The Leadoff Hitter dillemma.

[bjkrautk]

I posed a question yesterday in one of the TGJ threads in hopes of starting a dialogue on one of my favorite topics:

 

 

What level of slugging would a leadoff hitter with a .360 OBP need for a team to score the same number of runs as they would on a team with 8 league average hitters?

 

 

Just for argument's sake, I'm going to use the 2006 AL averages as my data-set. (This largely eliminates pitchers batting.)

 

5607 AB, 804 Runs, .339 OBP, .437 Slg. (147 OXS, .776 OPS)

 

I'm going to also assume that the leadoff hitter gets 1/9 of the total ABs for a team. There is some round-off there...it should be a bit higher....but I'm assuming that washes out when the leadoff hitter takes a few days off.

 

(Edit: I'm also going to standardize things by using Expected Runs Created = 830, rather than actual runs...to keep the formula consistent with expectations.)

 

RC = AB * OBP * Slg

830 = 5607 * (8/9 (.339) + 1/9 (.360)) * (8/9 (.437) + x/9)

830 = 5607 * (.3013 + .04) * (.3884 = x/9)

.4337 = .3884 + x/9

.0453 = x/9

x = .407

 

Feel free to re-check the math, but a player with a .360/.407 stat line (146 OXS) in the leadoff spot, surrounded by league-average hitters, would cause his team to score the same number of runs.

 

 

When I posed the question, I suggested that I thought the player's OXS would be below the league average.

 

 

I tend to reject the approach of trying to maximize stat production by simply maximizing OPS at every position individually - you have to make some attempt to view the team's production in the aggregate, IMO, to really determine whether a move benefits a team.

 

A player with a high, consistent OBP is far more valuable, IMO, than the OPS crowd would seem to assume that he is.

 

 

(Note: As I suggested back in the original thread, I'm not going to presume that Gwynn - or any particular hitter - is that consistent, high OBP player.)

[rluzinski]

OPS is a nice rough tool but you are right to point out that OBP is more valuable than SLG, on a point by point basis. A better estimate of offensive prowess would be:

 

OBP x 1.7 + SLG

 

Remember, that works for a team, not just a player (a player's OBP does not interact with his SLG but rather the team's).

[endaround]

Well yes and no. Linear weights tend to act like regressions. Which means that for an average player, say one with an OBP of .330 and a SLG of .440, 1.7 or what have you is the proper weight. Meaning a OBP of .331 is better than a SLG of .441. But when you start to move away from the average player things break down. When you have a Gwynn type who likely has an OBP equal to his slugging, you can't assume 1.7 makes sense.

[sbrylski]

Lineup position affects that number too. I've seen studies suggest OBP is close to 2.5 times as important as SLG out of the leadoff spot.

[bjkrautk]

One of the things I've been meaning to return to ever since posting my little experiment is to note that OXS was virtually unchanged (which makes sense, based on the formula).

 

That being said, the realization that a team will project to the same number of runs, so long as it's individual players maintain a consistent OXS, reminded me of my college economics courses. Not being up on all of my sabermetrics, has anyone ever compared productivity maximization in baseball to Indifference Curves?

 

Conceptually, I can visualize a series of parallel curves on a grid, representing each OXS line (OBP on one axis, Slg. on the other). Adding better offensive players would move the team's production to one of the higher curves (more projected runs scored).

 

Moreover, this model reinforces the conceptual problem that caused me to create this thread in the first place: demonstrating that a shift in the relative contributions of OBP and SLG along an individual curve will result in the team scoring the same number of runs. (Not sure if this helps anyone but myself in conceptualizing the numbers side of baseball....but I'm keen to find out.)