Most content on the website will be updated by Monday morning of each week. The Scratch Tools will be updated as fantasy salaries and betting odds are released on Monday. For major championship weeks, the entire site will typically be updated by Sunday night.

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.

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.

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. 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.

If you would like a detailed 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). 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 (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.

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.

There are several differences between the skill estimates listed on the rankings page and those used in other places around the site. 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. Conversely, the skill estimates used to generate finish and matchup probabilities incorporate a golfer's past performance by strokes-gained category, and also some course-specific adjustments. These additional factors are included because they (slightly) improve the quality of our predictions; for example, we know that some strokes-gained categories are more predictive than others (e.g. off-the-tee play is more predictive than putting). To get a sense of how much these adjustments matter in any given week on the PGA Tour, check out the handy skill decomposition page. The 'baseline' column on this page contains the estimates used to generate our rankings.

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.

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).

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 is 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. On our performance table, we include this version of true expected wins — i.e. the probability of winning an average PGA Tour event — and also another version: expected major wins. As the name suggests, this measures the likelihood that a given strokes-gained performance would be good enough to win a major championship. Continuing with our example above, a performance that is 3 strokes better per round than an average PGA Tour field (in the year 2000) would be expected to win a major just 10% of the time; that is, 0.10 expected major wins.

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.

This question will be explored in more detail in an upcoming blog. For now, the answer is simply 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. Again, this will be flushed out in detail in an upcoming 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. Currently, for example, at least an 8% edge (updated June 24th, 2020) is required to take a matchup or 3-ball bet; in the past, this threshold was only 3%. 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 3%, 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).

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.

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!