• Frequently Asked Questions

LAST UPDATED:

Over time we've recieved many of the same questions via email or social media. Hopefully if you've come to this page someone has asked your question before! If not, send us an email and we'll try to help you out.

General:

Q: When does the site typically update with new data each week?

A: Most pages will update by Monday evening of each week. The
Scratch Matchups page sometimes will not be updated until Tuesday morning
if there are no odds posted on Monday. For major championship weeks, the site
will be updated with the week's relevant data by Sunday night.

Q: What are your data sources?

A: As described below, all of the data incorporated into our model is at the round-level (i.e. round
scores, and round-level strokes-gained in the categories (i.e. OTT, APP, etc.)). This data is
publicly available from a variety of websites that display results from
professional golf tournaments.

Q: Is there a way to access your raw data? Do you have an API?

A: Currently we do not offer a means to access our raw data. This
may be something on offer for Scratch subscribers in the near future.

Predictive Model:

Q: What is the difference between the two models listed on the finish probability pages?

A: 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).

Q: Which model is used elsewhere on your site?

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

Q: In simple terms, what does your predictive model take into account?

A: If you would like a detailed description of the model methodology, visit this
blog post.

The model currently uses historical data from 6 professional tours: the PGA Tour, European Tour, Web.com Tour, Mackenzie Tour (Canada), Latinoamerica Tour, and the European Challenge Tour. Our database goes back as far as possible on each tour.

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). 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.

The model currently uses historical data from 6 professional tours: the PGA Tour, European Tour, Web.com Tour, Mackenzie Tour (Canada), Latinoamerica Tour, and the European Challenge Tour. Our database goes back as far as possible on each tour.

Using this historical database, the model produces estimates of each golfer's expected

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). We do incorporate round-level

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.

Q: How should I make use of your model's output?

A: 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 (we are
missing data from Amateur events, and some of the more obscure international tours).
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.

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.

Data Golf Rankings:

Q: What is different between the skill estimates listed in the Data Golf Rankings and
the skill estimates used to produce the weekly predictions and betting tools?

A: Currently the only difference between the skill estimates in the rankings and the
skill estimates used to generate finish and matchup probabilities is that the latter
takes into account a player's past performance by strokes-gained category
while the former does not. 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. We incorporate the strokes-gained categories into our modelling
process for making weekly predictions because we know that some categories are more
predictive than others (e.g. Off-the-tee play is more predictive than putting). In general
these two will be closely aligned, but there will be occasional meaningful discrepancies.

Betting Tools:

Custom Simulator:

Q: How frequently is this tool updated and what is changing on update?

A: The custom simulator is updated with new data every evening, as indicated by
the time stamp at the top of the page. The updated data includes our most
recent estimates of player skill. Our skill estimates are updated after
every round during a given week - they don't change much given that 1 round
of golf does not contain much information, but extreme performances (good
or bad) can result in meaningful differences (i.e. 0.1-0.2 stroke differences
in our predicted strokes-gained estimates).

Q: How do you incorporate the cut into your 4-round matchup simulation?

A: Each week when we simulate the weeklong finish probabilities (e.g. win, top5, etc.)
we also keep track of the average strokes-gained performance required to make the cut.
We then use this cutline estimate in our 4-round matchup simulations;
if either golfer's 2-round total (or 3-round total, for a select few tournaments) is below
our estimated cutline, they "miss the cut" in that simulation, and the result of the match
is recorded accordingly. If you select 2 players that are not competing in the same
event that week, or aren't competing at all, you will recieve a notice that we are
using a default cut rule (which is strokes-gained of 0).

Q: Why do the 4-round matchup and 3-ball win probability estimates differ slightly each time the page
is refreshed?

A: The win probabilities for 4-round matchups and 3-balls are obtained through simulation, whereas
the win probabilities for the 1-round matchups can be obtained via an analytical solution (i.e.
through math!). Even though we do 40K simulations (yes, they happen very quickly as the page is loaded),
there will still be small differences in our probability estimates on each run for 3-balls and 4-round
matchups.

Finish Tool:

Q: How are ties treated in the finish probability estimates?

A: Our pre-tournament finish probabilities are derived through simulations
in which ties are not possible. That is, the sum of the field's Top 20 probabilities
will equal 20, for example. This is the appropriate way to do things if you are
placing bets that use dead-heat rules (which nearly all books use).

Matchup Tool:

Q: How are you calculating expected value for matchups where ties are void?

A: We answer this question in the linked PDF
on the matchups tool page. Essentially the difference
is that we include the possibility of a tie, and hence voided bet, in the expected value
calculation. This seems the logical way to do things, as voided bets are still included in our running
totals of bets made, ROI, etc.

True Strokes-Gained:

Q: What is "true" strokes-gained?

A: True strokes-gained is simply raw strokes-gained (i.e. the number of strokes you beat
the field by in a given tournament-round) adjusted for the strength of that field. As with regular strokes-gained, true
strokes-gained requires a benchmark. For this we use the average player in a PGA Tour field in a given
season. Therefore, you would interpret a true strokes-gained number from a round in the 2018 season
as the number of strokes better than what we would expect
from the average player in 2018 PGA Tour fields. This interpretation
holds for performances from 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.

Because the benchmark is unique to each season, we are not taking a stand on how the skill level of the average PGA Tour player 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 player in a PGA Tour field in the relevant season).

Because the benchmark is unique to each season, we are not taking a stand on how the skill level of the average PGA Tour player 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 player in a PGA Tour field in the relevant season).

Q: How can you estimate a player's performance relative to the typical PGA Tour player for tournaments
other than those on the PGA Tour?

A: It is possible to make comparisons of performances on, for example, the Web.com Tour to those
on the PGA Tour because there is overlap between these fields. That is, each week in the Web.com event
there will be players who were in the PGA Tour event in the weeks preceeding or following it. It is due to this
overlap that makes direct comparisons across tournaments and tours possible. 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 that statistical
noise plays: what if the player played "poorly" one week? This would lead us to draw incorrect
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. That's 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 would expect.

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 to easily understand the quality of any one 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 this baseline.

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. That's 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 would expect.

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 to easily understand the quality of any one 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 this baseline.

Q: On the true strokes-gained page, why don't the strokes-gained
categories add up to strokes-gained total in the yearly summary tables?

A: 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.

Expected Wins:

Q: What are expected wins?

A: 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 does not happen. To get a better sense of the relationship
between strokes-gained and winning on the PGA Tour,
plotted below is the winning raw strokes-gained
average at every full-field PGA Tour event since 1983 (note: only players who play all rounds in a tournament
are included in the strokes-gained calculation).
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 graph below.)

When actually estimating expected wins, we also consider a few characteristics of the event. This includes the size of the field, the tour it was played on (i.e. PGA, Web, or European), the year it was played, and also whether the event was a Major or had no cut. Winners of majors typically beat fields by more strokes than at regular tour events, and winners of tournaments with larger fields typically beat the field by a larger margin, all else equal. Because professional golf has become deeper over time, the winners of golf tournaments today on average beat fields by less than in the past. Shown below is the actual function that maps from raw strokes-gained (again, this is raw strokes-gained relative to the players who made the cut and played all rounds) to expected wins for full-field regular PGA Tour events in the year 2000 (the function would look slightly different for events with smaller fields, or for majors, or for a different season etc.):
We also calculate *true* expected wins. This measures the likelihood of a given
strokes-gained performance resulting in a win at an *average full-field
PGA Tour event*. This is calculated by first adjusting the raw strokes-gained
performance for field strength, and then plugging it into the function shown
in the graph above. For example, suppose a golfer beat a European Tour field in the year 2000
by 4 strokes per round. This would be worth roughly 0.95 **raw** expected wins (that is,
we would expect this performance to win 95% of European Tour events).
After taking into account strength of field, suppose we find this performance
is equal to 3 strokes-gained per round over an average PGA Tour field. Then,
we would say this performance is worth roughly
0.55 **true** expected wins (using function shown above). Evidently, at events with an
average PGA Tour field, raw expected wins will equal true expected wins.
For reference, the Travelers Championship was an average quality full-field PGA Tour event
in 2018.

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.

When actually estimating expected wins, we also consider a few characteristics of the event. This includes the size of the field, the tour it was played on (i.e. PGA, Web, or European), the year it was played, and also whether the event was a Major or had no cut. Winners of majors typically beat fields by more strokes than at regular tour events, and winners of tournaments with larger fields typically beat the field by a larger margin, all else equal. Because professional golf has become deeper over time, the winners of golf tournaments today on average beat fields by less than in the past. Shown below is the actual function that maps from raw strokes-gained (again, this is raw strokes-gained relative to the players who made the cut and played all rounds) to expected wins for full-field regular PGA Tour events in the year 2000 (the function would look slightly different for events with smaller fields, or for majors, or for a different season etc.):

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.

Betting Results:

Q: What are the criteria you use to select the bets shown on the betting results page?

A: 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. For example, at least a 4.5% edge is required to take a matchup bet. 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.

Q: When are the bets displayed on the results page?

A: 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).

Q: How do you decide how many units to wager?

A: 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).

Live Predictive Model:

Q: Why do the Top 5 and Top 20 probabilities add up to more than they "should" (i.e. 500% and 2000%, respectively)?

A: This is the case because the live model is simulated with *ties allowed*. One of the live model's main
purposes is to accurately predict cut probabiltiies; evidently, this requires allowing for ties. As a consequence,
the 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. Win probabilities in the live model will always add up
to 100%, as any ties for first are resolved in each simulation.

Fantasy Projections:

Q: How do I interpret a golfer's fantasy points projection?

A: 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 the distribution of each golfer's
earned fantasy points (that
is, the probability of earning each point level); the projection is then simply the average point value across all
simulations.

Q: How does the weighting method of long-term form and short-term form work?

A: As said above, our fantasy projections are formed using the predicted skill levels from our predictive
model. As dedicated followers will know, these predicted skill levels are formed using a continuously decaying
weighting scheme, as opposed to a discrete long-term/short-term form weighting. The continuous scheme is simply a much more
a more robust way to form predictions. Therefore, *it is not* actually the case that our
default predictions are a weighted average of long-term form and short-term form, using the optimal
weights shown on the projections page (although, we chose the weights so that they correspond closely).
When you move the long-term weight, for example,
we compare the golfer's long-term (last 2 years) form to our optimal prediction, 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 course history and
short-term form. For example,
it could be the case that long-term form and short-term form are both lower than
the optimal projection. In this case, if you put more weight on long-term form, the
projection would increase if the golfer's long-term form is better than his short-term form (even though
both are lower than the optimal). This is the desired behaviour.
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.

Q: What role do course conditions play in the fantasy projections?

A: 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 respect to
of 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.

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.

Q: What is the role of ownership and exposure in fantasy golf?

A: 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.

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.

Q: How does the "diversity" slider work and why should I use it?

A: 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 they are contained in.

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 they are contained in.

Q: I don't believe you that ownership matters less in smaller contests. Can you prove it?
(Nobody actually asked this question)

A: 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:
*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.

$$ \normalsize \>\>\>\>\>\>\>\> w \cdot \frac{1}{x \cdot (\frac{N-1}{N}) + \frac{1}{N}} - 1 $$

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 How much does ownership matter in this simplified setup? With just 2 players (i.e. a head-to-head matchup), you should

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

To really flush out this point, below I examine a specific scenario. Consider a contest of size

Course Fit:

Q: Intuitively, how do I interpret the radar plot on the course
fit page?

A: 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.

Q: Statistically, how do I interpret the radar plot on the course
fit page?

A: 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.

Q: How do the course fit
plots relate to the variance decompositions shown on the
historical event data
page?

A: 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 form of the variance decomposition will fit intuitively with the form 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!