Golf Analytics

How Golfers Win

Optimal start hole (24 for 1 playoff)

Many of you have probably seen there was a 24 man playoff for the 64th place in match play at the US Amateur. The USGA sent 6 foursomes off the 17th hole planning to alternate the 17th and 18th holes until one player prevailed. In the end, two of the 24 made birdie at the 17th and advanced to the 18th where one made triple and the other made bogey to win. In total, the playoff took 90 minutes to complete (26 player-holes were played).

During I suggested it would be an interesting exercise to find the optimal starting hole for the playoff. In the end, 26 individual holes were played in 90 minutes, but as I’ll find later the median expected holes played was 31 starting with the 17th and 35% of the time the playoff was expected to extend past the 18th hole.

To determine the optimal hole, I looked at three different outcome statistics:

  1. median holes played (counting each time a player played a hole as a hole played, the minimum is 24 if there is one winner after the first playoff hole)
  2. don’t return to the starting hole (at the least the playoff ends after two holes)
  3. stay under 50 holes played total

These are arbitrary and I’m sure the USGA’s decision was mainly made based on proximity to the warm-up areas and clubhouse.

I used the scoring stats for the 2010 US Open at Pebble Beach as a USGA event in summer more represents the conditions than a PGA Tour event in February. The US Am scoring is available here for anyone who wants to replicate this analysis. Just organize your CSV as hole_no, score_to_par, count where score_to_par shows -2 for eagle, -1 for birdie, and so on.

Results
Based on these results in terms of limiting holes played (lowest median value) the 5th, 12th, and 17th (all par 3s) stand-out. In the case of the 5th and 17th, the par 3 is followed by a par 5. The 6th hole at 38 median holes is the least optimal.

In terms of reducing chances of returning to the starting hole (finish in two or fewer playoff holes), the 5th, 12th, and 17th again triumph with about 64-65% chance of lasting only two holes. The combination of #18-#1 comes in last with only 41% ending in two or fewer playoff holes.

The least interesting outcome is avoiding playing more than 50 holes. If 26 holes actually took 1.5 hours, a reasonable guess is that 50 holes would have taken around 3 hours – finishing as the first round of 64 match was nearing the end of the front 9.

In those terms, starting at the 5th and 6th holes gives only a 90% chance of finishing in 50 or fewer holes played, while starting at the 17th and 18th holes yields a 99.5% chance of finishing in 50 or fewer holes played.

Based on that, starting at the 17th hole ranks as one of the clear optimal options, if not the most optimal! Kudos USGA. Kudos to you too if you can keep your solution under my absurd 313 lines.

Code
I’ve posted my very for loop heavy code below for anyone who wants to replicate this.



library(dplyr)
library(tidyr)
library(readr)

# bring in prepared CSV showing data in form hole_no, score_to_par, count

scoring_data <- read_csv("pebble-beach-scoring-2010.csv")

# players qualifying, (just one player advancing here) and field size (# in playoffs)

PQ <- 1
FIELD <- 24

# calculates percentages of birdie, par, bogey, etc.

setup_scoring %
  
  group_by(hole_no) %>%
  
  mutate(perc = count / sum(count)) %>%
  
  ungroup() %>%
  
  select(-count) %>%
  
  spread(score_to_par, perc) %>%
  
  gather(score_to_par, perc, -hole_no) %>%
  
  mutate(perc = ifelse(is.na(perc), 0, perc),
         score_to_par = as.numeric(score_to_par)) %>%
  
  spread(score_to_par, perc) %>%
  
  # we'll use a random function later on so define which parts of the 0 to 1 continuum reflects probability of birdie, par, etc.
  
  mutate(eagle = `-2`,
         birdie = `-1` + eagle,
         par = `0` + birdie,
         bogey = `1` + par,
         worse = 1 - bogey) %>%
  
  select(hole_no, eagle:worse)

# we now enter the for loop hacks zone
# create a data frame with a row for each hole_no and competitor (24 players)

competitors <- vector("list", FIELD)

for(p in 1:FIELD) {
  
  d %
    
    mutate(comp = p)
  
  competitors[[p]] <- d
  
}

competitors <- bind_rows(competitors)

# link consecutive holes including #18 to #1
# with some knowledge of realistic back to back holes you could expand to cover all options (for example #3 to #17 or #16 to #4)

two_holes <- vector("list", 18)

for(h in 1:18) {
  
  d %
    
    filter((hole_no == h | hole_no == h + 1) | (h == 18 & hole_no %in% c(1, 18)))
  
  #
  
  two_holes[[h]] %
    
    mutate(start_hole = h)
  
}

two_holes <- bind_rows(two_holes)

# run the main simulation for loop

tictoc::tic()

#

it <- 1000

holes_data <- vector("list", 18)

#

for(h in 1:18) {
  
  data %
    filter(start_hole == h)
  
  sim_data <- vector("list", it)
  
  for(i in 1:it) {
    
    # the logic here is that we're just simulating a single run of the first hole & removing anyone who does not earn the best score
    # we then filter the data for the next hole and continue on
    # this can be for looped as well
    
    first_hole %
      
      filter(hole_no == h) %>%
      
      mutate(s = runif(n(), min = 0, max = 1),
             
             s = ifelse(s < eagle, -2,
                        ifelse(s < birdie, -1,
                               ifelse(s < par, 0,
                                      ifelse(s %
      
      mutate(rk = rank(s, ties.method = "min")) %>%
      
      filter(rk == 1) %>%
      
      select(comp) %>%
      
      as.list() %>%
      .[[1]]
    
    #
    
    left_after_1 <- length(first_hole)
    
    #
    
    second_hole %
      
      filter(hole_no != h & comp %in% first_hole) %>%
      
      mutate(s = runif(n(), min = 0, max = 1),
             
             s = ifelse(s < eagle, -2,
                        ifelse(s < birdie, -1,
                               ifelse(s < par, 0,
                                      ifelse(s %
      
      mutate(rk = rank(s, ties.method = "min")) %>%
      
      filter(rk == 1) %>%
      
      select(comp) %>%
      
      as.list() %>%
      .[[1]]
    
    #
    
    left_after_2 <- length(second_hole)
    
    #
    
    third_hole %
      
      filter(hole_no == h & comp %in% second_hole) %>%
      
      mutate(s = runif(n(), min = 0, max = 1),
             
             s = ifelse(s < eagle, -2,
                        ifelse(s < birdie, -1,
                               ifelse(s < par, 0,
                                      ifelse(s %
      
      mutate(rk = rank(s, ties.method = "min")) %>%
      
      filter(rk == 1) %>%
      
      select(comp) %>%
      
      as.list() %>%
      .[[1]]
    
    #
    
    left_after_3 <- length(third_hole)
    
    #
    
    fourth_hole %
      
      filter(hole_no != h & comp %in% third_hole) %>%
      
      mutate(s = runif(n(), min = 0, max = 1),
             
             s = ifelse(s < eagle, -2,
                        ifelse(s < birdie, -1,
                               ifelse(s < par, 0,
                                      ifelse(s %
      
      mutate(rk = rank(s, ties.method = "min")) %>%
      
      filter(rk == 1) %>%
      
      select(comp) %>%
      
      as.list() %>%
      .[[1]]
    
    #
    
    left_after_4 <- length(fourth_hole)
    
    #
    
    fifth_hole %
      
      filter(hole_no == h & comp %in% fourth_hole) %>%
      
      mutate(s = runif(n(), min = 0, max = 1),
             
             s = ifelse(s < eagle, -2,
                        ifelse(s < birdie, -1,
                               ifelse(s < par, 0,
                                      ifelse(s %
      
      mutate(rk = rank(s, ties.method = "min")) %>%
      
      filter(rk == 1) %>%
      
      select(comp) %>%
      
      as.list() %>%
      .[[1]]
    
    #
    
    left_after_5 <- length(fifth_hole)
    
    #
    
    sixth_hole %
      
      filter(hole_no != h & comp %in% fifth_hole) %>%
      
      mutate(s = runif(n(), min = 0, max = 1),
             
             s = ifelse(s < eagle, -2,
                        ifelse(s < birdie, -1,
                               ifelse(s < par, 0,
                                      ifelse(s %
      
      mutate(rk = rank(s, ties.method = "min")) %>%
      
      filter(rk == 1) %>%
      
      select(comp) %>%
      
      as.list() %>%
      .[[1]]
    
    #
    
    left_after_6 <- length(sixth_hole)
    
    #
    
    results <- tibble::tibble(a1 = left_after_1,
                              a2 = left_after_2,
                              a3 = left_after_3,
                              a4 = left_after_4,
                              a5 = left_after_5,
                              a6 = left_after_6,
                              total = (24 + a1 + a2 + a3 + a4 + a5 + a6),
                              ends_by = ifelse(a1 == PQ, 1,
                                               ifelse(a2 == PQ, 2,
                                                      ifelse(a3 == PQ, 3,
                                                             ifelse(a4 == PQ, 4,
                                                                    ifelse(a5 == PQ, 5,
                                                                           ifelse(a6 == PQ, 6, 7)))))),
                              start_hole = h)
    
    sim_data[[i]] <- results
    
  }
  
  holes_data[[h]] <- bind_rows(sim_data)
  
}

#

results <- bind_rows(holes_data)

tictoc::toc()

# calculate results based on the starting hole

hole_results %
  
  group_by(start_hole) %>%
  
  summarize(median_holes = median(total),
         mean_holes = mean(total),
         
         ends_in_1 = mean(ends_by < 2),
         ends_in_2 = mean(ends_by < 3),
         ends_in_3 = mean(ends_by < 4),
         ends_in_4 = mean(ends_by < 5),
         
         fewer_31 = mean(total < 31),
         fewer_41 = mean(total < 41),
         fewer_51 = mean(total %
  
  ungroup()


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Measuring Consistency

Consistency is often talked about in golf – by golfers themselves, by the media, and by fans – but it’s one of those undefined words that can be used in any desired way to get your point across. What I’m going to talk about today is week-to-week consistency of performance.

First, we need to set a baseline for performance to compare a player’s week-by-week play too. Finishing top 10 in an event represents a very positive performance for a Tour average player, but much closer to expectations for world #1. At 15th Club we use Performance Index to benchmark what we expect in a particular week from each player. For example, this week at the WGC Bridgestone we expect Dustin Johnson and Justin Rose to be the best performers and Kevin Na to be close to the middle of the pack.

With Performance Index shown in strokes versus the field, that’s the metric of choice for measuring performance. The truly elite performances in the last two seasons have been events like Brooks Koepka’s first US Open, Hideki Matsuyama at the Bridgestone, and Molinari at Quicken Loans. These are in excess of 5+ strokes versus the field per round.

With measures of performance and expectation established, it’s as simple as measuring how each player at each event measures up over 2017 and 2018. For example, Dustin Johnson had a low of about -5 strokes versus expected per round at the 2017 Memorial and a high of about +3 strokes versus expected per round at the 2018 Tournament of Champions. On the graphs later, I’ve chosen to show this measure as strokes per two rounds to show two round and four round events on the same level.

Measured this way performance is skewed with a longer left tail – in other words a player’s poor events will be further from 0 than his best events. There could be many reasons for this from injury, the effects of pressure when playing well, the tee-time effect (players playing well on the weekend play in the typically tougher afternoon), less motivation if far from the lead, and other more esoteric reasons behind how performance is judged. The average event for top-level players is about -0.5 strokes versus expected per two rounds.

10th percentile performance is roughly -5 strokes versus expected per two rounds and 90th percentile performance is roughly +3 strokes versus expected per two rounds. An elite player with a 10th percentile performance will very likely miss the cut, while an average player with a 90th percentile performance will have a great chance at a top 20.

To measure consistency, I’m taking the average absolute difference between actual and expected performance (difference from zero) of every event a golfer has played since the start of 2017. These range from about 1.6 strokes versus expected per two rounds for the most consistent to 5.0 strokes versus expected per two rounds for the least consistent. In other words, if the expected score for the most consistent player is 140 over two rounds, on average the difference between their actual score and 140 will be 1.6 strokes better or worse.

More consistent players in 2017-18

Less consistent players over 2017-18

Both lists have a range of players, with the less consistent featuring some guys like Kaufman and Willett who have struggled over the last two years along with guys like Landry and Mitchell who have played well. Same for the consistent list, Casey is one of the best in the world, while most are in the 100th to 250th best in the world zone.

Along with actually measuring consistency, it’s critical to discuss why it matters. Elite players whose games are very consistent will give themselves fewer opportunities to win than otherwise expected. At the same time, weaker players whose games are very inconsistent will win and be in contention often, but will also no-show most weeks. In a world where everything from your media/fan legacy to World Rankings to prize money is based largely on heavily rewarding victories, both of these facts skew how players are viewed.

I’ll close with a few notable players:

Justin Rose
Justin Rose-consistencyRose has managed to avoid any genuinely poor events with his worst being a T63 at the Bridgestone last year where he was 8 back after 36 holes and had a lackluster weekend. On the other hand, he’s had eight extreme over-performing events of which he’s won four and lost in a playoff in another.

Paul Casey
Paul Casey-consistency
An average player would be expected to have 7 extreme good or poor events in 37 events, but Casey has had only three – two of them being his only missed cuts and the third being his 6th at the 2017 Masters. Casey ranks as one of the best performing golfers in the world over 2017-18, but has struggled to generate the kind of winning performances his peers do.

Jon Rahm
Jon Rahm-consistency
Rahm has a reputation as a volatile player and that’s borne out here. He’s had more extreme events than expected, but mostly skewed towards the positive. He has made his poor events notable with the 2017 & 2018 US Opens and nearly the 2018 Open appearing among his low-lights.

My Favorite Pieces

I haven’t written anything for public consumption since July so I have collected a list of my favorite pieces of the last two years across 15th Club, Golf.com, NoLayingUp, SBNation, and this blog. Hopefully they will provide some insight or inspiration as we enter the new golf season.

15th Club

Review of 2016 To Date: Performance vs Results (url)

The PGA Championship Is All About Distance (url)

Who Is Best At Links Golf (url)

Can A Masters Rookie Win? (url) – wait for Jon Rahm in 2017

Golf.com

Masters Round Recaps

Round 1: Iron play fueled Spieth’s Round 1 (url)

Round 2: Rory finally conquering Augusta’s par 5s (url)

Round 3: Spieth misses the one critical fairway (url)

Round 4: Willett excelled across the board (url)

Other Pieces

The Masters Real Big Three (url)

Placing Golf’s Youth Movement in Context (url)

Spieth’s 2015 & Expected Wins (url)

Four Golfers Primed for Wins in 2015-16 (url) – a tidy 3/4

Accuracy Just Isn’t Important Anymore (url)

The European Tour Is Losing Talent (url) – a slight uptick in 2016!

Sergio Can’t Close (url)

SBNation

The Top Masters Chokes & Clutch Rounds (url)

NoLayingUp

Why Rickie Fowler Doesn’t Win More (url)

My Blog

Spieth’s Driving Propels Him to the Top (url)

Stenson Loves His 3 Wood Too Much (url) – somehow my most viewed post

Don’t Trust a Hot Putter (url)

Day Plays to win at Torrey Pines (url)

The Signal in First Round Performance (url)

ANA Inspiration Preview (2016)

The 34th edition of the ANA Inspiration – the renamed first major championship of the golf season – starts Thursday at the Mission Hills Country Club’s Tournament Course. Recent winners have included most of the top women in the game – Lexi Thompson (2014), Inbee Park (2013), and Stacy Lewis (2011). Notably, however, current women’s #1 Lydia Ko has stumbled to finishes of T25, T29, and T51 in her first three trips to the event.

Favorites

Lydia Ko is the betting favorite at 4/1 and after answering questions about her ability to win majors by edging out Lexi Thompson at the Evian Masters last year there shouldn’t be any questions about her holding that spot this week. As a bonus, she enters off a four stroke win at the Kia Classic last week.

Right now the gap between Ko and the rest of the field is immense. By my predictive ratings, Ko has never enjoyed the advantage (0.76 strokes per round) that she enjoys right now over the 2nd ranked Inbee Park. Since a four tournament cold spell last spring, Ko has played dominant golf, beating the LPGA field by over 3.5 strokes per round (about the level of peak Tiger Woods). While she hasn’t reached Tiger’s level of dominance over the long haul, Ko is the clear favorite this week despite the lack of results here.

Lydia Ko versus No 2

The next favorites are veterans and winners of this event: Inbee Park (8/1) and Stacy Lewis (11/1). Park has dealt with injuries this spring, but may have found some form at the last moment – finishing runner-up to Ko at the Kia Classic this week. Her game was good enough to win five titles last year including a 1st-T3-1st run at the Women’s PGA, Women’s US Open, and Women’s British Open last summer.

The big story with Lewis has to be her continued quest to finally win another tournament. Despite ranking as one of the three best in the game, her last win was in June of 2014. Over that period she’s finished second nine times – a streak that puts Henrik Stenson’s winning woes to shame. Lewis’s problem has been not generating the kind of truly elite events that win tournaments. She had four events where she’s gained around 4.0 strokes per round on the field just since last summer, but none at the 4.5 strokes per round level that wins the average LPGA Tour event. We know she’s capable of that level though as she hit 4.5 strokes per round or better in five events in 2014.

Big hitters Lexi Thompson and Sei-young Kim sit next in the odds sheet. Both have massive wins on the year; Lexi in Thailand by six strokes and Kim at the Founders Cup in Arizona by five. Lexi won here in 2014 and Kim led for two rounds last year before fading with a final round 75.

Dark Horses

Sung Hyun Park is one to watch after last week. Park is young Korean woman who has played great golf in all three LPGA starts in the last year. She has shown well on the Korean LPGA (the second best women’s tour and a steady source of top golfers) in recent years, finishing between a pair of major championship winners (Hyo-Joo Kim and In Gee Chun) in scoring average in 2013 and 2014 before winning four times in 2015. Park has delayed her arrival on the LPGA full-time, but may have to accelerate her time table with a high finish this week.

Further down the odds sheet, my numbers love the consistent recent play of Minjee Lee. Lee showed great length off the tee last year, winning once and finishing in the top 20 on the money list as a rookie.

Recent Play

Here are scoring average leaders (adjusted for the field) since the start of 2016 (LPGA rounds only)

Pre ANA Inspiration Performance

Ha Na Jang’s run to start the year has her as high as #3 in my predictive ratings (though she would be dragged down slightly based on a so-so 2014 season on the Korean LPGA Tour).

Historical Performance at Mission Hills

And these are the historical scoring averages versus expectations (so performance compared to a weighted scoring average in the events leading up to each season’s event).

ANA Inspiration History

Pettersen is a two time major champion and has five top fives in ten trips to this event. Her and Anna Nordqvist stand out as top golfers here who haven’t won.

 

Presidents Cup Picks

With the automatic qualifiers set and the captains ready to fill-out their teams tonight, I thought I’d break-down the possible captains picks for both sides. While obviously not as prestigious as the Ryder Cup, the Presidents Cup still is one of the few opportunities to observe and comment on team construction in golf. The main things I’m looking for when evaluating golfers in this team setting is simply overall level of play. Match play is different in a number of ways from stroke play tournaments, but one factor that’s often overlooked is that to win a stroke play tournament golfers have to perform much better than normal. To win, you have to be capable of having everything click one weekend and be able to handle pressure of closing. However, to win a match play match, it’s often enough to just play consistent good golf. This factors into the selection process; captains should be much more interested in looking at the full view of how each golfer has performed over the season (good scoring average, few missed cuts, top 10s, etc.), rather than focusing on tournaments won or performance at major championships.

United States Team

The top eight Americans in adjusted scoring average over the last 52 weeks qualified for the Presidents Cup yesterday (Spieth, Furyk, D.Johnson, Bubba, Kuchar, Reed, Fowler, and Z.Johnson). Jimmy Walker (20th best) and Chris Kirk (37th best) joined them. Walker’s been playing poorly for months, but managed to finish 3rd in the standings on the strength of his five Tour wins during the qualification period. Kirk earned the last spot despite missing the summer due to injury; he’s won three times during the past two years.

To fill out the team, Brooks Koepka and Brandt Snedeker are the next two best Americans in adjusted scoring average over the last year. Despite playing like one of the ten best Americans, Koepka finished only 20th in qualifying because the PGA Tour has chosen to ignore results from non-PGA Tour events. While splitting time on the European Tour in 2014, Koepka racked up a win, two 3rds, and another top 10. Koepka is a pretty obvious selection for me. Not only has his performance warranted the pick, but his bomber style is perfectly suited for the four-ball portion and it will be good to get him acclimated to the team experience ahead of a likely berth on next year’s Ryder Cup squad.

Snedeker narrowly missed qualifying on points – finishing 12th largely because of his struggles in 2014. However, if you look at his last five seasons below, it’s pretty obvious that his struggles with the putter caused his down year. His other four seasons have all been played at a top 25 level. With his putting squared away this year, I think he’s definitely the next best option beyond Koepka. While guys like Robert Streb may have done more this year and Phil Mickelson has the name recognition, Snedeker’s combination of good play this season and a track record of past great seasons stands out.

Strokes gained by Snedeker 2011-15For me, selecting Phil Mickelson would be ridiculous. His overall record of performance is no better over the past season or two than a dozen other Americans receiving no consideration like Kevin Na or Ryan Palmer. Even worse, he’s only had two great performances (2014 PGA Championship and 2015 Masters) since winning The Open in 2013. This pick would be on legacy only, but it’s not like Mickelson has a Poulter-esque team match play record to lean back on. Mickelson’s won just 50% of the possible points in his Ryder Cup and Presidents Cup career. I understand there’s pressure to pick Phil (he hasn’t missed a US team event since 1993), but judging him objectively he doesn’t come close to deserving a spot.

Whether Jay Haas would pick Bill Haas has been the big story recently, with Bill having several chances to earn his way on from the 11th spot in the standings. Unfortunately for Jay, Bill didn’t play anywhere near well enough in his last two starts. For me, Bill Haas isn’t deserving of a pick. You won’t find anyone who advocated more strenuously for Bill’s inclusion in last year’s Ryder Cup team. His performance last year was clearly great; I had him ranked as one of the twenty best golfers in the world a year ago. However, despite a win in 2015, his season just hasn’t been as good as 2014 judged by overall scoring average. This pick would be a mix of nepotism and a make-up call for Webb Simpson’s bamboozling of Tom Watson last year. Neither is a good look for Jay Haas with plenty of other candidates who have done as much or more than Haas this year.

Robert Streb was probably in the conversation a few weeks ago because his overall play certainly deserved a selection, but he was probably always going to have to earn his way on this team and he didn’t.

I’ve seen Billy Horschel’s name mentioned, often accompanied by a list of intangible factors backing his selection. The problem is that his overall level of play hasn’t been good enough to earn his way on these US teams. He got hot and won the FedEx Cup last year, but he has seven top 10s in 54 events over the 2013-14 and 2014-15 seasons and his adjusted scoring average ranks 35th among Americans in the last 52 weeks. Those results are just too erratic to know what you’re going to get in Korea.

Picks: Brooks Koepka and Brandt Snedeker

International Team

The International Team qualified their five clearly superior golfers – Day, Matsuyama, Oosthuizen, Grace, and Scott – easily. Beyond those five, the performances of the remaining five qualifiers have fluctuated dramatically in the past year. Charl Schwartzel would’ve been one of those clearly superior golfers in the past, but his form has been wildly inconsistent over the past two years. Anirban Lahiri qualified, deservingly; he’s had a handful of truly stand-out tournaments mixed with a lot of crap this year. Danny Lee’s been one of the break-out guys on Tour this summer. Marc Leishman’s been a steady above-average Tour pro over his career. Thongchai Jaidee has mostly busted in his US events this year, but has some high finishes elsewhere.

I think as many as half a dozen golfers are solid contenders for picks, but I’d pick two guys who are off the radar for most PGA Tour fans – Ben An and Emiliano Grillo. Both are European Tour based and very young, but they rank 6th and 7th in adjusted scoring average over the past year. An was tearing up the European Tour earlier this year, winning their flagship event at the BMW PGA Championship in May. His world ranking is depressed from where it should be because he was on the European minor league tour last season where it’s difficult to earn points even for high finishes. Grillo performed well in two US appearances this summer (Barbasol and Canadian). He’s been very consistent (only three missed cuts in the last year), which I’d prefer over more boom and bust golfers if I were captain.

The big omission here is probably Steven Bowditch. He just missed qualifying in 11th place and has two PGA Tour wins in the last two years, so why isn’t he an obvious pick? In short, he’s just way too inconsistent. After winning the Texas Open in 2014, he missed six of his next eights cuts. This year, he started out missing seven of nine cuts. He’s played better this summer, but he’s alternated good tournaments with bad for the last two months. In short, you don’t know whether you’re going to get a golfer who at his best deserves a spot on the team, but at his worst is a 4&3 loss waiting to happen.

Picks: Emiliano Grillo and Ben An

Expected Tournament Wins

I first discussed the concept of expected wins in my March article on Rickie Fowler over at NoLayingUp. Basically, I wanted to look at how often a certain level of performance on the PGA Tour results in a win. This way, there’s some sort of context neutral benchmark when we talk about why certain players are winning more or less than someone thinks they should. Rickie Fowler was the perfect introduction to this topic; he had been slammed for several years for only winning once on Tour, but when viewed through the lens of expected wins, Fowler had played some really good tournaments that would’ve normally resulted in wins, but others beat him. Of course, Fowler has gone on to win two high profile tournaments already this season

Calculation of Expected Wins

I gathered all PGA Tour tournaments (2010 to present) from the Official World Golf Rankings site, noting the winners and each player’s performance in strokes versus the field (also adjusted for strength of field so the US Open credits players for a harder field and Mayakoba debits their performance). I did the same for all European Tour tournaments over the same time period. I discarded all tournaments that did not reach four rounds and all players who missed the cut or withdrew.

I then performed a logistic regression of performance in strokes per round on the binomial variable of whether the player won the tournament or not. This produced the curves below for the PGA Tour and European Tour. I should note, I included all tournaments in each Tour’s data regardless of whether they were co-sponsored, alternate field, limited field, invitationals, or majors (majors and WGCs were included only in the PGA Tour dataset). However, this is supposed to measure how often a player should win in a typical event. Obviously the listed figure for win expectancy will be lower for majors and higher for alternate field or limited field events like the Tournament of Champions.

PGA Tour results

PGA_Tour_Win_ExpectancyIn a typical PGA Tour event, it’s extremely rare to win with a performance less than 3.0 strokes per round better than the field. However, increase to 4.0 strokes and a player is expected to win just over half of the time, while victory is nearly guaranteed at 5.0 strokes per round better than the field. In fact, only Louis Oosthuizen at the 2012 Deutsche Bank has exceeded 5.0 strokes per round without winning.

The best performance in a tournament between 2010 and 2015 was Rory McIlroy’s eight shot victory in the 2011 US Open where he beat the field by 5.7 strokes per round.

European Tour results

European_Tour_win_expectancyThe curve for the European Tour is broadly similar, but the 50/50 point is reached earlier – around 3.5 strokes per round – indicating the average European Tour event is won with a slightly less impressive performance. In fact, at around 4.0 strokes per round a player would be expected to win a typical European Tour event about 80% of the time versus 50% in a typical PGA Tour event.

The best European Tour tournament between 2010 and 2015 was Sergio Garcia’s eleven shot win at the 2011 Castello Masters.

Best Results from 2010 to 2015

bestperformances20102015Only PGA Tour or European Tour events from 2010 to present.

Applying to Rickie Fowler…again

What’s interesting about Rickie Fowler’s success this season is that both of his wins have come in big events with quality fields, but have required less impressive performances than normal. His Players Championship victory was actually slightly less impressive than his 2012 loss to Matt Kuchar, while his Scottish Open performance earlier this month rarely results in victory – even on the European Tour. In other words, after getting the short end of the results for the first few years of his career, Rickie’s gotten some good luck and has taken advantage of both opportunities to win this season. Below are Rickie’s ten best performances of 2010-15.

rickiefowlerperformances

British Open at Old Course Preview – 2015

Advantage of Long Hitters:
The Old Course is popularly seen as a strong spot for the guys who hit it longest, and the results from 2005 and 2010 bear that out. Every five yards greater than the field a player hit their average drive in all events was worth 0.15 strokes/round in 2005 and 0.30 strokes/round in 2010 beyond their normal level of performance. In other words, long hitters had a sizable advantage in each of the last two Opens contested at the Old Course.

As to why that advantage persists, longer driving distance is correlated with larger absolute misses off the tee. On regular courses, the danger off the tee increases as the miss gets larger as bunkers, rough, trees, etc. are brought further into play. Also, the danger is typically equally distributed with rough/trees/etc left and right. If you look at the Old Course (especially holes from #9 onward) there are pot bunkers spread across normal driving zones. A drive that misses slightly could catch one of the penal bunkers, while another that misses by more ends up in fine shape. Also, take a look at the danger off the tee; on a half-dozen or more holes it’s solely to the right. Certainly a left miss leaves a worse angle, but there’s no way that’s equivalent in penalty to the rough or bunkers right. In addition, holes like #1, #7, and #18 feature little danger off the tee at all. Distance also gives the ability to hit over bunkers on a number of holes.

The Old Course is also deceptively short. Although it’s listed at 7300 yards – roughly average for a PGA Tour course – it’s almost 300 yards shorter than you would expect if each hole was as long as its average par is on a PGA Tour course because of the unique fourteen par 4 layout. This would place it as one of the very shortest on the PGA Tour alongside Pebble Beach and others.

Par 4 Advantage:
That unique layout also gives an advantage to players who struggle with par 3s or par 5s. A great example is Hunter Mahan; Mahan has been awful on par 3s in recent seasons, a symptom of his overall struggles with his iron play. However, his great driving and putting has bailed him out and allowed him to score on the par 4s at a high level. This week sees three additional par 4s and two less par 3s than normal. Ian Poulter, Ryan Palmer, and Lee Westwood are others should see an advantage, while Dustin Johnson is the one notable who has really killed it on par 3/5s.

Travel and the John Deere/Scottish Open Debate:
A lot has been made over Jordan Spieth’s decision to play at (and win) the John Deere last season. Typically that event is skipped by most top players to allow them to either compete in the Scottish Open (as about a dozen or two PGA Tour players chose) or travel over to the UK at their leisure. I wrote up a piece on the impact of playing in the Scottish versus John Deere last year and I largely stand by the conclusions. US based players all suffer to some degree coming over – probably because of a mixture of the time zone and links golf – but players who compete in the John Deere under-perform their normal performance level significantly more than players who chose to play the Scottish Open.

As to whether this affects Spieth, obviously the most important factors affecting his performance this week will be random fluctuation in talent and the weather. I expect his play to be slightly degraded this week because he played the John Deere last week, but it’s far more likely catching the bad end of the draw weather-wise or missing a few putts will cost him the Claret Jug rather than the impact of travel/time change.

Links Experience/Performance:
A lot is made of past performance on links courses, but it’s important to remember just how few true links events are played each year. Since 2008, the Irish Open has been contested on links land three times and the Scottish Open five times. Add to that the once yearly playing of the British Open and the Alfred Dunhill Links and you get 24 events that were indisputably links golf. Perhaps a more liberal definition would include a course like Chambers Bay or Whistling Straits. Perhaps a few European Tour events played at seaside venues could be included as well, but overall you’re looking at 3-4 events per season.

Several players do stand out for their links performances though. All numbers here are relative to a normal performance level baseline of rounds played prior to the events in question. Of guys with at least 40 links rounds since 2008, Marc Warren, Shane Lowry, and Darren Clarke have fared best. Expanding to greater than 24 rounds, Rickie Fowler, Adam Scott, and Stewart Cink also emerge. No shockers there as all have contended for or won major links events. Major names who have struggled include Joost Luiten, Matt Kuchar, and Ian Poulter. Ideally we would look at more detailed markers of links success (creativity around the greens?, lag putting?, low approach shots?), but this general performance data will have to suffice for these purposes.

Spieth’s Driving Propels Him to the Top

With Jordan Spieth’s massive success so far this season – three wins, including the first two majors of the season – it’s become common to attribute his success to either his fantastic putting (especially from long range) or his, in general, well-rounded overall game. This phenomenon represents a continuation of Spieth being cast as a generic blank canvas onto which fans can paint any picture they want. But more importantly, it’s incorrect. Not only is Spieth a fantastic putter, but his elite driving ability has fueled his greatness this season.

The bomb and gauge mentality has so infused the PGA Tour in the past decades that driving ability is almost completely conflated with distance off the tee. Sure there’s some lip service paid to the idea that accuracy is important, but when we talk about the best drivers in the game we talk about the longest guys – Rory, DJ, Bubba, etc. However, along with the guys who bomb it out there 310 yards, there’s another more rare category of driving stars: those who can hit for average or slightly better length while hitting it extremely straight. In this category, you normally see Henrik Stenson, Billy Horschel, and Hunter Mahan – guys who hit it longer than average, while keeping it play more than almost anyone else on Tour.

stenson_mahan_spiethIn 2013, Jordan Spieth was also in this group of guys. He drove the ball slightly longer than average (283 yards vs. 280 average), while hitting 68% of his fairways (16th best on Tour). My estimate of his driving performance shows him gaining strokes at a top 10 rate – similar to Mahan and Stenson. Things went sour for him in 2014; despite an overall game that was buoyed to a top 25 level by an elite short-game and strong putting, Spieth slipped well down the list in terms of driving performance. He again hit it about 3 yards further than average, but he was spraying drives everywhere – hitting only 58% of his fairways. This put him in trouble often, and led him to rank in the 90s in terms of his strokes gained on drives.

This year, it’s clear that he’s hitting his drives at or better than the level we saw in 2013, but not because he’s added much distance to his game. He’s still out-hitting the average pro by 3-5 yards, just like in 2013 and 2014. However, he’s doing a much better job of keeping his drives in play. He’s hitting 63% of his fairways and he’s also greatly reduced his average miss using driver – indicating he’s hitting that club much straighter. And it’s clearly paying off on the course; he’s gaining about 0.04 strokes/drive more with his driver this year than last year. To put that in context, it’s increasing his chance of birdie by 4% or reducing his chance of bogey by 4%.

Spieth with DriverWhere he’s really seeing gains is in his par 5 scoring. Last year, he made birdie or better on par 5s 45% of the time. The Tour’s stats had him going for the green in two on half his opportunities (roughly average for the Tour). He putted well overall on par 5s, gaining about 0.01 strokes/non-gimme putt. This year, he’s making birdie or better on par 5s 47% of the time, despite really struggling with the putter (-0.02 strokes/non-gimme putt). So he’s scoring better on the par 5s, despite a cold putter. Most of that can be attributed to him upping his going for the green rate to 58%.

That’s where the impact of his re-found accuracy really shows through. Spieth’s decision making on par 5 second shots mirrors an average Tour player; ie, he’ll normally go for it in the fairway, but lay-up in the rough. His ability to be aggressive on par 5s is completely determined by how well he’s hitting it off the tee. The bombers on Tour can be more aggressive from the rough because they’re facing shorter shots. Last year, when Spieth wasn’t consistently hitting fairways, he wasn’t able to keep up with the bombers who were going for greens. This year, he’s at least able to compete with those guys despite not hitting it anywhere near their distance.

With Spieth and Rory McIlroy holding all four major trophies and being in their twenties, it seems almost certain that the game will be centered around them for the next decade and a half. What’s great about their coming rivalry is the contrast in their games. The battles between Tiger, Phil, and Vijay Singh in the 2000s were ones of pure power – each had great distance off the tee, allowing them to play aggressively. Rory mirrors this approach, gaining most of his advantage off the tee. On the other hand, it’s Spieth’s accuracy off the tee that’s fueling his success, along with a reliable short game and one of the top putting strokes on Tour.

Henrik Stenson Loves His 3 Wood Too Much

Henrik Stenson is an anomaly, and not just because he’s one of the best golfers on the planet. Of 225 pros who have appeared regularly in PGA Tour events in 2014 & 2015, Stenson has used something less than driver on his tee shots the 2nd most. Across the Tour, golfers use driver on approximately 72% of par 4/5 holes. For longer hitters the percentage falls to around 64% and for shorter hitters the percentage rises to around 81%. Stenson, however, uses driver only 33% of the time. Despite this, Stenson ranks around 25th on Tour in Strokes Gained: Driving over the past two seasons. However, based on how well he hits driver, he could rank among the truly elite of the sport off the tee if he would only use the club more often

To establish how much of an anomaly Stenson’s driver usage is, take a look at the graph below. I have plotted the driving distance and driving accuracy for all regular Tour golfers when using driver only. Driving distance is shown as yards and accuracy as degrees off-line from center (in other words, less means straighter drives). The color indicates the percentage of holes where each golfer used driver – with blue indicating most often and orange indicating least often. The further towards the upper right corner a golfer is, the better his drives. Unsurprisingly, Rory McIlroy, Bubba Watson, and Adam Scott are in that range, while a little further down are the long, super-accurate guys like Hideki Matsuyama. Henrik Stenson (the dark orange dot) is directly between those two groups – meaning he’s both very long (11th longest) and accurate (64th best) with driver. Performance with Driver You’ll notice that of the golfers near Stenson, all of them are hitting driver at least 62% of the time. They recognize that their length provides a huge advantage and their accuracy allows them to keep it in play most of the time when they do use driver. However, Stenson only uses driver 33% of the time, much less often than even the wildest guys like Aaron Baddeley and John Daly.

Below I’ve charted Stenson’s tee shot strategy (driver vs. fairway wood) based on how often the field is hitting driver (>67%, 33-67%, <33% of the time). You can see on holes where more than two thirds of the field hits driver, Stenson performs 0.06 strokes better when he uses driver. On these holes where the field sees an advantage to hitting driver, but Stenson plays very conservative golf, using driver only 41% of the time. Stenson only makes the aggressive play – using driver when the field mostly lays-up – on 8 of 129 holes (6%). Usage by Field Average I compared the Strokes Gained with driver vs. fairway wood for my sample and the gap for Stenson between driver and fairway wood was the twelfth largest (of 225 golfers). In other words, when he chooses fairway wood over driver, he loses the twelfth most strokes on Tour. The top ten on this list uses driver on 69% of holes; Stenson on only 33% of holes. Largest Gaps Driver vs Fway Wd I came up with three reasonable hypotheses for why Stenson could be making the right play by hitting so few drivers. I’ll address them one by one.

1. The course dictated lay-ups: In the fifteen Shot Link events Stenson has played since the start of 2014, the field has used driver on between 61% (Valspar 2015) and 87% (WGC-Bridgestone 2014) of holes. The average is 71% on the courses he has played compared to 72% on an average Tour course. The courses he has played do not explain why he doesn’t use driver more often.

2. Stenson actually hits fairway woods better than driver: Stenson does actually hit his fairway woods better than almost every other golfer on Tour. He has ranked 14th in distance and 15th in accuracy with a fairway wood (compared to everyone else with a fairway wood) over 2014-15, so it is clearly the strength that everyone thinks it is. However, as stated above, he has ranked 11th in distance and 64th in accuracy with driver, so his driver is similarly strong. It’s not as if he’s wild with the driver. In fact, Stenson hits driver well enough that he gains the 4th most strokes on the field when he uses driver (only McIlroy, Dustin Johnson, and Bubba rank ahead of him). Stenson performs well with fairway wood also, but gains only the 42nd most strokes with a fairway wood because he lays-up so often on holes where most other golfers are hitting driver. His ~278 yard drives with a fairway wood are being compared to 290 yard drives by the rest of the field. In total, he gains about 0.07 strokes more per drive with driver compared to fairway wood.

Performance by Club

3. Stenson’s game requires him to hit fairways, so he plays conservatively: Most Tour pros (~80%) are more accurate when hitting fairway wood than driver. In general, this equates to hitting 67% of fairways with fairway wood and 57% with driver. For Henrik Stenson, the gap is slightly larger – 72% of fairways with fairway wood and 55% with driver. If Stenson is hitting fairway wood in order to hit more fairways, he’s achieving that goal. And that could be valuable for Stenson because he has one of the largest gaps between his approach shot play from the fairway versus from the rough. Golfer ability from the fairway versus rough varies like any other skill; those who play best from the fairway gain around 0.07 strokes on fairway shots versus rough shots and vice-versa for those who play best from the rough. For a pro that falls on the ‘better from the fairway’ side of the spectrum, prioritizing hitting fairways makes some sense because each extra fairway hit leverages his skill at playing from the fairway. Stenson falls into this category – gaining 0.07 strokes on the field on approach shots from the fairway and losing -0.01 strokes on approach shots from the rough.

So if Stenson is hitting a lot of fairway woods because he prioritizes hitting fairways, is he making the right play? In short, no. Using a fairway wood only increases his odds of hitting the fairway by 17%. Multiply that 17% by the 0.08 strokes better he performs on approach shots from the fairway and he gains only 0.01 strokes worth of value per hole from hitting more fairways off of lay-ups. Contrast that with the value he loses because he is hitting fairway wood shorter than driver. He loses 0.07 strokes for each fairway wood he hits, all because he is losing an average of 28 yards of distance when using the shorter club. He hits about four more fairway woods than the average bomber each round, meaning he is losing a quarter of a stroke just because of his club selection.

Stenson is already one of the best in the world, but he has the real opportunity to change up his strategy and gain a huge amount of on-course value. I quoted a figure of 0.25 strokes gained if he adopts a similar club selection strategy to other bombers like Adam Scott. Such a gain would jump him from 24th best on Drives to 5th best. Playing more aggressively in situations where the field is hitting driver and he is currently hitting fairway wood would allow him to better exploit his ridiculous length and accuracy with driver, gaining that quarter of a stroke on the field and drawing closer to McIlroy and Spieth’s level at the top of the game.


All Henrik Stenson drives (2014-15) are linked here.

Quick Masters Thoughts

This is just a quick run-through of my thoughts on some of the big names and a few others for this week.

Rory McIlroy
It seems like there’s some trepidation over installing McIlroy as the favorite this week, despite him playing clearly the best golf of anyone in the world for the past year. I’ve seen some insisting that Bubba is the favorite – two Green Jackets in three years and all – while others think Jordan Spieth’s success here last year and hot run over the past month plus means he’s the favorite. Sport fans struggle with perspective, especially around the biggest stars, and in the case of McIlroy and the Masters, perspective is critical.

It’s true that his PGA Tour play this season has been spotty (MC-9th-11th in three events in Florida), but his missed cut came on a 3 wood heavy course that he’s generally struggled at over his career. Rory relies so much on the advantage of blowing his driver 20 yards past the field that when he’s forced to ease up off the tee he’s a different golfer. Besides that MC, Rory has finished 2nd at a strong European Tour event, won another strong European Tour event, and then finished around 10th at two strong PGA Tour events. The quality of his golf in 2015 has been the same as in 2014.

As for his Masters history, it’s mostly mediocre for a player of his caliber, but this is a course which clearly favors guys who can bomb it around and feast on par 5s. However, during his career at Augusta National McIlroy has suffered from an inability to score on the par 5s (4.76 average compared to 4.70 for the field) and a tendency towards big numbers (3.5% double/triple bogey rate compared to 2.5% for the field). Basically, if you think McIlroy will struggle here you believe that he’s unable to score on the par 5s here (with that huge, high draw I think that’s unlikely) and uniquely snake-bitten in terms of posting big numbers (rather than the victim of bad luck).

Adam Scott
Perhaps because of his sparse schedule, Adam Scott hasn’t gotten enough credit for the three year run he put together between 2012 and 2014: 48 official Tour events, 47 made cuts, 21 top 10s, and three victories including the 2013 Masters. Perhaps some criticism of his lack of wins is warranted, but he plays at events with mostly very strong fields and he’s taken a very solid 6% of his events. Until McIlroy hit the gas last summer, there was definitely a debate over whether he or Scott was the best in the world. Obviously not now, but in my estimation Adam Scott enters this year’s Masters Tournament as the solid second best in the field.

Scott has great course history here, which is to be expected with his distance and ability to hit his irons so well, and he’s entering with his tee to green game looking really sharp. His performance on the Florida swing was consistently elite tee to green (+1.5, +1.7, +1.7 strokes gained/round against strong fields), but he struggled while trying out the short putter and that absolutely torpedoed his overall results in Tampa and Orlando. He’s back to the anchored long putter this week and if he can just be his normal mediocre self on the greens, he’ll be in line for a high finish.

Phil Mickelson
Phil has owned Augusta National to the tune of three wins and a yearly tradition of top finishes, but the results the past couple years just haven’t been there. What’s illuminating is that when you plot Phil’s average driving distance alongside his Masters performances, there’s a pretty obvious trend. Prior to 2012, his worst finish in driving distance was 35th. During this period his combination of power off the tee, great irons/wedges, and a really strong short game made him one of the best in the world (and made up for the fact he had no clue where his tee shots were going). In 2012 he slipped to 53rd on Tour in driving distance, then 93rd and 70th the next two years.

Mickelson Driving Distance Masters Play

Along with that distance decline, his Masters results in 2013 and 2014 were both his worst since missing the cut in 1997. Phil went from scoring an average of 4.36 on the par 5s between 2008-12 to 4.70 in 2013-14. Now, this year it looks like he’s got some of his power back (driving distance and club head speed are both up), so there’s definitely some hope he’ll return to former levels of success here.

Jordan Spieth
Spieth’s run over the past two months has been great to watch and he’s fully recovered from his struggles off the tee in the second half of last season. What is interesting is how he’s changed his game even from his rookie year in 2013. Spieth was one of the most accurate guys on Tour that season, with above-average distance. Last year, his driving numbers weren’t nearly as strong and he spent the last half of the season spraying his drives off the tee, making a bid for the Tour Sauce Hall of Fame. This year he’s gotten significantly longer (~5 yards), and he’s kept his tee shots in play like in his rookie season. That’s driven his long game to elite levels.

He’s riding a bit of a lucky putter right now so it’s important to view his recent play in a slightly skeptical light. But he is one of the top 10-15 putters on Tour, so it’s not like he’s going to fall off much.

Keegan Bradley
I haven’t heard Keegan’s name mentioned at all this week, which shows the power prior play at Augusta National has over people. Keegan’s three starts here have been mediocre as a whole, especially for a guy who’s been around the 20th best in the world over that time, but he absolutely fits the mold of a guy who should shine here. He launches the ball off the tee with a solid draw, he doesn’t struggle on bentgrass greens, and he has putted better than average on similar lightning quick greens at Firestone, Houston, and Muirfield Village.

Chris Kirk
Kirk played well last year in his first Masters trip and stands out as a pretty attractive long-shot pick. His game has been messy this year, especially when contrasted with his successes at the end of last season. The common theme so far has been just really poor putting. Kirk’s established himself as a very strong putter over the last few years, but he’s not making anything so far in 2015. Kirk’s been especially poor at making long putts (2% of his 25+ footers have gone in), despite a recent history where he’s one of the best on Tour at making putts from distance over 2011-14. I’ve written about how long putting seems to be especially random, driving putting results up or down without reflecting genuine improvements or declines in putting ability. Based on that, I expect Kirk to start producing better results on the greens and overall.

Weather
The forecast looks wet all weekend which I’ve seen taken as evidence that McIlroy, in particular, will be in good shape considering his wet weather record (his WGC-Bridgestone and PGA Championship wins last year were both on wet courses). I took a look at how players with high or low ball flights played in a handful of clearly wet rounds (WGC-Bridgestone 4th round & PGA Championship rounds 2-4). Players who bring it in high onto damp greens should be able to stick it closer than those who bring it in low.

It turns out that just looking at those four rounds (~250 individual rounds), that hypothesis was borne out in the data. I specifically measured Strokes Gained on Iron shots (par 4/5 approach shots & par 3 tee shots) and compared performance in these specific rounds to all the data I have more a player since last season. This controls for talent hitting irons. The correlation with the PGA Tour’s Trackman derived Apex Height stat wasn’t strong, but the coefficients suggest a player with an extremely high ball-flight – J.B. Holmes, Keegan Bradley – could gain about a 0.15 or more strokes from their normal level of play just on their iron shots if the course plays wet this week.

Apex Height vs Wet Weather play

This is definitely a subject worth a more formal investigation, but the data points to high ball-flight players being advantaged to a small degree in wet weather.