Wrong.
You have to build your roster according to certain constraints; you need to fill out specific positions. Only your bench (and utility/corner infield/middle infield/undifferentiated pitcher spot, if you have these) have even the slightest bit of latitude in how they can be filled. This means that, at some point, you have to take a player because of his position and not because he has the most value of anyone left.
This leads to only one conclusion: drafting is about minimizing inefficiency, and not maximizing efficiency. That is, in a draft your strategy has to hinge on giving away as few potential points as possible when reaching for a player, and not on gaining points on having a player fall to you (though that can and will happen).
For there to be even the possibility of having player A fall to you at a spot below his value, someone has to make a pick where that person takes another player (who is not player A) at a spot above his value. At some point, someone has to make an inefficient pick. And everyone will have specific needs to fill at various points during the draft. So at some point, everyone will make an inefficient pick. The question then becomes how you can manage that inevitability in the best possible way.
Again, this is best illustrated using an example. I'll do so using the draft strategy I laid out in my rankings post here. To recap, it's a points league and rankings were made by averaging total projected points rank-order (off ESPN's 2011 rankings) and adj. PAR rank order and sorting. Adj PAR and the scoring system for the league are detailed in the post. Though I'm using my points league as an example, this will work for any points league or any roto league with similarly-generated rankings.
Let's assume you have what many consider the best spot in a 10-team snake draft, which is the 10th pick in the first round. That means you pick back-to-back in odd-even rounds, ending up with (using the 23 round draft I did) picks 10, 11, 30, 31, 50, 51, 70, 71, 90, 91, 110, 111, 130, 131, 150, 151, 170, 171, 190, 191, 210, 211, 230. Assuming everyone picked according to those rankings (i.e. perfectly efficiently) and without regard to position, here's the team you would end up with:
Evan Longoria (3B), Felix Hernandez(SP1), Andre Ethier(OF1), Justin Verlander(SP2), Jayson Werth(OF2), Roy Oswalt(SP3), Ben Zobrist(2B), Stephen Drew(SS), Chris Young(OF3), Ian Kinsler(Util), Paul Konerko(1B), Colby Lewis(SP4), Jason Bay(OF4), Mike Stanton(OF-Bench), David DeJesus(OF-Bench), Ricky Romero(SP5), Colby Rasmus(OF-Bench), CJ Wilson(SP-Bench), Derrek Lee(1B-Bench), Randy Wolf(SP-Bench), Jeremy Hellickson(SP-Bench), Edwin Jackson(SP-Bench), Chris Ianetta(C).
This is actually one of the more complete teams you can get in this fashion, but there are still no RPs on the roster. Moreover, even if the picks are "perfectly efficient" relative to the rankings, they're inefficient for roster completion. Mike Stanton may be the appropriate pick in round 14, but he's going to sit on the bench inactive most weeks (since he's the 5th best OF you drafted) while players who could be active (such as an SP, RP, or C) are passed over. In fact, catcher Matt Wieters is ranked one spot below Stanton and well above Ianetta in the position rankings. In fact, Ianetta shouldn't be starting since he's the 13th best catcher in a 10-team league; be it as it may that he's the 230th ranked player. So shouldn't it be better to draft Wieters instead of Stanton/Ianetta? Moreover, you are going to have to draft those RPs at some point. So where should you do it?
There are several ways to go about this. The easiest way, though, is to calculate a metric that quantifies the cost or benefit of picking a player at an inappropriate spot (either too low or too high, respectively). Ideally, this would be interpretable as points. But since the rankings are based on both xPts and adj PAR, that's difficult and time consuming. Besides, there is a simpler way instead.
At the center of the question is where a player is actually going to be picked (aPk) versus where a player is expected to be picked based on the rankings (xPk). So the starting point for the analysis is simply aPk-xPk. If you're reaching for a player lower in the rankings, then aPk is smaller than xPk, and the value is negative (since the player should have been taken later). If a player is falling in the draft, then aPk is larger than xPk and the value is positive (since the player should already be off the board).
But calculating a simple difference isn't enough. Reaching for a player when there are many needs that can be filled (and therefore more players who could fit on your roster) makes less sense than reaching for a player because a specific need has to be filled (when there are fewer such players). The first scenario is more likely to happen early, while the second is more likely to happen later on. This means the difference needs to be scaled somehow. This scaling can be done using either xPk or aPk. xPk is a constant, and so the value wouldn't scale enough based on the degree of the reach. To put it another way, if I take the 200th best player with the first pick, that is an incredible reach. If I take the 10th best player with the same pick, it's less of a reach. But if I divide by xPk, the two values end up being very similar. If I divide by aPk, they won't be; reaching for the 200th ranked player will result in a more negative value.
So right now, we have (aPk-xPk)/aPk. This is the ratio of picks reached to the expected pick for any given player. This is OK enough, but it has one serious flaw. In a 10-team league, the top 10 players are all first round draft picks. If I take the 10th best player with the 5th overall pick, I may have bypassed better players but I'm still taking a 1st round talent. If I take the 100th best player with the 50th overall pick, that's a much bigger stretch. But if I calculate the cost of both reaches using (aPk-xPk)/aPk, the values come out the same.
The solution to this is to convert aPk in the denominator into some approximate indicator of the round the pick is in. The simplest way to do this (without actually labeling each pick with a round manually) is to add ten and divide by ten [(10+aPk)/10]. This yields a number where the round is to the left of the decimal point, and the pick within that round is to the right. As an example, the 8th pick in the 6th round is pick #58, and gives a value of (10+58)/10= 68/10= 6.8. This is a good number to use, because most of the value is contained in the round of the pick, but there is some small variation based on where in the round the pick is located. Moreover, the earlier the round is the more the location of the pick within the round matters. Since extra points are more scarce on the top end, using the early picks efficiently matters more.
(The exception to all this is the last pick in each round, which instead becomes pick 0 of the following round; i.e. the 10th pick of the 6th round is 7.0. This makes sense since the same player picks back-to-back when one round ends and another begins; the person who has the 10th pick of the sixth round also has the first pick of the seventh round. The former pick can be reinterpreted as a pick before the seventh round starts, or pick 0 of round 7)
Using this round approximation yields a formula of (aPk-xPk)/ (.1(10+aPk)). Written another way, that's 10[(aPk-xPk)/(10+aPk)]. Using our earlier example, taking the 10th best player with the 5th pick gives us a value of 10(5-10)/(10+5) = 10(-5)/15 = -3.3333. Taking the 100th best player with the 50th pick gives a value of 10(50-100)/(10+50) = 10(-50)/60 = -8.33333. Thus, reaching five rounds for the 100th best player is far worse than taking the 10th best player earlier than expected in the first round.
This formula doesn't translate strictly into points, or adj PAR, or any such metric. It's essentially a scalar value of the degree of penalty/benefit from a certain pick.
So what does this formula tell us? Mostly, it tells us that reaching for players in the early rounds is disproportionately costly relative to the size of the difference in picks. The denominator for those calculations is going to be small, so even small reaches will be costly. Conversely, a player who drops even a little bit early on gains disproportionate value from the drop for the same reason. So early in the draft, when your roster is still relatively open and there are many needs to be filled, the best strategy is to draft the best player left as per your rankings. Even if you have to draft a player who will sit on the bench, that player's value as a trade chip is likely greater than the penalty you'll amass reaching for a need.
Using my draft as an example, there were two early one-pick reaches. Hanley Ramirez was drafted #2 overall (ranked #3), and Ryan Braun was drafted #6 overall (ranked #7). The calculated penalty was -.8333 for Ramirez, but only -.625 for Braun. Even later in the first round, the penalty for reaching one pick drops substantially (about 25%). As the rounds progress, the penalty for a single pick of reach decreases. In the 14th round, Daniel Hudson went one pick early at a cost of -.068 (about one-tenth the Braun pick). To amass a penalty similar to the Braun pick in the 14th round, you have to reach roughly 10 picks (or one full round).
When "early in the draft" stops being the case is a matter of preference, but I would argue it's not good to reach for need by more than a few picks in the first five rounds at least, and probably the first ten. Since the cost calculated doesn't have a direct translation to VORP, adj. PAR, or points, there is no hard-and-fast rule about when a reach is worth making. It's simply a matter of assessing the size of the cost, the players involved, and deciding if it's worth it or not.
Circling back to the example from my draft, taking Wieters instead of Stanton yields a penalty of -.071, which is probably small enough to be worth the reach- especially because Wieters has a positive VORP for a catcher, while Stanton has negative VORP for an outfielder. Stanton will still get more points, but Wieters is worth the pick. This is especially true since Ianetta- the catcher taken instead- has a slight negative VORP himself (-.072) for a catcher.
Whether or not a reach is worth it also depends on how much the other people in the draft have been reaching with respect to your rankings. If they've been reaching a lot, then a reach for you (while still negative) is less bad than if everyone is drafting efficiently, since they will still have more accrued cost than you do from those picks.
It's possible to keep a running spreadsheet in Excel of exactly how much each player has cost himself with a reach or gained by picking a player who's fallen a few spots. Chances are, though, that the draft will pass by too fast to keep that updated in real time. Instead, the best bet is to make a quick note on paper each time someone significantly reaches for a pick (or has a player fall), the number of picks difference between the expected and actual pick, and the actual round of the pick. This is more crucial early, of course, and the later it gets the larger the difference has to be for it to be worth noting without falling behind on the action. You can then keep in mind a rough idea of how much each team has cost itself in picks and keep your value below that.
I've made occasional references to picks gaining value when a player falls in the draft, and that's important. But it's also something no one really has a problem with; taking a player you like who is still hanging around is an easy decision. Reaching for a need is a tougher decision, and that's where the analysis comes in more handy.
This is also especially useful in situations where the draft software (assuming the draft is online) ranks players differently from your rankings. For example, ESPN drafts always have players ranked by the ESPN standard rankings, which are calculated under the assumption the league is 5x5 rotisserie scoring. Even people who have done serious prep and have their own rankings will tend to follow the order given to them more than they should. This will allow you to use a pick on a low-cost reach by these calculations, comfortable in the knowledge that you can gain back value with another player who will fall instead.
**Update**
It's important to note that this formula is non-identical. That is, the aggregate value of taking the #2 ranked player first and the #1 ranked player second does not equal zero. The formula has a tendency to skew negative instead, with the cost of reaching for a player generally exceeding the benefit of taking a player who falls in the draft. Taking the #2 player first overall yields a value of -10/11, while taking the #1 player second yields a value of 10/12.
This means that, while the formula is good for any given pick, or comparing any given set of picks in cost, it does not work over the course of an entire draft. In the above scenario, the player picking at #3 has the expected set of players to draw from, so he cannot gain value with his pick. However, the draft overall at this point has a negative scalar inefficiency value. I hope to figure out how to remedy this at some point (ideas I've tried so far that work for small differences like the one above break down for larger differences), but for now this is what I have to work with. It's not ideal, but at this point when going through a (theoretical) draft it is best to simply assess the situation as is (i.e. if the top ten players are off the board with the first ten picks, then the aggregate scalar inefficiency to that point is best ignored no matter how inefficient the picks have been).
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