A Nonlinear Draft Strategy

We as humans have a well-documented malfunction that does not allow us to properly understand non-linearity. Several wonderful and influential books have been published over many years across a range of disciplines that all conclude that we expect things to follow a steady trend. Several of these writers posit that it is inherent in our thinking just below the surface and rooted in irrationality that we struggle to fully appreciate. We see symptoms of it throughout industry specific models such as projecting the profitability of a new oil well, the future earnings of a company, or the growth trajectory of a new business. In this article, we’ll explore the expression of linearity bias in baseball statistical projections and attempt to uncover certain players whose potential impact on your fantasy team is not properly explained by these figures. We’ll then generalize individual player analysis to draft strategy and roster construction. Hopefully you find these concepts interesting, informative and applicable to your upcoming draft.


Before jumping in head first, it is essential to think about the typical projections systems that we all use. Whether we create our own forecasts or outsource from our favorite service provider (ESPN, CBS, Yahoo, etc), every draft strategy begin with forming educated guesses about each player’s contribution to the relevant scoring categories in your league. We’ll start by defining fantasy baseball projections. While on the surface this may seem a fruitless exercise, understanding the actual intentions of a projection system is central to our strategy. Let’s start with a basic definition:

Definition #1:

Any given player’s projection represents the author’s expectations of what they will produce in the upcoming season.

While this statement is simple, it’s often exactly what the author is trying to achieve. Many forecasters make projections with the intentions of coming up with an ending point that can be read as expected outcomes. They base these estimates on a wide range of basic or advanced statistics from prior seasons along with any number of external adjustments, such as age, role change, injury history or any number of other factors. Expected statistics for each player, accounting for adjustments, are then sorted using some system (ESPN Player Rater comes to mind) to determine the final expected draft order.

The exercise of ranking players based on a system is certainly useful. It provides us a list, in a quantifiable way, to justify which players we prefer over others. It also easily demonstrates the gaps between any two consecutive players, helping to determine tiers at a position and on the player universe as a whole. Many successful owners enter the draft with exactly this type of list and use it to great effect. Quality projections are often the bread and butter of a winning draft strategy.

However, projections made in this way describe nothing of the confidence of the forecaster. The consideration and likelihood of several potential outcomes are often important considerations for player selection. Recognizing this concept, let’s tweak the definition of projections:

Definition #2:

Any given player’s projection represents the forecaster’s probability-weighted expectations of what they will produce in the upcoming season.

When truly pushed to justify their numbers, most forecasters will say that this definition better describes what they produce. Projections defined in this way represent a range of possible scenarios with a likelihood of outcome assigned to each possible result. The average value of those outcomes, weighted by their chance of occurrence, results in the statistical projections which are again sorted using Player Rater or a comparable service.

There are many advantages of this method over the single projection system first proposed. Firstly, probability-weighted outcomes offer more objectivity than expected results. By construction, they are less reliant on the single forecast and judgment of the individual making the projection. Secondly, the data set of potential outcomes is larger since several scenarios are considered in the estimate for each player. This makes sorting using Player Rater more reliable and allows for greater confidence when making pairwise comparisons between two players. Lastly, external adjustments (e.g. aging, injury, regression) are seamlessly integrated into such a system without forcing the forecaster to take a clear stance on the issue. The single projection system relies on increased subjectivity from the forecaster about key issues (e.g. Bryce Harper will get injured), which can drastically influence rankings.

However, there’s something to be said for using actual expected outcomes rather than a weighted average. The difference is analogous to a weatherman justifying a temperature or precipitation forecast by saying "I don’t actually expect my forecast to happen, but instead I’m giving you the average of all weather forecasts!" This is maddening to some degree since he is replacing his own subjectivity with an estimate that is by construction inaccurate. Perhaps instead we want a certain amount of opinion in our forecasts so that we can achieve a real world outcome while retaining the advantages of the weighted average method.

Lastly, and most critically, neither of these methods imposes any anticipation of the range of potential outcomes for each player. For example, consider Player A and Player B below:

Player A: 89 R, 25 HR, 94 RBI, 8 SB, .280

Player B: 83 R, 27 HR, 97 RBI, 6 SB, .280

ESPN ranks them one spot apart in their hitter rankings, which is completely understandable just given these forecasts. That is, until you consider that Player A and Player B are Josh Donaldson and Albert Pujols who could not have had more dissimilar seasons and carry drastically different sentiments heading into 2014. While the weighted average projection is almost identical for Donaldson and Pujols, the ranges for what these players could produce in the upcoming season contrast dramatically. Hence, selecting either Pujols or Donaldson requires a wholly different strategy throughout the rest of the draft.

It was out of the desire to balance these effects – subjectivity of opinion, probability of multiple outcomes, and range of potential – that my nonlinear draft strategy was born.


The pillars of the strategy are fairly simple but offer one important nuance from standard draft plans. Instead of focusing on your own opinions of each player relative to rankings, the key to this strategy is threefold; (1) understanding what the consensus opinion implies about each player’s value, (2) constructing a roster of players that takes advantage of misconceptions in consensus value, and (3) insuring yourself against key risk factors.

I: Start with the most heavily used rankings system for your particular league.

Chances are in most novice and intermediate leagues, the most trafficked system is that of the hosting platform (ESPN, Yahoo, CBS, etc). These will most likely dictate the baseline projections you should use.

The important part about the consensus ranks is not how much you like them, but rather to understand what the common opinion is about each player. For example, how much of a discount are you getting on David Ortiz based on his advancing age? What kind of a premium must you pay for the potential that Eric Hosmer becomes an elite 1B option? These are the questions that you are seeking to understand going into your draft by assessing the general sentiment on each player.

II: Understand the expected value trend for each player and its justification.

For any given player, does the consensus expect him to improve, worsen, or stay the same, and by how much? What is the main factor you believe to be driving the trend?

While it may surprise you, this step is usually pretty easy. The main factors impacting changes from one year over another are usually some combination of age, pedigree, expected underlying rates, health or external factors (ballpark, lineup, manager, etc). In general, there is one prevailing story involved which is easy to understand. If all else fails and you have questions on the narrative for a player, read the blurb for that player on any of the hosting platforms.

Going back to David Ortiz, ESPN projects him at 80 R, 29 HR, 93 RBI, 2 SB and a .298 batting average, ranking 36th among hitters with an 8.08 score on the Player Rater. Based on his numbers last year when he was 15th on the player rater (with relatively similar numbers to the projection), it would appear that you’re getting a discount on his potential based on injury and age risk. Understanding prevailing sentiment and rank drivers is very important to the upcoming steps.

III: Determine a dream and a nightmare scenario for each player and quantify.

While this stage is very subjective, I would imagine many of our scenarios are fairly similar.

Back to Ortiz.

Last year was about as good as it gets at this stage for Big Papi. He produced 84 R, 30 HR, 103 RBI, 4 SB, .309, which was good for 9.51 units of Player Rater value. A nightmare scenario for him likely involves aging and injury, and might look a lot like his 2012 season (65/23/60/0) in terms of final numbers and his 2008 in terms of bad batting average luck (.238). That’s pretty bad, and would be roughly a ~2.75 player rater value.

IV: Observe how close the projection is to either extreme and imply a projected outcome.

To summarize for David Ortiz

Best: 9.51

Baseline: 8.08

Worst: 2.75

Upside = 9.51 – 8.08 = 1.43

Downside = 8.08 – 2.75 = 5.33

Upside/Downside Ratio = 1.43 / 5.33 = 0.27, or 3.73 for Downside/Upside Ratio.

Implied Downside Probability = 0.27 / (1 + 0.27) = 21.2%

These numbers tells you that in order to justify drafting Ortiz at the ESPN ranking; you must believe that the upside is more than 3.73 times more likely than the downside. Alternatively, the implied downside probability tells us that in order to justify drafting Ortiz at his ESPN ranking, you must believe that there is at most a 21.2% chance of the downside case.

Since I believe neither of these things to be the case, I would argue that Ortiz exhibits negative non-linearity. Based on his draft position and expected outcome, you have to have strong conviction that he has another great season left in the tank at age 38 to justify his draft position in ESPN.


You may realize at this point that there are some important basic assumptions that we have made in the pillars of this strategy. The most important of these assumptions is that the rankings used as a baseline generally define the average perceived value of all players in the league. As you would expect, the accuracy of this assumption will vary directly with the inexperience of the league. Less seasoned players are unlikely to come up with their own projections and will usually stick quite closely to those provided by the hosting platform. For more serious competition, be sure to customize the projections system to those which you believe will be most commonly used by your league.

Related to this point on rankings, we must also rely on our projections to be internally consistent within each position. For example, it is important that the ranks accurately show the 19th best outfielder adding more value to your team than the 20th ranked outfielder. Often times following this assumption requires a slight resorting of the rankings system, but typically most major sites do this fairly well.

Another major assumption needs to be made with respect to the potential downside of players. It is important to recognize that the worst possible outcome a player can have is the expected value of a replacement player on the waiver wire of your league. We use this assumption since rational owners would have the option to release an injured or under-performing player in exchange for the best possible replacement player. For the purposes of this article, I use 2.33 as the Player Rater value of a replacement, or the 277th best player from last season (12 team, 5x5 league and 23 roster spots). Changing the Player Rater value of a replacement alters the downside and should be used to adjust the analysis accordingly should your league settings vary.

There is one last point of note. While upside, downside and baseline forecasts are all done in isolation for any one player we are considering, in the context of the draft, we must constantly make comparative decisions. As players are selected or passed over, our information changes and our perception of value should follow suit. This consideration is extremely important and will be taken into account in our analysis.

Back to David Ortiz for a minute. We have already shown that we have no interest in drafting him as the 36th best hitter (45th player overall) this year. However, suppose he slides in the draft to the point where he is still available at the 80th overall pick. We can alter our analysis by inserting the Player Rater value of the best available player, other than Ortiz, at the same (or similarly deep) position instead of using our original Ortiz projection. Using Jason Heyward as that best available player, for example, we substitute a 7.04 Player Rater rank to obtain an upside/downside ratio of 1.74. While this might imply that drafting Ortiz is still less than ideal, his value at this point is substantially better than it was at the 45th overall pick in the draft. Such considerations are important to bear in mind as your draft evolves.


While David Ortiz is a player whose potential reward, in my view, does not justify the risk, let’s look at some other players which are among my favorite nonlinear options this year at their current ESPN ranking. These five players demonstrate different applications of this strategy at various points of the draft.

Everth Cabrera, SD, ESPN Rank 109

A personal favorite of mine, Everth Cabrera was highlighted entering 2013 by this system as a potential superstar sitting in the latter third of the draft. Out of the gates he broke out in a major way, exceeding even my wildest expectations with a 54/4/31/37/.283 line over his first 95 games. We all know the story from there; Cabrera was suspended for the remainder of the season for steroid use, ruining the fantasy seasons of many and creating a cloud of uncertainty about his 2014 value. ESPN projects that Cabrera will regress to his 2012 statistics and post a 77/2/39/47/.243 line.

Upside: 2013 was more the result of skill improvement than steroid abuse.

Downside: 2012 is closer to the reality for Cabrera.

Projection: 77/2/39/47/0.243 - Player Rater 5.94

Upside: 85/5/50/55/0.278 - Player Rater 9.86

Downside: 70/2/35/45/0.245 - Player Rater 5.41

Upside: 3.92

Downside: 0.53

Ratio: 7.40

Implied Probability: 88.1%

Cabrera provides a unique instance where the ESPN projection is very close to what I believe is a worst case scenario. In your review prior to your draft, be sure to look for these types of cases to extract maximum value from your selections.

Hisashi Iwakuma, SP, SEA, ESPN Rank 123

Iwakuma may not be a name you’d expect to surface using a nonlinear draft strategy. After all, he has shown two sustained seasons of success at the major league level, posting a 2.66 ERA and 1.07 WHIP since being anointed a starter in 2012. However, underlying statistics, such as a low ground ball rate, high strand rate, low BABIP and modest strikeout rate suggest perhaps he’s been consistently lucky rather than especially effective. Compounding the negative sentiment from these peripheral statistics is his preseason finger injury, reports of which currently suggest Iwakuma’s absence until mid-April at the earliest. ESPN projects regression, with 13 W, 166 K, 3.30 ERA, 1.17 WHIP for a perfectly respectable 5.54 Player Rater value.

Upside: Iwakuma continues to out pitch his peripherals and his finger injury costs him minimal time.

Downside: His finger injury lingers or he regresses to an average pitcher.

Projection: 13/166/3.30/1.17 - Player Rater 5.54

Upside: 16/175/2.77/1.07 - Player Rater 8.15

Downside: 10/154/3.75/1.23 - Player Rater 3.71

Upside: 2.61

Downside: 1.83

Ratio: 1.43

Implied Probability: 58.8%

Iwakuma is a case where you have the potential to get ace production at the price of a third tier starter.

Francisco Liriano, SP, PIT, ESPN Rank 197

Since bursting onto the scene at age 23 with a stellar rookie season, Liriano’s career has been rocky to say the least. Following Tommy John surgery in 2007, Liriano produced just one plus year (2010) with the Twins before being dealt to the Pirates in 2012. Liriano has been substantially better with his new team, posting a strong 2013 season with rock solid peripheral statistics to support his performance. Still only 30 years old and with consistent pitch velocities throughout his career, it isn’t hard to believe that Liriano has more production left in the tank. However, ESPN projects him at 11 W, 175 K, 3.80 ERA, 1.32 WHIP for a meager 3.21 value on the Player Rater.

Upside: Liriano continues to produce with his new team, building on his 2013 season.

Downside: Liriano is as fickle as ever and falls below replacement level.

Projection: 11/175/3.80/1.32 - Player Rater 3.21

Upside: 16/217/3.02/1.20 - Player Rater 7.28

Downside: Replacement - Player Rater 2.33

Upside: 4.07

Downside: 0.88

Ratio: 4.63

Implied Probability: 82.2%

The clear ace upside combined with Liriano’s low cost make him an attractive proposition in the draft.

Adam Eaton, OF, CHW, ESPN Rank 207

Eaton is a bit of a unique case. Largely seen as a trendy sleeper selection last year after a stellar minor league career and respectable audition at the show, Eaton dealt with a lingering and difficult preseason injury which cost him the majority of his season. Prior to the season, he was dealt to the White Sox in a somewhat surprising move, casting further doubt on his future prospects. While still young, at age 25, he is no trendy phenom but rather just a steady lead off type with a proven ability to get on base. ESPN projects: 89/8/41/23/.267, for a Player Rater rank of 5.37.

Right off the bat this Player Rater value should tell you something – the projection itself indicates that Eaton is undervalued. A 5.37 unit Player Rater season would have been rank 123, ahead of such higher valued players as Ben Zobrist and Desmond Jennings.

Upside: Eaton plays a full season and reaches his full potential.

Downside: Eaton struggles through injuries and poor performance and falls to replacement level or below.

Projection: 89/8/41/23/0.267 - Player Rater 5.37

Upside: 95/8/50/35/0.295 - Player Rater 9.01

Downside: Replacement - Player Rater 2.33

Upside: 3.64

Downside: 3.04

Ratio: 1.20

Implied Probability: 54.5%

Eaton’s draft position is artificially deflated based on the difference between the implied Player Rater rank of 5.37 and the realized rank of his draft slot in 2013. Eaton is easily a player who won’t cost much on draft day, but could make a huge difference to your team.

Nate Jones, RP, CHW, ESPN Rank 217

Another White Sox player makes the list. No longer particularly young (28) and relatively unheralded, Jones pitched well on the surface in 2012 while seeming to fade in 2013 with a 4.15/1.22 ERA/WHIP over 78 innings. However, delving below the surface, we see a vastly improving pitcher in his age 27 season, as measured by a rising strikeout rate, a falling walk rate and a resulting drastic improvement in FIP/xFIP measures. Jones was handed the closer role by default this year with only marginal experience (12 saves in AA during 2011). ESPN projects Jones for: 5 W, 26 SV, 72 K, 3.26 ERA, 1.25 WHIP, for a player rate rank of roughly 3.82.

Upside: Jones’ season looks a lot like Steve Chishek’s last year, with a few more wins and saves. 5 W, 36 SV, 77 K, 2.33 ERA, 1.08 WHIP. Player Rater Value of 6.87.

Downside: Jones falls to replacement level RP and you ultimately replace him with another closer in waiting.

Projection: 5/26/72/3.26/1.25 - Player Rater 3.82

Upside: 5/36/77/2.33/1.08 - Player Rater 6.87

Downside: Replacement - Player Rater 2.33

Upside: 3.05

Downside: 1.49

Ratio: 2.05

Implied Probability: 67.2%

I believe that most people would agree the upside and downside are close to equally as likely here, making Jones a potential bargain late in the draft.

In each of these cases, I believe the downside to be far less likely than the ratio would imply, suggesting that each of these players offer a potential bargain to their ESPN ranking. Whether you agree with my assessment of each of these five players or not, the framework of analysis is most important and can be applied easily to any player in your draft.


Thus far in our discussion we have focused exclusively on player selection. While player selection is certainly the most important component of a winning strategy, roster construction is not far behind. We all have our personal tilts towards certain player profiles (e.g. rising stars, proven veterans, post injury sleepers), making the way these types interact especially relevant. If we were to select players for our teams without considering the roster as a whole, we could be blindly exposing ourselves to unnecessary and unwanted biases.

In the early rounds of the draft, we typically see players that are proven elite contributors or highly touted upside players that have shown evidence of success at the major league level. Casual fans and baseball executives alike are overwhelmingly positive on these players resulting in a low range of opinion. The typical risk factor for an early round player is injury, the effect of which would be hugely detrimental to your fantasy team. Consequently, I would recommend staying away from the high-risk-high-reward options at this stage (Yasiel Puig, Chris Davis, Albert Pujols to name a few) since the cost of replacement is so high and you will have ample opportunities for upside later in the draft.

We begin to see the player profile shift during the middle rounds. The elite talent is replaced by above average proven contributors and the high upside players have less evidence of major league success. Range of opinion becomes wider, albeit generally positive for all players in this tier. While the range of possible outcomes is highly player dependent, upside and downside are typically close to equal at this stage of the draft. Therefore, we should be looking selectively for nonlinear options (Everth Cabrera and Hisashi Iwakuma were two examples highlighted earlier) while otherwise filling our roster with players that have a lower range of potential outcomes. It is difficult to win the draft at this stage but quite easy to lose it with mistakes.

Moving towards the later rounds we see the player landscape further evolve. Proven players have become increasingly average while we begin to consider aging former stars for our rosters. Prospects remaining at this stage are even earlier along in their developmental curve and often have limited or no major league experience. Range of opinion widens further while many players start to show a greater upside than downside above replacement level players. At this point, I would recommend focusing on profile filling, or selecting players that diversify your strategy from the early to middle rounds. Have higher risk players in the early to middle rounds? Take lower risk players at this point of the draft. Played it conservatively to this point? Take more risk. Just make sure that each player selected at this stage of the draft has that same nonlinear profile that we highlighted earlier. Make sure you do not select a single player where you believe the chances of their downside are greater than those implied by your upside/downside cases.

In the true end of the draft, take a great deal of risk. The difference between the expected value of any given player and a replacement is very low. Therefore, selecting the low-risk-low-reward players of the game that guarantee to offer little value over replacement players is entirely pointless. Use the nonlinear framework to select players which you believe to have the best upside for each remaining selection.


I hope you found this illustration of a nonlinear draft strategy helpful. Many people that I talk to daily about fantasy baseball have excellent knowledge of these concepts but fail to regularly apply them come draft day. Whether you agree or not, hopefully it can be a tool to help you improve certain areas of your draft plan. There are many ways to expand beyond what I’ve written here to further optimize your decision making at each step of the way. While I look forward to your feedback, I don’t look forward to seeing this draft strategy used against me.

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