Is it possible to draft aggressively?

Drafting in a snake format is, by and large, a passive affair. The only true action is the first pick in the draft, since every pick after that is at least partially conditional on the pick(s) made before. Who you choose with the third pick depends on who is there after the first two picks, and who is there at the second pick depends on who is chosen first. You may think you've acted in taking Hanley Ramirez second overall among the alternatives, aggressively filling a need at shortstop. But, if Albert Pujols were still there with the second pick, would you still draft Hanley Ramirez even if he were still available? I would guess not.

But, within these constraints, is it possible to draft aggressively? That is, can you make a draft decision that forces other people to change their strategy and/or alter the value of their picks?

To that end, one possibility easily comes to mind: drafting your utility player early. As I said inmy post on calculating value, in a 10-team league there are ten starting players each at first, second, third, short, and catcher (since everyone plays multiple outfielders, it's difficult to accomplish this task using the outfield position). Drafting an extra player from the top ten at one of these positions to put in your utility spot changes this equation, though. When such an action occurs, a player who was originally below replacement now has to be drafted into a starting spot.

This clearly puts the person who gets stuck with this player at a disadvantage. But, because this player must be drafted and started, it also changes replacement value. If someone drafts two of the top-10 second basemen, the #11 second baseman is now a starting-caliber player instead of a top reserve. This means replacement value, which is calculated using the last two rostered players and the first two reserves, is now the average of the #10-13 players instead of #9-12. This will lower replacement value by some amount a. Lowering replacement value raises adj PAR. The change in adj PAR is calculated thus (x is projected points, r is pre-draft replacement value, and a is the change in replacement value from drafting a utility player):

This simplifies into the following formula:

If adj PAR rises enough then his adj PAR ranking (relative to the remaining players available) will rise. If the adj PAR ranking rises, then the expected draft position (calculated by averaging adj PAR ranking and total points ranking) rises as well. Because you've increased the scarcity of this position, you've changed the dynamics of the draft. It may be by a little or a lot, but the dynamics have changed.

One more thing to note- the change doesn't just happen within the position. Overall draft rankings are created by averaging adj PAR rankings and total points rankings. If you change the adj PAR for one position, you change the adj PAR rankings of every remaining player. This creates a ripple effect that changes the averages, and therefore the order, of the entire rest of the draft.

You can maximize the change in rankings the following ways. First, choose a position where many of the remaining players are further down in the rankings of players left. If a player is near the top of the rankings of players remaining, then there's nowhere for him to rise to. More valuable players will see a greater increase in adj PAR, since the amount of change is directly proportional to the square of expected points. But these players are more likely to be near the top of the rankings of players left.

Second, the shallower the position, the greater the increase in adj PAR. Adj PAR has an inverse relationship with the square of original replacement value [r(r-a) = (r^2)-(a*r)]. Therefore, shallower positions will see a greater increase in relative value among the remaining players. This has to be balanced with the fact that you may be getting fewer total points from a player by drafting out of a shallow position.

Last, adj PAR increases more the larger the difference in replacement value you create. The difference is a positive multiplier in the numerator and subtracted out in the denominator, so as a increases the numerator increases and the denominator decreases.

Here are the a-values for the first utility pick at each position (using ESPN's 2011 projections):

Catcher: 5.75

First Base: 4.5

Second Base: 3

Third Base: 5.6

Shortstop: 3

Now, every way to maximize the advantage of this move has a counterpoint that could hurt you. You are likely to get fewer total points drafting a second player out of a shallow position as opposed to a deep one. Players in deep positions, being more likely to have more total points, will see a greater increase in adj PAR, but they are already likely near the top of the remaining players. So the best position with which to do this has a) low replacement value, and b) a top-heavy skew in the distribution.

This sounds an awful lot like catcher.

Replacement value for a catcher, pre-draft, is 398.5 points, the worst among hitters. It's top-heavy, with the top two catchers ranked #23 (Mauer) and #30 (Victor Martinez) overall in total points, and gets very bad in a hurry. In fact, the rest of the position looks like this (overall point ranking in parenthesis): McCann (96), Posey (97), Santana (111), Suzuki (121), Wieters (181), Montero (188), Yadier Molina (195), Jaso (207), Soto (235) and Ruiz (241). The a-value for taking an extra catcher is 5.75, highest among the five relevant positions.

Well mock this possibility up in a subsequent post, but first I'd like to roll out another example. This actually happened twice in the first five rounds in my draft. One owner took first basemen with back-to-back picks in the first and second round, and then I took a second third basemen in the fourth round after taking one in the second round.

The first 11 picks of the draft went like this: Pujols, Hanley Ramirez, Crawford, Cano, Longoria, Braun, Tulowitzki, Carlos Gonzales, Cabrera, Fielder, Adrian Gonzales. So the same owner drafted Fielder and Adrian Gonzales, leaving (since Pujols and Cabrera were already drafted) seven owners competing for six above-replacement first basemen. Now, I think Votto or Teixeira would have been a better choice than Fielder, but a) the quantitative effect on whomever remains is the same so long as both players are above-replacement, and b) there's no dissuading a Brewers fan from drafting Prince Fielder.

Here's how the next handful of first basemen ranked overall before the draft as compared to after the pick:

Texeira (#22 pre-draft, #22 post-pick)

Votto (#25, #23)

Youkilis (#35, #31)

Butler (#41, 41)

Carlos Lee (#84, 82)

Dunn (#92, #88)

Gaby Sanchez (#100, #97)

Ryan Howard (#101, #98)

Paul Konerko (#110, #105)

Justin Morneau ( #118, #107)

James Loney (#126, #114)

There wasn't much change, but players did move up; this effect was greater as the players dipped below replacement value. This is, of course, is in part due to the fact that a) the remaining top-4 had little room to move, and b) many of them are closely clustered in value. And the optimal next ten picks, instead of looking like this:

Halladay, Holliday, Felix Hernandez, Mauer, Pedroia, Victor Martinez, Cliff Lee, Tim Lincecum, Andrew McCutchen, Ryan Zimmerman.

instead look like this:

Halladay, Holliday, Mauer, Felix Hernandez, Pedroia, Victor Martinez, Andrew McCutchen, Cliff Lee, Ryan Zimmerman, Tim Lincecum.

It's not a large change, but the ripple effects of selecting a utility player early are noticeable right away.

After I picked in the fourth round of the draft, there was a similar situation with third base. With Longoria, Wright, Zimmerman, Alex Rodriguez Bautista, and Beltre off the board, five teams were competing for four above-replacement third baseman. Here's how the next handful of third baseman stack up in overall rank pre-draft, after the Fielder/Gonzales duo, and after the Beltre pick:

Casey McGehee (#73 pre-draft, #63 after Fielder/Gonzales, #71 after Beltre)

Michael Young (#75, #65, #76)

Placido Polanco (#95, #85, #96)

Miguel Tejada (#96, #86, #98)

Pablo Sandoval (#99, #91, #101)

Jhonny Peralta (#163, #140, #150)

Aramis Ramirez (#166, # 151, #155)

Pedro Alvarez (#174, #156, #162)

**Update**

(Initially, I really screwed this part up. Below is the corrected version)

After (if not because of) the Beltre pick, the rankings of the remaining third basemen were re-depressed with respect to the beginning of round two. I would argue that this is due to the fact that, at pick #37, the draft had proceeded relatively inefficiently. That is, after 37 picks there remained a full seven players available who should have already been drafted. By contrast, after the Gonzales/Fielder picks, there were only three players out of eleven who should have been drafted. The less efficient a draft has been up to that point, the less the effect of a utility pick.

The simple reason for this is any player who remains but should already be off the board has disproportionately high value, and so should be picked next regardless of any change in positional scarcity. As an example, here (using pre-draft rankings) are the expected 38-50 picks (x indicates a player already drafted by that point):

Prado, Cruz(x), Reyes, Butler, Huff, Kershaw, Delmon Young, Haren, Alex Rodriguez(x), Tommy Hanson, Vernon Wells, Greinke, Werth.

Using the pre-draft rankings, here are the expected 38-50 picks after the draft started to unfold (y indicates should have been picked before):

Victor Martinez(y), Victorino(y), Etheir(y), Verlander(y), Markakis(y), Pence(y), Ichiro Suzuki(y), Prado, Reyes, Butler, Huff, Kershaw, Delmon Young

That's a full half of the picks. Those seven players will top the rankings of remaining players either way. Any ripple effects will only be apparent after the players who have fallen are off the board.

Put another way, let's look at the aggregate scalar inefficiency value of players left on the board who should have been taken. We'll assume aPk is the next pick after the utility pick, which is #12 for the Fielder/Gonzales picks and #38 for the Beltre pick. At pick #12, the players left who should have been taken are (scalar inefficiency value in parentheses):

Roy Halladay (6.667), Matt Holliday (4.667), and Felix Hernandez (0.455).

The players at this point who should not have been taken are (scalar inefficiency calculated at #12 again) are:

Prince Fielder (-7.73), Carlos Gonzales (-2.73), and Tulowitzki (-0.455)

Aggregating the values (sum of players who fell minus sum of players who were picked early), we get a value of about 22.704.

By contrast, after the Beltre pick (#38), here's the values of the fallen players left:

Victor Martinez (6.05), Victorino (3.68), Ethier(2.11), Verlander(1.84), Markakis (1.32), Pence (0.53), Ichiro Suzuki (0.26)

And here's the value of the players who should have been left:

Chase Utley (-40.833; that's what ignoring an injury gets you), Alex Rodriguez (-1.667), Josh Hamilton(-5.0), Matt Kemp(-3.125), Ryan Howard(-13.125), Justin Upton(-2.92), Nelson Cruz (-0.208).

Aggregating the same way as we did before, we get a whopping 82.665 for our scalar inefficiency value. The way other teams used their picks was so glaringly inefficient that it dwarfed any effects of changing replacement value.

So is it possible to draft aggressively using the utility spot? Yes, but only to the extent that people are drafting efficiently. If people are letting players fall relative to their rankings, then the benefit of drafting those players greatly outweighs any possible benefit of drafting a utility player. The more inefficient the draft, the less the relative value of changing replacement level at a position.

It's also worth noting that the other league members have to respond to this aggressive pick. If they don't then the only effect is someone drafts a below-replacement player at that position. The benefit, however, is that if they take note of it (in a naive, intuitive way since they're not doing these actual calculations) you create a different set of rankings for the other members, while you can follow the original rankings. This inefficiency is something that can then be exploited to your benefit in the draft.

Given all of these conditions, it is likely best to draft a utility player early only if he is among the top players left in your rankings and none of the other players around him fill a need or you have concerns about them. The potential benefit is relatively small, and the draft is likely to have plenty of inefficiencies due to players falling, so the change in the rankings is more of a side benefit of being able to draft a utility player rather than a sound strategy in and of itself. You may still leave yourself with a valuable trade chip, especially at a shallow position, so it's not necessarily a bad strategy. It's just that the strategy doesn't have a big enough impact to seriously consider in most cases.

Later, I'll mock up what is likely the best-case scenario for this: drafting both Mauer and Victor Martinez early in a fairly efficient draft.