stroke lead is pretty hard. Stanley shot a 74 to cough up a five-stroke margin in San Diego and Levin a 76 to blow a six-stroke lead in Phoenix as Stanley bounced back with a victory. <\/p>\n
Is it really that difficult to nurture a large margin on a Sunday? I looked back at PGA Tour events from 2000 to the present to try to find an answer, and the results show that entering the final round with a large cushion is not as comfortable a situation as we might think. <\/p>\n
In that span there have been 71 occasions when a player led by four or more shots entering the final round, and on 14 of those the leader didn\u2019t win. Even the victories often turn into nail-biters: 11 big-leaders ended up winning by just one stroke and nine by two strokes. All three events that went to playoffs ended up with the 54-hole leader losing. Only 14 times did they finish with a larger victory margin than they entered the round with. <\/p>\n
Tiger Woods is an exception to this vulnerability. He had at least a four-stroke margin 12 times during this span, never lost, and increased his margin six times. Let\u2019s face it, Woods\u2019s record in this era has been pretty freakish. So it\u2019s instructive to take him out of the equation and see how mere mortals have done. <\/p>\n
That reduces the winning percentage to 45-for-59, with 10 of them winning by just one stroke. And they ended up with a larger margin at the end of the day only eight times (compared to Woods\u2019s six times out of 12). <\/p>\n
What\u2019s really striking is what happens to the leaders\u2019 scoring. These non-Woods leaders set a scorching pace through three rounds with a 65.88 scoring average. But they were over par 22 times in those 59 final rounds while shooting in the 60s only 16 times. Their scoring average was 71.14, or 5.26 strokes worse than they shot in the preceding rounds. (Woods\u2019s averages were 66.42 in the first three rounds and 68.92 in the final round for a difference of 2.50 strokes. The fact that he generally plays on tougher courses accounts for his higher average in the opening rounds and makes his final-round average impressive.) <\/p>\n
I was about to speculate on some possible causes for the final-round struggles of players with big leads\u2014maybe the relatively high scoring results from playing it safe, maybe they\u2019re too worried about how bad it will look if they give the lead away, maybe it\u2019s hard to recover once the lead does start slipping away. Then I decided to look at players holding leads of one to three strokes entering the final round\u2014and found that their scoring average in the final round isn\u2019t any better; in fact, it\u2019s a little worse. <\/p>\n
I may be burying the lead here, but the takeaway is how poorly leaders perform in the final round. Here\u2019s the startling fact: Players who enter Sunday with an outright lead post an average final-round scoring average that is worse than the median scoring average of PGA Tour players as a whole<\/em>. <\/p>\n For one- to three-stroke leads I used the period 2009-11, yielding a similar sample size to the big-margin leaders from 2000-present. The 85 outright leaders by one to three strokes shot an average of 66.80 in the first three rounds, and their average final-round score was 71.27. (Adding in leaders by four or more strokes in 2009-11, we get 102 outright leaders shooting an average of 66.74 in the first three rounds and 71.35 in the final round.)<\/p>\n The median scoring average for all PGA Tour regulars\u2014those who played a minimum of rounds to qualify for statistical rankings\u2014was 70.76 in 2009-11. So, with the tournament on the line, the final-round leaders played more than a half-stroke worse than a typical Tour player in a typical round and 4.61 strokes worse than they did in the preceding rounds. And since the subset of third-round leaders is undoubtedly a stronger group of players than the set of all Tour regulars, the leaders shot something like a full shot worse than their own scoring average in all rounds. <\/p>\n This raises a question. Is each round by a Tour player independent of all others, so that the expectation in any given round is an average performance, regardless of how he played in the previous round (or how he\u2019s played that week if we\u2019re talking about the final round)? Doesn\u2019t being \u201cin the groove\u201d count for anything? If it doesn\u2019t, this would largely account for the drop-off in performance. Further investigation is required; I\u2019ll look into this for my next post. <\/p>\n For now, let\u2019s assume that there\u2019s at least some carryover from playing well through three rounds, even if the effect is not as large as we intuitively think it is. In any case, third-round leaders actually perform worse<\/em> than their average, so what\u2019s up with that? <\/p>\n The concept of regression to the mean (or, more colloquially, \u201cthe law of averages\u201d) could come into play. Those grounded in statistics know that exceptionally-above-average performances are not sustainable in the long run. In the course of time, a player\u2019s performance will tend toward his baseline. This fits right in with the intuitive thinking that a player can\u2019t stay hot forever. So we tend to think that while the third-round leader is \u201cin the groove\u201d and should play well, we don\u2019t expect him to play quite as well as he did in the first three rounds. <\/p>\n This is consistent with what we see out of Tiger Woods, who, remember, was two-and-a-half strokes worse in the final round when he had a big lead but converted all of his opportunities, most of them pretty easily. <\/p>\n But the rest of the Tour is worse than average when they lead, which fits neither our expectations nor regression to the mean. Statistical regression is a long-term process, it doesn\u2019t mean that three exceptionally good rounds make a \u201cbalancing\u201d poor round more likely in the fourth round. <\/p>\n