Most free content on the website will be updated by Monday morning during a normal week. The Scratch Tools are updated after fantasy salaries and betting odds are released on Monday; there should be a notice on the homepage with the expected update time for the Scratch Tools. For major championship weeks, the update schedule will likely be pushed up a bit as betting odds are released earlier.

As described below, most of the data used on our website is at the round-level (i.e. round scores, and round-level strokes-gained in the categories). This data is publicly available from a variety of websites that display results from professional golf tournaments: e.g. PGATour.com, OWGR.com, WAGR.com . We also have a partnership with the PGA Tour that gives us access to shot-level data from their ShotLink program. This data is not publicly available.

As of December 2020, we have an API!

Our default model is now one that includes course-specific adjusments: a golfer's course history, course fit, and also course-specific residual variance. More details on these updates to the model can be found here. On our pages this model is referred to as 'baseline + course history + fit'. The other model referenced, the 'baseline', is described in detail here. It does not take into account the aforementioned course-player specific characteristics. The baseline skill estimates are obtained by equally weighting golfers' historical performance across all courses (but the weighting is not equal over time – recent results are weighted more). We list both models for a couple of reasons. First, one way you could use these models is to put more trust in a specific prediction when both models agree (e.g. when both models show positive expected value on the same bet). Second, the inclusion of both models gives a sense of how the course history / course fit adjustments map to changes in finish probabilities. This should help you build intuition about how changes in skill estimates (strokes-gained per round) impact the outcomes we care about (i.e. finish probabilities).

Unless otherwise noted, it is the full model (i.e. including course-specific adjustments) that is used on the site.

Any time there is an update to a field (for any of the events we cover: PGA, European, or Korn Ferry Tour), we re-run our model and generate updated finish probabilities. We also re-run when tee times are released (typically some time on Tuesday for Thursday-start events) to account for differences in predicted course conditions in the first two rounds (see Q&A below for more information on this). These finish probabilities are produced through a simulation exercise, which means that even if the field is unchanged our estimated probabilities will be slightly different with each run of the model. (We perform 40,000 simulations, which is large enough to eliminate any meaningful — from a betting standpoint — fluctations in the probability estimates, but it can still be noticeable, e.g. at most a difference of 0.5%-1% can arise from one set of simulations to the next). This "simulation error" is why a top player can withdraw and yet some golfers see a slight decline in their, e.g., probability of finishing in the top 20. For PGA Tour events with spots allocated to Monday qualifiers, we use dummy players with the typical skill level of Monday qualifiers to run our simulations before Monday evening. Once the qualifiers are known, we sub in the new players and remove the dummy golfers.

When predicting wave splits — that is, the difference in scoring conditions between the morning and afternoon waves — we mainly use historical data (and data from earlier rounds in the current week after the tournament has started). We also incorporate weather conditions, both to adjust historical scores and for predicting scoring conditions in future rounds. Historically, the morning wave on average faces a course that plays 0.15-0.20 strokes easier than the afternoon wave on Thursday, while that figure increases to 0.25-0.30 on Friday. These will be the typical wave split projections before making additional adjustments for weather; the Friday projection is also impacted slightly by how the course played on Thursday in the morning versus afternoon.

Pre-tournament we also provide the predicted wave split over the first two rounds for the Thursday morning wave ("Early-Late") versus the Thursday afternoon wave ("Late-Early"). Historical data from both the European Tour and PGA Tour indicates that the Late-Early wave on average has a 0.1 stroke advantage over the Early-Late wave (this advantage remains after accounting for any skill differences between the waves). You can speculate as to why that may be the case. Therefore with no information on weather, this is the typical value for our weeklong projected wave split. On weeks and rounds where there are not clearly defined waves (e.g. limited-field events, multi-course events) we don't predict splits.

Finally, let's clarify the interpretation of our wave split notes. If it is a morning/afternoon split prediction for a given round, the listed advantage (in strokes, or fantasy points) indicates how much easier we think the course will play for morning wave that day. If the listed number is negative, that indicates that we expect the morning to play more difficult than the afternoon. The same interpretation applies to notes on the weeklong split, except now we are comparing expected scoring conditions for the Thursday morning wave to the Thursday afteroon wave over their first 2 rounds.

If you would like a detailed (and up-to-date) description of the model methodology, visit this blog post.

The model uses historical data from any OWGR-sanctioned tour and a very comprehensive database of amateur events that includes most American college golf events, and any event that is included in the World Amateur Golf Rankings.

Using this historical database, the model produces estimates of each golfer's expected strokes-gained relative to an average PGA Tour professional. To obtain these estimates there are basically just two steps: 1) properly adjusting scores across tournaments and tours (e.g. accounting for the fact that beating fields by 2 strokes on the PGA Tour is better than doing so on the European Tour), and 2) producing a weighted average of these adjusted scores to project future performance (more recent rounds recieve more weight). With these predicted strokes-gained estimates we can then derive any outcome of a golf tournament we would like: e.g. a Top 20 finish probability, or a head-to-head matchup win probability.

This last point is important: once we have our skill estimates for each player (in units of strokes-gained relative to an average PGA Tour professional), we can translate skill differences into probabilities (of various sorts). This depends critically on how much random variance in performance there is in golf. Dig deeper into this here.

The inputs to our model only include round-level information (i.e. no hole-level or shot-level data is used). (Update: this is not true anymore.) We do incorporate round-level strokes-gained category performance (e.g. Off-the-tee, Approach, etc.) where it is possible. This latter adjustment makes use of the fact that long game performance is more predictive than short game performance.

Importantly, our model does not account for course-specific characteristics. (Update: This is now true only in the baseline model — we have moved to a model that includes course-specific adjustments as the default model.) For reference, a golfer's last 150 rounds (roughly) contribute to the estimate of their current ability level.

To make use of our model, you first need to understand what it is good at. Our model provides a set of baseline estimates that likely do not warrant big deviations from. We are confident in saying that our model's output gets you most of the way to accurate predictions. The majority of the value-added of our model likely lies in two areas: first, we are missing very little relevant data on golfers' recent performance. There are several models out there that are only using PGA Tour data; this immediately puts those models at a large disadvantage. Second, we are properly adjusting scores across tours; being able to directly compare performance across professional tours that differ drastically in quality is very important. Doing these two things well gets you most of the way to obtaining good estimates of golfer ability.

Our estimates are not perfect, however. As said above, currently we do not account for any course-and-player specific effects. This would include, for example, certain players performing better on certain types of course layouts. In our past work, we have found course-and-player-specific characteristics to be difficult to incorporate into the model in a systematic manner. We are always working to improve the model, so course history and course fit may be incorporated soon; this page will be updated when it is. (Update: This is true only in the baseline model — we now provide estimates from a model that includes course history and course fit.)

Apart from just using our model's output directly, there are a couple of ways you could incorporate your own information with our model's output. First, it could be useful to take our estimates as a baseline and make manual tweaks when there are particularly strong indications of player-course fit (e.g. Luke Donald at Harbour Town, Phil Mickelson at Augusta National). These adjustments should never be too large in our opinion (work we have done shows that course fit does not have much predictive power). Second, if you have your own predictive model, combining (e.g. taking a simple average, or a weighted average) our estimates with yours is one possible strategy to produce an even more accurate model than either model alone.

In the near future, we will be providing Scratch subscribers with the ability to download our model's estimates of player skill (i.e. expected strokes-gained per round) which will make it easy to incorporate our model's output into models of your own. We also plan to work on other ways that allow subscribers to customize our model's predictions (e.g. allowing users to tweak skill estimates in terms of strokes-gained per round, and then translating those tweaks into relevant probabilities for weeklong finish position and head-to-head matchups). Look for these features to be live in the near future.

The Data Golf Rankings are our rankings of the best golfers in the world. Any golfer that plays in OWGR-sanctioned events or WAGR-sanctioned amateur events is eligible. The rankings are determined by averaging the field strength-adjusted scores of each golfer, with recent rounds receiving more weight. The index listed on the page — the DG Index — is this weighted average (adjusted slightly for players with fewer rounds played), and should be interpreted as our expectation for a golfer's next performance, in units of strokes-gained relative to an average PGA Tour field. That is, if a player has a value for the DG Index of +2, that means we currently expect them to beat a PGA Tour field by 2 strokes per round. Approximately the last 150 rounds that a golfer has played contribute to their DG Index. Finally, to be included in the rankings, a golfer must have played at least 40 rounds in the last 2 years and at least 1 round in the last 6 months.

The Data Golf Amateur Rankings are our rankings of the best amateur golfers in the world. The rankings are based off the same DG Index described in the answer above this; the only difference is that we report the DG index as strokes-gained relative to the average golfer in the Division 1 NCAA Championship, which we estimate to be about 2.3 strokes worse per round than an average PGA Tour field. Therefore an amateur golfer with a DG index of +3 would be expected to beat the D1 NCAA Championship field by 3 strokes per round, and a PGA Tour field by 0.7 strokes per round. The data used to form the rankings includes any US college event that is listed on Golfstat, any WAGR-sanctioned events, and any professional events that amateurs happen to play in. To be eligible for the amateur rankings, a golfer must be an amateur (wait, what?!), and have played at least 20 rounds in the last 2 years and at least 1 round in the previous 12 months. If you want to understand more about the true strokes-gained metric that powers these rankings, and how our rankings compare to those of the WAGR, check out this blog.

A golfer's skill level at any given point in time is their expected performance (according to our model) in their next round. Golfer skill is in units of strokes-gained per round relative to an average PGA Tour field at an average PGA Tour course. We also sometimes refer to this as a golfer's ability. The word "expected" here is important. Different estimates of skill can be formed depending on what goes in to that expectation. For example, the Data Golf Rankings are based off skill estimates that only use total strokes-gained as inputs (we call these skill estimates the DG Index). Conversely, in the model that is used to generate our weekly predictions, we draw on as much information as possible when forming our estimates of skill (e.g. strokes-gained category performance). This Q&A provides more information on this difference.

Just as with a golfer's overall skill level, our predictions of skill in the strokes-gained categories, or for driving distance or driving accuracy, should be interpreted as an expectation (or prediction) of a golfer's next performance in that specific skill at an average PGA Tour course. For example, a skill estimate of +0.4 in strokes-gained putting means that we would expect that golfer to gain 0.4 strokes on the greens over an average PGA Tour field in their next round (again, at an average PGA Tour course). For driving distance the units are yards-gained relative to an average PGA Tour field, while for driving accuracy the units are in percentage of fairways hit relative to an average PGA Tour field. (See examples here for more clarity on this.)

Next, some details on how these specific skill estimates are actually formed. These are estimated in a similar fashion to our overall skill estimates, e.g. the estimate of driving distance skill is mostly driven by historical driving distance, with recent data receiving more weight. (You can read more about this in our model methodology blog post.) For various technical reasons, the main one being that not all golf tournaments provide detailed SG data, the sum of our skill estimates for SG:OTT, SG:APP, SG:ARG, and SG:PUTT will not necessarily add up to our overall estimate of a player's skill. Therefore, we calculate this discrepancy and adjust the category SG estimates so their sum matches the overall skill of a player. The difference is distributed unevenly to the SG categories, with more of it going to OTT and APP skill as they vary more than ARG or PUTT skill. That is, if the sum of our SG estimates is 0.2 strokes lower than our overall skill estimate, 70% of that (or .14 strokes) might be allocated to OTT and APP skill, while the remaining 0.06 strokes would be added to ARG or PUTT.

There are several differences between the skill estimates listed on the rankings page and those shown on the skill ratings page. The former only take into account a player's past performance in terms of total strokes-gained (adjusted for field strength). We do this because we believe rankings should solely reflect the quality of a golfer's historical performance, which in golf is defined by total strokes-gained. The latter make use of other data with the aim of improving predictive power; for example, a golfer's past performance by strokes-gained category. The full set of adjustments can be seen on the skill decomposition page by looking at the columns to the left of "course history". (The 'baseline' column on this page contains the (approximate) estimates used to generate the DG rankings.) The skill estimates used in our full model to generate weekly predictions are equal to the estimates on the skill ratings page plus some course-specific adjustments.

True strokes-gained is simply raw strokes-gained — the number of strokes you beat the field by in a given tournament-round — adjusted for the strength of that field. If the average golfer in field A is 1 stroke better than in field B, then beating field A by 1 stroke and beating field B by 2 strokes would yield equal true strokes-gained values. As with regular strokes-gained, true strokes-gained requires a benchmark. For this we use the average performance in PGA Tour events in a given season. (That is, the average true strokes-gained for all PGA Tour rounds in a season is zero.) Therefore, you would interpret a true strokes-gained number from a round in the 2018 season as the number of strokes better than the performance we would expect from the average 2018 PGA Tour field. Note that, throughout the site, slightly different wordings are used to describe the true strokes-gained benchmark — e.g. average PGA Tour player, average PGA Tour field — they are all meant to describe the same benchmark, which is the average performance in PGA Tour events. Importantly, this interpretation holds for performances across all the tours in our data — for example, the average true strokes-gained performance on the 2018 Mackenzie Tour was about -2.5 strokes per round. This is, after all, the purpose of the true strokes-gained metric: having a measure of performance that can be directly compared across all tournaments and tours.

Because the benchmark is unique to each season, we are not taking a stand on how the average skill level of the PGA Tour is changing over time. This "true" adjustment is also applied to each of the strokes-gained categories, and the interpretation is the same (i.e. performance in that category relative to the average PGA Tour performance in the relevant season).

It is possible to make comparisons of performances on, for example, the Web.com Tour to those on the PGA Tour because there is overlapping golfers in these fields. That is, each week in the Web.com event there will very likely be a few golfers who played in a PGA Tour event in the weeks preceeding or following it. It is due to this overlap that direct comparisons are made possible across tournaments and tours. For example, if a player beats a PGA Tour field by 1 stroke per round one week, and then beats a Web.com field by 2 strokes per round the next, we could conclude that this PGA Tour field is 1 stroke better per round than this Web.com field (if we assume the player's ability was constant across the 2 weeks). Of course this example doesn't seem very realistic because we are ignoring the role of statistical noise: what if the player played "poorly" one week? This would lead us to draw misleading conclusions about the relative field strengths. This is mitigated in practice by the fact that we don't have just one player "connecting" fields, but many.

But what about tours like the Mackenzie Tour or Latinoamerica Tour — surely there is very little overlap between these tours and the PGA Tour in a given season? This is true, but to make comparisons of the Mackenzie Tour to the PGA Tour we don't actually need direct overlap. It is sufficient that there are players from the Mackenzie Tour events who also play in Web.com events, and then there are some (different) players in the Web.com events that also play in the PGA Tour events. It is in this sense that we require Mackenzie Tour events to be "connected" to PGA Tour events. The accuracy of this method is limited by the amount of overlap across tours and fields; in general, we find there is a lot more overlap than you might expect. Now that we have recently expanded our database of golf scores to include any event played on an OWGR-sanctioned tour as well as any event included in the World Amateur Golf Rankings, there are many ways that PGA Tour events can be connected to other, smaller, tours.

Once we run this statistical exercise, we are left with a set of strokes-gained numbers that can be compared relative to one another. But, we would like to have a useful benchmark to easily understand the quality of any single performance in isolation. Therefore, as said above, for each season we make the average true strokes-gained performance equal to 0 on the PGA Tour. This gives us the nice interpretation for all true strokes-gained numbers as the number of strokes gained relative to the average PGA Tour field in that season.

Only events that have the ShotLink system set up provide data on player performance in the strokes-gained categories. Therefore, the true strokes-gained numbers in each category are derived from this subset of events, while the true strokes-gained total numbers are derived from all events in our data (PGA Tour, European Tour, Web.com, etc.). If every tournament a golfer played in a given season had the ShotLink system in place, then the sum of the true SG categories will equal true SG total.

Imputation is only necessary for some — but really most — European Tour events. The Euro Tour started tracking strokes-gained category data in late 2017. On their website they only make available event-level strokes-gained averages rather than the raw round-level data (unless you pull the data immediately after each round is played, which has its problems as there are often data errors). For the (few) European Tour events where we have successfully collected the round-level data for each SG category, we obviously just display that. (It's also worth noting here that the SG category data from the Euro Tour is typically missing for a few players in each event.) In the other events where only event averages are available, we have to get creative. For the purposes of incorporating this data into our predictive model this is not a big issue; ideally we would like to know the values for individual rounds as more weight is applied to more recent rounds, but using the same value for all rounds played within an event only changes things slightly. However, given the information we have — event-level strokes-gained category averages and total strokes-gained for each round — we can actually do a bit better than just using event averages. We fit a regression model using PGA Tour data (where we actually have round-level strokes-gained) to estimate the relationship between the relevant variables (i.e. use event-level SG category averages and total SG in a round to predict the SG category values for that round). We can then use that model to predict (i.e. impute) our missing round-level data on the European Tour (with the obvious caveat that we are assuming this relationship is similar on the PGA and European Tours). A few notes on these imputed values: they will add up to the actual event-level averages in each category; they will show less variation than the true (unobserved to us) round-level data; and the imputed values for putting and approach will vary more than off-the-tee and around-the-green. That is, if a golfer gained (in total) 5 strokes more in round 2 than round 1, more of that difference will be attributed to strokes-gained approach and putting than to off-the-tee and around-the-green. These imputed values will only make a difference in the true SG query tool if you select a sample (e.g. last 50 rounds, last 3 months) that falls in the middle of an event that uses imputed data.

Hello, interested reader! Welcome to the weeds.

In a perfect world, true strokes-gained as it appears on our website would be equal to raw strokes-gained (i.e. a golfer's score minus the field's average score) plus field strength as it appears on this page. However, this is not quite true for two reasons. The first reason is fairly innocuous: our field strength page shows the average skill level for the players in round 1 of a tournament. Therefore, for rounds played after a cut is imposed on the field, the average skill level will differ slightly from that listed. The second reason is more technical, and accounts for why even round 1 true SG values will differ from raw SG plus the field's listed strength. The issue is that to estimate true strokes-gained, we require estimates of players' skill; but, to estimate a player's skill, we require true strokes-gained! In theory, we could perform our entire estimation procedure in a big loop, and stop once our estimates of player skill converge from one iteration to the next, but this would be very computationally expensive and result in marginal gains. Therefore, the problem is this: the measures of field strength used when estimating true strokes-gained are ultimately not the same as those that appear on the field strength page. The details of the strokes-gained adjustment are here. One good reason to keep things as they are now, is that the field strength measures estimated in the score adjustment method use data from both before and after a tournament. That is, when we retroactively estimate true strokes-gained values for the 2020 Travelers Championship (as we do every week), the fact that Scottie Scheffler played very well after that tournament increases the field strength (and hence the true SG values) compared to what our estimate was the week immediately following the Travelers. In contrast, field strength as estimated in our predictive model only uses data from before an event is played, as, naturally, that is all we have when making predictions! (And these are the values that are displayed on the field strength page.) In general, these two measures of field strength should be very similar (within 0.1-0.2 strokes of each other).

Adjusted driving distance (which only uses the two officially-measured drives for each round) is the number of yards gained over the field's average drive, adjusted for the driving distance strength of that field. Adjusted driving accuracy is the percentage of fairways hit gained over the field's average, again adjusted for the driving accuracy strength of the field.

Some examples will be illustrative. First, for every golfer in a given field we have an estimate of their expected driving distance and expected driving accuracy. That is, an estimate of how far we expect them to hit their next drive, and an estimate of the percentage of fairways we expect them to hit. We express these relative to an average PGA Tour player: e.g. +2 yards or +5%. For clarity's sake, let's call these estimates "distance skill" and "accuracy skill". Now, suppose a golfer hits their 2 measured drives in a round an average of 315 yards while the field averages 300 yards. Further, suppose the average distance skill of this field is +2 yards. Then, the adjusted driving distance value for this golfer would be +17 in that round (they gained 15 yards over a field that is on average 2 yards longer than the PGA Tour average). Next, suppose the golfer hit 10/14 fairways or 71.4%, while the field averaged 65%, and suppose the field average's accuracy skill is -1%. The adjusted driving accuracy value for this golfer would be 5.4% (they hit 6.4% more fairways than a field that on average hits 1% fewer fairways than the average PGA Tour player). Note that we are talking about percentage points here, not percent differences. We could equally describe driving accuracy in terms of fairways hit (i.e. +5% equals +0.7 fairways gained, assuming there are 14 non-par 3 holes).

Our skill profiles, displayed as radar plots, show the number of standard deviations better or worse a player is in each skill relative to the PGA Tour average. Driving distance skill is measured in yards, driving accuracy in % of fairways hit per round, and the strokes-gained categories are measured in strokes per round. Standard deviation is a measure of the spread of the data; for our purposes, here are the relevant standard deviations: driving distance 8.1 yards, driving accuracy 4.7%, strokes-gained approach 0.37 strokes, strokes-gained around-the-green 0.16 strokes, and strokes-gained putting 0.24 strokes. Therefore, if you are 1 standard deviation above average in driving distance, this means you are 8.1 yards longer than the PGA Tour average. Nearly all of the data will be within 3 standard deviations of the mean (i.e. if you are 3 SD above the mean in distance, you are one of the longest players on Tour). For more intuition on standard deviation, take a look at this Wikipedia entry.

For an explanation of how the skill estimates are formed, see this Q&A. The skill ratings page displays skill estimates in their raw units; we simply divide these values by their respective standard deviations (listed above) before displaying them in the radar plots.

Expected wins measure the likelihood of a given strokes-gained performance resulting in a win. For example, averaging 3 strokes-gained per round (over the golfers who played all rounds in the tournament) at a full-field PGA Tour event will result in a win about 55% of the time. Why would this be good enough to win some events, but not others? Sometimes another player may also happen to have a great week and gain more than 3 strokes per round, while other weeks this doesn't happen. The intuition behind the expected wins calculation is simple. For example, to estimate expected wins for a raw strokes-gained performance of +3 strokes per round, you could just calculate the fraction of +3 strokes-gained performances that historically have resulted in wins. (In practice, it's not quite this simple as the number of strokes-gained performances exactly equal to 3 will be small. Therefore some smoothing must be performed — see graphs below.)

Expected wins based on raw strokes-gained as a statistic carries with it the same drawbacks of raw strokes-gained: it can't be compared across tournaments of differing field strengths. Further, tournament characteristics like field size also confound raw SG-based expected wins comparisons (all else equal, the larger the field, the larger the raw SG typically required to win). For these reasons our website dispays what could be called "true" expected wins. In words, this measures the likelihood of a given 4-round performance winning some baseline event (e.g. an average full-field PGA Tour event). Like true strokes-gained, true expected wins from any tournament or tour can be compared.

To get a sense of the relationship between true strokes-gained and winning on the PGA Tour, shown below is a histogram of the 4-round true SG average of every winner from 2004-2021 at what I've dubbed "average" PGA Tour events (i.e. non-majors with field sizes between 130 and 156, and an average skill level between -0.2 and +0.2; 182 events fit this criteria):


On our performance table, we display two versions of true expected wins: one uses the average PGA Tour event (as described above) as the reference event, while the other uses the average Major championship as the baseline event. We refer to these as xWins PGA and xWins Majors respectively. (Note that on the performance table only non-major performances count towards a golfer's xWins PGA, while only major championship performances count towards a golfer's xWins Majors. Of course, this is a somewhat arbitrary choice — any true SG performance has a corresponding xWins PGA or xWins Majors value.) To calculate these two variations of true expected wins we first must estimate the relationship between 4-round true SG averages and winning on the PGA Tour. (This relationship is allowed to vary over time as golf has become deeper in recent years, meaning that there is generally less separation between winners and the field today than in years past.) We estimate the SG-win relationship for our set of "average" PGA Tour events, and for major championships; both of these curves are shown below:


Using this graph it's simple to calculate expected wins given any true SG performance. For example, at the European Tour's 2021 Gran Canaria Lopesan Open, Garrick Higgo won with a performance of 2.8 true SG per round. Eyeballing the blue line above we can see that 2.8 true SG will only be good enough to win an average PGA Tour event ~3% of the time (i.e. that performance is worth 0.03 xWins PGA). As you would expect, a given true SG performance results in a lower probability of winning a major championship than it does a regular PGA Tour event. For reference, but mainly because it's mind-boggling, Phil Mickelson's true SG average in his 2nd place finish at the 2016 British Open was 6.6 strokes (weather-aided, however)! This predicts a win probability of 100% if the performance came at a regular PGA Tour event and 99.9% at a major. Alas, the record books show only a big fat zero.

Expected wins provide a means of quantifying the number of high-quality performances a golfer has had while avoiding the noise that is built in to using number of wins for this purpose. "Expected" statistics are used in many sports (e.g. expected goals in soccer), and they are all based on a similar premise. In golf, we were first introduced to the concept of expected wins from an article written by Jake Nichols of 15th Club.

The simple answer is that it is because our model is not perfect. That is, the bookmaker's odds contain information that is not reflected in our model's probabilities that is useful for predicting performance. This is not suprising. The only way our actual profit would match our expected profit (in the long-run) is if our model's estimates could not be improved upon by incorporating the bookmaker's odds. One way to get around this is to include the bookmaker's odds in your modelling process. This would make actual profit line up with expected profit (under a few assumptions). We talk about related ideas in an old betting blog. The fact that our model's expected profit overestimates 'true' expected profit is why we use a threshold rule to determine when to place a bet. For more details on the relationship between our model's EV and actual returns, see the final section of this blog.

All bets are placed through Bet365, so the first criteria is that the bet is offered there. For each bet type (matchups, 3-balls, Top 20s, etc.) there is an expected value threshold that must be met to place the bet. The specific value of these thresholds have tended to evolve over time. The longer are the odds, the higher the threshold is. Currently (updated Dec 1, 2021), at least a 5% edge (that is, an expected value of 0.05 on a 1-unit bet) is required to take a matchup bet, 7% for a 3-ball bet, and somewhere in the range of 8-20% for Top 20s, Top 5s, and Outrights. The purpose of imposing a threshold is to ensure that you are in fact placing positive expected value bets; our model is not perfect, so when the model says expected value is 5%, the 'true' value is probably closer to 0. We also do not place 3-ball or matchup bets if we have very little data on any of the players involved (cutoff is around 50 rounds). We do this because our predictions for low-data players have much more uncertainty around them.

Bets are typically displayed on the page as soon as play begins on a given day (sometimes a half-hour to an hour after play begins). For Scratch members bets can be viewed as soon as we make them ourselves (typically well before play begins).

We use a scaled-down version of the Kelly Criterion. The Kelly staking strategy tells you how much of your bankroll to wager, and is an increasing function of your percieved edge (i.e. how much greater your estimated win probability is than the implied odds) and a decreasing function of the odds (i.e. longer odds translates to smaller bet sizes, all else equal). Importantly, the Kelly is designed for sequential bets; i.e. your first bet is resolved before you placed your second, and so on. However, in golf betting we will often have many simultaneously active bets. We don't have a fully worked solution to this, but sometimes we will lower the Kelly fraction if there are already a lot of units in play. This is one reason you won't be able to find a consistent Kelly fraction when analyzing our wagers; the second reason is that we vary the Kelly fraction by bet type and have also varied it over time as our (poorly-formed) betting strategy has evolved.

How we arrive at our pre-tournament estimates of player skill and our pre-tournament finish probabilities is described in detail here. Once the tournament is underway, the largest updates to a golfer's finish probabilities are due to their performance so far in the tournament (e.g. making bogey on the first 2 holes). However, we also use the live scoring data to update our pre-tournament predictions of golfer skill, and to update our estimates of each hole's difficulty. Regarding the latter, we also predict how each hole will play in the morning and afternoon (when there are distinct waves) of each remaining round. As with our pre-tournament simulations, the effects of pressure are accounted for in the live model. This has an effect on a player's projected skill for the 3rd and 4th rounds. Therefore, for the Matchup Tool, Props Tool, and Custom Simulation (which all use the live model simulations), our probabilities account for any changes to golfers' predicted skill due to their performance so far in the tournament and their position on the leaderboard (i.e. pressure effects), as well as the predicted difficulty of the course they will face (this will only matter if some of the golfers are playing in different waves or on different courses for multi-course events).

For interested readers, here are a few more details. With respect to predicting hole difficulty, it is critical to correctly account for the uncertainty in difficulty. For example, on Thursday evening, not only is it important to be able to accurately estimate the expected difference in scoring conditions between Friday morning and afternoon, but also to accurately characterize the range of possible conditions. If the afternoon wave is expected to face a course that is 0.3 strokes harder than the morning wave, but there is a 10% chance that they face a course that is 1 stroke harder, that 10% will have important implications for everyone's cut probabilities. Back in the earlier days of the live model we didn't properly account for this uncertainty, and took a lot of grief for it when projecting the cutline. With respect to updating golfers' skill levels, we have fit models that inform us on how much to update a golfer's Round 2 skill level based on their pre-tournament data and their Round 1 performance (and analogous models for Rounds 3 and 4). When available, we incorporate the strokes-gained categories into these updates. All of this information is finally put to use in the simulations that ultimately generate the coveted finish probabilities. Each simulation starts by drawing random numbers to determine the course conditions, e.g. Thursday's morning wave faces a course that is 0.5 strokes easier than the afternoon; then, given these conditions, golfers' remaining scores in their current round are simulated (i.e. randomly drawn) according to their skill; before the next round, new course conditions are simulated, taking into account the (simulated) course conditions from the previous round(s), and golfers' skills are updated based on their (simulated) performance and any pressure effects are accounted for. This process repeats itself until the 4th round is simulated, at which point each golfer's finish position can be determined; perform many simulations like this and you end up with probabilities (e.g. a win probability is simply the fraction of simulations where the golfer of interest won). Hopefully this illustrates that our live model is internally consistent; every update that we will eventually make once the real data comes in (e.g. golfers' Round 1 performance affecting their skill for R2) is also made in each of the simulations.

This the case because the live model is simulated with ties allowed. As a consequence, the default Top 5 and Top 20 probabilities provided are not suitable for making in-play bets where ties are resolved by dead-heat rules. They will indicate more value than they should because they do not take into account the reduced payouts received when there are golfers tied for the final paid finish positions. Win probabilities in the live model will always add up to 100%, as any ties for first are resolved in each simulation.

First, if needed, read this for a primer on what dead-heat rules are. Second, recall that an 'implied probability' from a bookmaker is the probability required for the bet to have an expected value of zero. With a simple bet (where there are only 2 possible outcomes — win or loss) this is equal to 1/european_odds. Once you have this implied probability, a simple comparison with our predicted win probability is all that is required to assess the expected value of the bet. In the case of bets where dead-heat rules apply, we construct an analogous probability that can be easily compared to the bookmaker's implied probability (1/european_odds). By way of example and for simplicity, suppose there is a top 5 bet where the only possible outcomes are for a golfer to finish in the top 5 golfers (with no players tied for 5th), to finish tied for 5th with 1 other golfer, and to finish outside the top 5 golfers. The expected value for a 1 unit bet would be equal to: P(finish_in_top5) * euro_odds + P(tie_for_5th) * euro_odds/2 - 1, which can be simplified to (P(finish_in_top5) + P(tie_for_5th)/2) * euro_odds - 1. The first term in brackets here is what we are calling a 'probability that accounts for dead-heat rules'. This is intuitive: in cases where the golfer's finish position results in the application of dead-heat rules, we multiply the probability of that outcome occurring by the dead-heat fraction that gets applied to the payout (e.g. 3 golfers tie for 1 paid position means we multiply the probability by 1/3). These probabilities will add up to 500% for a top 5 bet and 2000% for a top 20 bet, and can be directly compared to the bookmaker's implied probabilities to assess their expected value.

These match values are meant to capture how influential a given match is on the outcome of the tournament. Consider a match between Golfers A and B. For every golfer in the field, we estimate two win probabilities: their win probability if A wins the match, and their win probability if B wins. We then take the magnitude of the difference between these win probabilities for each golfer, sum them up, and we have our match value.

In the first round of the Match Play tournament, the match values are mainly driven by their effects on the win probabilities of the golfers involved in the match. For example, in the 2021 edition of this event, Jon Rahm was the favourite at 6.5%. A win in his first round match against Sebastian Munoz would give him a win probability of 8.9% and a loss a win probability of just 1.9%, yielding a difference of +7%. The difference for Munoz between a Rahm win and a Rahm loss was -1.4%, while for the rest of the field the differences are all slightly negative. To arrive at our final match value of 0.14 (14%) we simply add up the absolute value of all these win probability differences.

In the second and third rounds of the group stage the match values can get more interesting. Here there can be large effects on the win probabilities of golfers not involved directly in the match of interest. These affected golfers will most likely be in the same group as those involved in the match, but there can also be scenarios where large effects are seen on golfers outside the group. For example, suppose in the third round Jon Rahm is playing a lower-ranked player and Rahm must win the match to advance. As the best player in the field, if Rahm is eliminated this substantially increases the win probability of the field compared to the scenario where he wins.

Hopefully these match values can provide some interesting insight as the tournament progresses.

We've tried to follow the PGA Tour's methods for calculating strokes-gained as closely as possible, but inevitably there will be differences given we don't know exactly what their process is. Here are a few of the common sources of disagreement: 1) labelling "recovery" shots. The expected strokes to hole out changes substantially if a shot is deemed to be hit from a recovery position (see p.15 of Mark Broadie's paper). Labelling a shot as a recovery will have the effect of decreasing the previous shot's SG and increasing the SG of the current shot. This is commonly the source of discrepancies in SG:OTT and SG:APP; 2) Labelling shots as "Around-the-Green" versus "Approach-the-Green". Our method is simple: all shots within 50 yards from the pin are labelled as ARG; the PGA Tour's method (I believe) is more complicated. This is commonly a source of discrepancies in SG:ARG and SG:APP between DG and the PGA Tour; 3) We subtract the mean SG by category-hole, whereas the PGA Tour only subtracts the mean SG by category-round. We perform this adjustment by hole because we are also providing hole-level SG estimates (read more on this in the next Q&A). If a player doesn't hit a shot in every category on every hole, these two adjustment methods will yield different SG estimates. SG:ARG is the category most commonly affected by this; 4) We make the adjustment mentioned in (3) regardless of how many players have finished a hole (read more below), whereas the PGA Tour only starts making their adjustment later in the round. This will contribute to discrepancies for all categories while a round is ongoing. Overall the correlation between our SG figures and the PGA Tour's is high; for a randomly selected round, SG:OTT, SG:APP, and SG:ARG values typically have a correlation of 0.96-0.98, while SG:PUTT is >0.99.

To arrive at the final SG category values displayed on the scorecard, we subtract the average baseline strokes-gained value in each category. This adjustment occurs regardless of how many players have played the hole. For example, if only 2 players have played a hole and they both made 20-foot putts, their strokes-gained putting is zero on that hole. Clearly this adjustment is not ideal for assessing the quality of a player’s performance (i.e. we can be virtually certain by day’s end that these 2 golfers will have positive SG:P on that hole). However, we view the purpose of our hole-level strokes-gained breakdown as an accounting exercise, answering the question: where did the player gain/lose strokes relative to the other players who have played this hole so far? This adjustment ensures the strokes-gained categories always add up to total strokes-gained.

One byproduct of this adjustment method is that players can have non-zero SG in a category on a hole even if they don’t hit a shot in that category. To see why this happens, consider a hole that is of average difficulty on approach shots but is harder than average around the green (i.e. the average ARG shot misses the green more often and / or ends up further from the pin than what we would expect at the typical PGA Tour course from the same lies). For a player that hits it to 20 feet on an approach shot from 200 yards — and therefore does not hit a shot in the ARG category on that hole — our SG accounting might look something like this: SG:APP = +0.25, SG:ARG = +0.03. Because the average baseline SG:ARG is negative on this hole, subtracting the category means results in a positive value for this player’s SG:ARG on that hole. Intuitively, this player gained strokes around the green by not having to play from a location (e.g. greenside rough) that plays harder than that location at a typical PGA Tour course.

An alternative method would be to tailor a baseline strokes-gained function to each hole. That is, to have hole-specific estimates of how many strokes it takes an average pro to hole out from each location. Done perfectly, this would result in players having an SG of zero in a category where they didn’t hit any shots. In our example above, the player would have all their SG allocated to the approach category. This comes from the fact that the expected strokes to hole out from 200 yards would be higher (because missing the green comes with a bigger penalty), and so a shot hit to 20 feet might gain 0.28 strokes on that hole compared to the usual 0.25. Compared to the previous accounting, we’ve moved the 0.03 strokes the player gained around the green to approach.

It’s possible to construct extreme examples that highlight "flaws" with this second method: consider a hole where everyone who misses the green chips it to an inch due to a funnel pin; hitting an approach shot from 200 yards to 25 feet on the green would gain approximately 0 strokes using a baseline function specific to this hole. This is a drawback in the sense we get very little information regarding the true quality of the players' approach shots on this hole. Using the first method to adjust SG would yield something like SG:APP = +0.25, SG:ARG = -0.25 — also not ideal, but at least we retain useful information on the approach shot. In any case, the more important consideration here is that the second method is very hard to implement, especially live during the tournament. It's mainly for that reason that we stick to the simple adjustment of subtracting off the mean SG by category and hole.

A golfer's projection is the expected number of points we are predicting they will earn. We form these projections by using the output from our predictive model to simulate each golfer's performance at the hole level. A hole-level simulation is necessary to simulate fantasy scoring points, which depend on hole-specific scores as well as a golfer's performance on consecutive holes. By performing many simulations we can obtain a distribution for each golfer's earned fantasy points; the projection is then simply the average point value across all simulations.

As said above, our fantasy projections are generated using the predicted skill levels from our predictive model. Dedicated followers will know that these predicted skill levels are formed using a continuously decaying weighting scheme, as opposed to a discrete long-term/short-term form weighting. Therefore, it is not actually the case that our default fantasy projections are a weighted average of long-term form and short-term form. When you move the long-term weight, we compare the golfer's long-term (last 2 years) form to their short-term (last 3 months) form, and adjust the projection accordingly depending on whether it is higher or lower, and whether you've increased or decreased the weight. The same applies for short-term form. The weighting adjustment has to be done this way to accomodate the fact that we want our optimal projection to use a continous weighting scheme, while also giving users the ability to make their own simple adjustments to long-term form versus short-term form. A couple final points: a weighting scheme of 7/3 is the same as 70/30; we simply add up the weights you input and normalize them to sum to 1. If a golfer does not have any short-term data, they are assigned the field average projection. The one exception to this is rookies, who are given the average historical point values for rookies.

Easier course conditions increase the projected scoring points for all golfers, but the increase is largest for the top players. Conversely, harder course conditions decrease expected scoring points for all players, with the decrease being larger for the better golfers. Therefore, the relevant effect from toggling the course difficulty parameter is that easier conditions spreads the projections further apart, while harder conditions brings them closer together. If course conditions simply shifted everyone up or down by the same amount, this would be irrelevant with regards to forming optimal lineups.

To understand why this happens, let’s focus on the example where course conditions are made to be easier (i.e. a lower expected scoring average). There are two reasons why this causes projections to spread apart. First, easier course conditions means there are more points scored per round (on average), which makes playing the additional weekend rounds more valuable. Because better golfers make the cut more often, they benefit more from the easier scoring conditions. The second reason for the widening of projections when conditions are made easier is the non-linear scoring point breakdown in fantasy golf. That is, the point difference between birdies and pars is greater than the point difference between pars and bogeys (in all three formats — DK, FD, Yahoo — we offer). Additionally, there are points for birdie streaks and bogey-free rounds. This means that on courses where the difference between good scores and bad scores is 3-4 extra birdies, as opposed to courses where the difference is 3-4 fewer bogies, the point separation between the top players and the field will be greater. As a result, even at no-cut events, easier course conditions will spread projections apart (albeit to a smaller degree than at cut events). This second reason is, of course, the only relevant one when considering course conditions for Showdown or Weekend slates.

Broadly speaking, you want to maximize expected points (i.e. the projection) of your lineups while minimizing the overlap your lineups have with the other players in your fantasy contest/tournament. The reason is that the more players who own the winning lineup, the smaller the payout will be for owning that lineup. However, in all but the largest tournaments, it's unlikely that your lineup will be exactly duplicated. Even so, it is better to play low-owned golfers conditional on having same projection in the bigger tournaments (why this is true is actually not obvious; we discuss this more below). Therefore, if two golfers have similar projections, but one has a lower projected ownership, then it is better to play the lower-owned golfer. A more difficult question is how much a slightly lower ownership is worth in terms of projected points. That is, if golfer A is projected to score 5 fewer points than golfer B, how much lower does golfer A's ownership need to be than golfer B's for it to be profitable (in expectation) to play him? This is a hard question whose answer depends on the size of the contest under consideration. In general, it is the case that ownership matters less the smaller is the number of contestants involved. In the limit case of a head-to-head matchup, ownership (i.e. who your opponent is playing) is irrelevant to your strategy; you should always play the golfers with the highest projections. This is shown below with a simplified example.

Ignoring ownership considerations, the exposure profile you take will just be a matter of risk preference. If you were risk-neutral, meaning that all you care about is expected value (as opposed to also disliking variance), then exposure is not relevant. A risk-neutral player should just play the highest projected lineups (again, ignoring ownership considerations). However, most of us are risk-averse, in which case you may not want to have your entire week of fantasy golf riding on the performance of 1 or 2 golfers — especially if the golfer is coming off 3 straight missed cuts (a common DG recommendation). Thus, if you aren't a glutton for punishment, it is a good idea to reduce the variance in weekly returns by limiting exposure to any single golfer. Of course, by limiting variance you are trading off positive expected value (if our projections are somewhat accurate). How much of this tradeoff you are willing to make comes down to personal preference. Finally, the difference between one golfer making 100% of the top 20 lineups and another one missing them entirely is often only a couple projected points; given that our projections certainly aren't perfect, this is another reason to diversify to some degree.

When set to zero, the optimal lineups are returned based on the actual projections. By moving the slider to the right, projections are given a series of random shocks. That is, a first shock will be applied to each player's projection (e.g. increasing golfer A's projection by 2 points) and the best lineup will be found and returned based on these shocked projections; then, a new shock will be given and a second lineup based on these new projections will be returned; this process repeats itself until the correct number of lineups have been returned. The further the slider is to the right, the larger is the size of the shocks applied. In this process, the highest projected players are more likely to get negative shocks, while the opposite is true for the lowest projected players.

The effect of adding these shocks is that a more diverse set of players will make it into the returned optimal lineups. That is, the set of player exposures will become more uniform the larger are the shocks. Limiting exposure by using the diversity slider will tend to have a different effect than limiting it directly (with the maximum exposure setting). For example, if you request 20 lineups with a maximum exposure of 50%, it's likely that the first 10 lineups will have the same 2 golfers in all of them. By using the diversity slider, you may be able to achieve 50% exposure to both of these golfers while having less overlap between the lineups that include them.

Suppose that each entrant in the contest chooses just 1 golfer, and that the prize pool is winner-take-all. Ownership here will be taken to be the percentage of players other than you that are playing a given golfer. Given this setup, the expected value to playing a golfer with a win probability of w and an ownership of x percent, in a contest of size N, is equal to: where I've assumed the buy-in is 1 unit and there is no "take" (or vig/juice/rake). The denominator is the fraction of players that played the golfer (\( \frac{1}{N} \) is your contribution to this fraction). Using the formula, if you play a golfer that nobody else is playing, then the payout if you win is equal to N units (and so profit is N-1).

How much does ownership matter in this simplified setup? With just 2 players (i.e. a head-to-head matchup), you should always play the golfer with the highest win probability. If your opponent is playing the highest-win-probability golfer, then you should also play this golfer thus ensuring a profit of 0; playing any other golfer will yield a negative expected profit (because w will be less than 0.5). If your opponent is not playing the best golfer, profit is clearly maximized by you playing the best golfer. Therefore, irrespective of your opponent's decision, you should play the highest-win-probability golfer, which means that ownership is not relevant to the decision in a head-to-head matchup. At the other extreme, if N is very large, expected value is equal to 0 if a golfer's win probability is equal to their ownership in the contest (\( w=x \)). In these contests, ownership will be important: whenever a golfer's ownership is below their win probability, it will be positive expected value to play that golfer.

To further build intuition, consider the case of a 3-player contest, and suppose there are just 2 golfers to choose from: golfer A who has a 67% win probability, and golfer B who has a 33% win probability. If the other 2 entrants are both playing golfer A, then (using the above formula), the expected profit will be 0 from playing either golfer. That is, even though the ownership of golfer B was 0%, a win probability of greater than 33% is required to make it profitable to play golfer B. If one of the other 2 entrants is playing golfer A, while the other has golfer B, then you should play golfer A. And finally, if both other entrants are playing golfer B, then clearly you should play golfer A. So we see that in this case ownership does matter, but a golfer's win probability is probably still the most important consideration in your decision. In general, as N increases, ownership becomes more important to the optimal decision.

To really flush out this point, below I examine a specific scenario. Consider a contest of size N, and suppose you are deciding between playing a golfer with a 30% win probability and whose ownership is 30%, and a golfer with a 25% win probability whose ownership is unknown. In the plots below, the horizontal dotted line in each plot indicates the expected value from playing the golfer who has a win probability of 30% and an ownership of 30%. For small contests, it is negative expected value to play this golfer (because, by playing the golfer, you have a substantial impact on the payout); as N grows, expected value converges to 0 because the impact of your decision to play the golfer on the payout becomes negligible. The bolded black curve in each plot indicates the expected value from playing a golfer who has a 25% win probability at various ownership levels (as indicated on the x-axis). We see that in a contest with 10 players, even at 15% ownership it is still more profitable to play the 30% owned / 30% win probability golfer. As N increases, we see that the level of ownership that makes playing the 25% win probability golfer equally profitable (i.e. where the bold line intersects the dotted horizontal line) converges to 25%, as expected. For example, the second plot shows that in a 50-player contest, an ownership of 24.6% or lower will make the 25% win probability golfer the more profitable play. The final plot below shows the full relationship between break-even ownership and contest size. The specific relationship will depend on the parameter values (i.e. the golfers' win probabilities and ownerships), but the overall pattern will be similar. For the smallest contest sizes, it is evidently not possible to even have 25% or 30% ownership; in any case, the curve captures the idea that in the smallest contests there is no level of ownership that will warrant playing the lower-win-probability golfer. Another implicit assumption here is that your decision does not affect the win probabilities; this will be true as long as every golfer is being played by at least 1 person in the contest. (For example, if nobody is playing the 25% win probability golfer, and you also decide to not play him, this will increase the win probability of all other golfers in that contest.) Of course, this analysis is only possible because we've assumed an incredibly simple format; once we allow for 6-player lineups and complex payout structures... things get difficult. More on those complexities later.

This visualization indicates which types of golfers are expected to over-perform or under-perform their baseline at each course on the PGA Tour. If a data point is further from the center of the plot than the average course, golfers who possess above-average values for that attribute should be expected to perform above their baselines at that course. It is important to take into account all 5 attributes when drawing conclusions about a golfer; for example, if both driving distance and driving accuracy have above-average predictive power at a course, then a golfer who is long but inaccurate will have adjustments to their baseline that go in opposite directions, meaning the net adjustment could be positive or negative. If you flip through the plots (in the default view), you will notice that the course-specific values for putting and around-the-green do not vary much, while the driving distance and driving accuracy values do. This indicates that PGA Tour courses differ meaningfully in the degree to which they favour golfers with length (or accuracy) off the tee, while they don't appear to differ much in how much they favour good putters or around-the-green players (at least not in a way that can be easily measured in the data). Another unusual thing you may notice is that certain courses have below (or above)-average predictive power in most attributes; Waialae CC is an example of a course where nothing seems to predict performance particularly well. This means that overall performance at Waialae is more unpredictable than the average PGA Tour course. As a result, we should downgrade our expectations for players who have above-average values in each attribute, meaning that Waialae is a course where worse players are expected to perform above their baselines and better players below them. Intuitively, randomness as a property of a course can be thought of as providing good course fit for below-average golfers (e.g. would you rather try to beat Rory McIlroy at a PGA Tour course or at the mini putt from Happy Gilmore with the laughing clown?). A final note on interpretation: if you toggle to the 'relative importance' view, the data for each attribute is scaled to take on values between 0 and 1. This makes it easier to see differences between courses in the less predictive attributes (SG:Putting and SG:Around-the-green). However, in this view it is no longer possible to make direct comparisions of predictive power across attributes.

As stated in the plot information on the page, the default view for the radar plot shows the predictive power of each golfer attribute (driving distance, driving accuracy, etc.) on total strokes-gained at each course. The value of each attribute at the time of a tournament is equal to a weighted average of historical performances. For example, the 'driving distance attribute' is a weighted average of past driving distance performances; it is the predictive power of this weighted average on performance that we are estimating. More detail on how these averages are formed can be found here. Predictive power is a function of both effect size — for a 1 unit increase in some skill, how much does performance improve on average — and variance — how large are differences in the skill under consideration across golfers? To make things more readily interpretable, we normalize each attribute to have a mean of 0 and a standard deviation of 1. Then, by running regressions of total strokes-gained on the set of attributes, the coefficients provide us with an estimate of each attribute's relative predictive power (because the variance has been made equal across attributes). It is these coefficient estimates that are displayed in the visualization; in practice, we estimate all of the course-specific estimates at once, using a random effects model. Note that the predictive power of each attribute is estimated while holding constant the values of the other attributes (that is what a regression does, intuitively). Often you see analyses where raw correlations are shown between, for example, a golfer's historical strokes-gained approach and their subsequent performance. This raw correlation picks up the fact that good approach players are also good drivers of the ball, on average. We do not want to pick up this spurious part of the correlation, which is why all 5 attributes are included in the same regression. Finally, the numbers that actually go on to the plot are scaled to takes values between 0 and 1 and therefore by themselves do not have any meaning; they are only meaningful in relation to values from other courses and other attributes. For more related reading on this, see the updated model methodology blog.

The variance decompositions from the historical event data page indicate how much each strokes-gained category contributed to the total variation in scores (i.e. total strokes-gained) in a given week. It is a descriptive exercise. Conversely, as described above, the radar plots on the course fit page indicate which golfer attributes (e.g. strokes-gained approach) predict performance at each course. It is a predictive exercise. Most of the time the variance decomposition will fit intuitively with the shape of the radar plot: for example, at Colonial CC a golfer's driving distance is significantly less predictive than at the average course. As intuition would suggest, we also see on the historical event data page for Colonial that strokes-gained off the tee accounts for less variation in scores than at the average course. Generally, when a given strokes-gained category accounts for a smaller (larger) share of the variation in scores at some course than it does at the average course, we should expect this strokes-gained category to be less (more) predictive of performance at that course relative to its predictive power at the average course. But this does not always have to be the case. For example, driving distance is more predictive of performance at the South Course at Torrey Pines than the average course; typically we would expect this to result in SG:OTT accounting for a larger share of the variance in scores at Torrey Pines. In fact, we see the opposite. Several stories could explain this: perhaps longer players have more of an advantage on approach shots at Torrey Pines, or perhaps there is just a tighter relationship between distance and SG:OTT at Torrey Pines than at other courses. Ultimately, if the goal is to predict performance, the precise explanation does not really matter (..an economist rolls over in their grave..). As said above, the variance decompositions are mostly just an interesting descriptive exercise; on the other hand, the information from the course fit plots is entering directly into our predictive model. If you find an especially puzzling pair of variance decomposition-radar plots, let us know!

The SG Difficulty statistics should be interpreted as the number of strokes easier (positive values) or harder (negative values) a specific shot type plays at each course relative to that shot type on the average PGA Tour course. For example, at the 2021 Masters, putts over 15 feet played on average 0.06 strokes harder than putts over 15 feet at a typical PGA Tour course.

Now, some details. First, recall that to calculate strokes-gained a baseline function that provides the expected strokes to hole out from every distance and lie (fairway, rough, etc.) is required. By using the expected strokes to hole out for the starting and ending point of each golf shot, strokes-gained is easily defined and calculated. (See here for some examples.) We'll call this baseline strokes-gained because it is an unadjusted number calculated directly from the baseline function. The SG Difficulty statistics are equal to the average baseline strokes-gained for the relevant shot type. (We do make strength-of-field adjustments as well so that these values can be interpreted as the expected baseline strokes-gained for an average PGA Tour field.)

The baseline function is estimated using data from all PGA Tour courses. Therefore, using data from all PGA Tour courses, the average baseline strokes-gained value will be zero for off-the-tee shots, for approach shots, and for any group of shots with a large enough sample size. However, specific courses may play easier or harder than what is predicted by this baseline function. For example, the average baseline strokes-gained value for off-the-tee shots at the Plantation Course at Kapalua was +0.1 at the 2021 Sentry Tournament of Champions. This is because Kapalua has easy-to-hit fairways and several holes where 400-plus yard drives are not uncommon. The fact that the average strokes-gained value for tee shots is positive means that players hit their tee shots to "better" (i.e. closer to the pin, and in easier, e.g. fairway vs. rough, lies) locations at Kapalua than at the typical PGA Tour course. Harbour Town is an example of a course that has a negative average baseline strokes-gained off-the-tee value, as it has one of the lower driving distance averages of PGA Tour courses. (As an aside, note that the official strokes-gained numbers by category on the PGA Tour website subtract off the mean baseline strokes-gained in each category by round, meaning they will have always have a mean of zero.)

There is some nuance to interpreting these numbers, however. For example, Augusta National had the 6th lowest baseline strokes-gained on approach shots in 2021; as described above, this means that approach shots at Augusta were hit to worse locations (again, "location" as defined only by distance and lie) than approach shots at the typical PGA Tour course. However, Augusta National was also rated as the hardest around-the-green course on the PGA Tour in 2021. It is thus tempting to think that Augusta's approach shots are actually much "harder" than we've given them credit for: not only are players at Augusta hitting their approach shots to worse lies and longer distances from the pin than the average course, these around-the-green shots also play much harder than their distance / lie predicts! However, I think the most informative way to display this data is as we've done it; average baseline strokes-gained by category tells us exactly why it's so difficult to hole out from 150 yards at Augusta National: the approach shots end up slightly further from the pin than the average PGA Tour course, and the shots that miss the green result in the hardest around-the-green shots on tour.