just last friday we were playing with a gizmo called steve's lineup toy; by saturday there was a new, better lineup toy to tinker with. this one, another of david pinto's many gifts to the baseball universe, is called Baseball Musings Lineup Analysis. it's similar to steve's lineup toy but more versatile, as i'll illustrate forthwith.

let's begin by taking the lineup that steve's lineup toy recommended:

eckstein, ss
encarnacion, rf
pujols, 1b
edmonds, cf
rolen, 3b
spivey, 2b
bigbie, lf
molina, c
pitcher

per steve, that batting order should generate 5.1 runs per game (i erroneously reported 4.8 runs/game last week; oops). but as i noted in friday's post, that result means nothing because it's based on player stats from 2005 -- and more than half the stl regulars had aberrant numbers (relative to their career norms) last year. david eckstein outslugged scott rolen in 2005, and larry bigbie lagged abe nunez by 40 points in obp; neither of those things is gonna happen again.

pinto's toy, thankfully, doesn't confine us to last year's numbers; you get to plug in whatever batting stats you want. so i typed in PECOTA projections for 2006 and ran them for the st louis lineup recommended by steve's toy. per pinto's gadget, with new and improved stat lines, that lineup would be expected to produce . . . . 5.0 runs a game. almost exactly the same as the projection based on 2005 numbers.

how far can we trust that estimate? as a check, i input the 2005 cardinals' stats by batting-order slot -- e.g., the cards' #6 hitters posted an aggregate .265 / .318 / .389; their #7 hitters put up .308 / .362 / .436 -- and ran the program to see how close it came to the cards' actual 2005 scoring average of 4.97 runs/game. the answer: 4.90, a variance of 1.4 percent. that's pretty damn good, but the difference still amounts to 12 runs over the course of a year -- which is worth more than a win in the standings. so the prudent reader will consider all the figures in this discussion as midpoints of a range -- estimated averages, give or take ~12 runs.

what happens if we move larry bigbie into the #2 hole -- as derrick goold persuasively advocated over at Bird Land this weekend -- and drop encarnacion to #6 and spivey to #7? no change, per this instrument: 5.0 runs / game. how 'bout (my own preference) we put edmonds in the #2 hole, with rolen hitting 4th and encarncion 5th? still no change: 5.0 runs a game. seems like it doesn't matter how you line these guys up, they score 5.0 runs a game. . . . well, that is, unless you line 'em up like this:

pujols, 1b
edmonds, cf
molina, c
rolen, 3b
bigbie, lf
encarnacion, rf
spivey, 2b
pitcher
eckstein, ss

this, according to pinto's toy, is the best way to order the cardinal hitters. the toy says that lineup would produce 5.2 runs a game, or 30 runs a season more than the other, more orthodox permutations. would you not love to see -- just once -- TLR trot that lineup card out to home plate? (and if any manager in baseball is nutty enough to do it, it's tony.) even if the cards got shut out, it'd still be worth it, if for no other reason than to hear shannon run through it during the pre-game. ("well folks, you'll never guess what ol' tony's got up his sleeve tonight.")

there's a bunch of math behind this madness; for those so inclined, you can get it from two posts (one and two) by cyril morong at SB Nation brother site Beyond the Boxscore. (dan scotto's saturday followup at BtB is also illuminating; or go back to this old retrosheet study for add'l discussion in this vein.) the basic rationale, as far as i can understand it, is this: you score the most runs if you a) get your best hitters the most at-bats possible -- hence they bat 1st and 2d -- and b) you keep your two worst hitters as far apart in the lineup as possible, in this case batting 3d and 8th. you cluster your best remaining hitters in slots 4 through 7 -- but you reserve a good OBP guy to bat 9th, to set the table for your 1-2 hitters when the lineup turns over. if we consider the pitcher to mark the endpoint of any (nat'l league) batting order, then this crazy lineup really functions like this:

eckstein, ss
pujols, 1b
edmonds, cf
molina, c
rolen, 3b
bigbie, lf
encarnacion, rf
spivey, 2b
pitcher

it's just that the cycle doesn't start at the top. it starts at station #2.

as crazy as the idea sounds, i actually like it; indeed, i endorsed something only slightly less weird at my old blog roughly one year ago -- to use larry walker as a leadoff hitter. my reasoning:

walker, rf
pujols, 1b
edmonds, cf
rolen, 3b
sanders, lf
grud'k, 2b
molina, c
pitcher
eckstein, ss

-- would have scored 5.3 runs a game, based on 2005 stat lines. the standard lineup (eckstein, walker, pujols, etc.) scores an estimated 5.2 a game, per to pinto's toy. that's a 16-run bonus -- and consistent with the result james click of baseball prospectus got last winter when, at my request, he ran some simulations to compare the walker-led lineup to the eckstein-led one.

again, this strange lineup isn't nearly as radical a departure as it first appears. if you look closely, you'll see that the walker-led alternative is identical to the standard batting order -- it simply begins at station #2, as i described above. to quote myself from the old blog:

as much as i enjoy exercises like this, i gotta take 'em with a grain of salt. as i like to say (but haven't said in a while), ballplayers are not strat-o-matic cards; you can't just shuffle them around at will with changing their properties. the strat-o-matic jim edmonds v2005 is gonna slug .533 no matter what, but would the real-life version do the same if -- referring to the lineup that pinto's toy recommends for 2006 -- he had molina batting behind him all the time? ref'ncing the same lineup, would albert post the same obp and slg if his first at-bat in every game came with the bases empty?

i believe managers for no-chance-to-win teams have a duty to help us build up some real-life data in this regard. (clint hurdle, joe maddon, joe girardi -- are you listening?) they should be obliged (by order of the budly one) to write out a conventional lineup for 81 games a year and, for the other 81 games, to use the lineup recommended by pinto's toy. we'd quickly learn whether the funky lineups actually gets better results; for that matter, we'd be able to test cyril morong's underlying theories vis-vis the interrelationships among batting order slots.

here's one final tidbit: if you remove sanders, walker, and grud'k from the standard 2005 lineup and replace them with encarnacion, bigbie, and spivey, your production per pinto's toy falls from 5.2 runs a game to 4.8. ouch. that's 65 runs over the course of the season, 6 to 7 wins in the standings. . . . . but just remember: it's only a toy. it's only a toy. it's only a toy.