This is probably too dorky/nerdy/geeky/whatever for almost anyone reading this, but hey, this isn't Seattle MariNERDS for nothing.

Anyway, as some of you know, I like puzzle games a lot. I participate in events like Microsoft Puzzle Hunt and play an inordinate amount of puzzle video games and such. I like to solve puzzles for the heck of it, and I'm usually pretty determined to figure things out.

So, in the midst of attempting to calculate some game-by-game breakdowns for my latest baseball history obsession/project (which I'm almost dubbing "The Truth About Losing Pitcher Mulcahy" in my mind, sort of like my Jack Nabors thing a few weeks ago), I've been reading box scores from the New York Times from the Phillies 1940 season, trying to get Mulcahy's game-by-game log, which means figuring out his earned and unearned runs per game. Sometimes this is really easy, like if (as he often did) he pitched 9 innings and nobody made any errors. Sometimes it's not that simple but the flavor text in the article gives it away by saying when the errors were made.

And sometimes it's nigh impossible to reconstruct the game events at all.

In other words, I've stumbled across a boundless set of baseball logic puzzles. This is both beautiful and frightening.

Currently, I'm puzzling over the box score from a game between the Giants and the Phillies on July 5, 1940 (PDF file, copied from the New York Times archive, I hope I'm not going to hell for this). My goal is to figure out: when did Mulcahy get taken out of the game, and how many earned runs were assigned to him?

Let's see what we know, shall we? I'm going to retype the box score just because I know some of the numbers are hard to read on the original scan, and I'll include the relevant text from the bottom (the fact that there were 4702 paid patrons and 5532 ladies since it was Ladies' Day is irrelevant, I think):

Philadelphia New York

AB R H PO A E AB R H PO A E

Schulte, 2b 5 0 1 0 4 0 Whitehead, 3b 6 1 3 2 1 1

Mueller, rf 3 0 0 1 0 0 Rucker, cf 4 1 1 2 0 0

Marty, cf 4 0 0 0 0 0 Moore, lf 5 2 2 3 0 0

Rizzo, lf 4 1 1 3 0 0 Young, 1b 5 2 2 7 1 0

May, 3b 3 1 1 1 3 0 Danning, c 4 0 1 6 1 0

Bragan, ss 1 0 0 0 0 0 O'Dea, c 1 0 0 1 0 0

Monchak, ss 3 0 1 3 0 0 Ott, rf 4 2 1 3 0 0

Mahan, 1b 4 0 2 8 3 0 Cuccinello, 2b 4 2 2 1 0 0

Millies, c 0 0 0 1 0 0 Witek, ss 4 3 2 1 1 0

Warren, c 4 0 1 4 0 0 Melton, p 5 2 3 1 4 0

Mulcahy, p 0 0 0 0 1 0

L. Brown, p 3 0 0 3 0 1 TOTAL 42 15 17 27 8 1

Atwood ph 0 0 0 0 0 0

TOTAL 34 2 7 24 11 1

Philadelphia 0 1 0 1 0 0 0 0 0 2

New York 2 8 0 3 0 2 0 0 x 15

Runs batted in - Young 3, May, Melton 2, Whitehead 5, Moore 2, Danning,

Ott, Cuccinello, Mahan. Two-base hits - Danning, Whitehead. Three-base

hit - Whitehead. Home runs - Young, May. Left on bases - New York 7,

Philadelphia 8. Bases on balls - Off Mulcahy 2, Melton 3, L.Brown 2.

Struck out - By Melton 7, L.Brown 4. Hits - Off Mulcahy 6 in 1 1-3

innings, L.Brown 11 in 6 2-3. Wild pitches - Melton, L.Brown.

Relevant notes from the flavor text include:

"Young opened fire with a two-run homer in the first inning"

[in the second inning] "Two passes and four singles routed Mulcahy. Three more hits greeted Brown which, with an error, made the Giant total for the inning eight."

"A cluster of three runs came in the fourth, a triple by Burgess Whitehead banging in these three. Whitey also drove two more tallies across in the sixth with a double, his third blow of the day."

"When Brown, along with his catcher, Benny Warren, entered the game in the second..."

Irrelevant notes from the flavor text include:

"Young was so elated over his homer, his third of the year, that on rounding first he tripped and went sprawling inelegantly right in front of all of the ladies."

So, much like a logic puzzle, let's gather facts and try to piece together this crazy second inning and see if we can figure out the earned runs per pitcher. Welcome to my brain, ladies and gentlemen -- it's going to be a bumpy ride, so hang on to your hats!

Firstly, Burgess Whitehead hit in 5 runs -- three in the fourth inning and two in the sixth inning, which we found out in the text. Babe Young hit in 3 runs total, and 2 of them were in the first inning off his home run. If you're looking at the inning-by-inning count of runs...

**Every other run batted in by a Giant batter happened in the second inning**. Namely, RBIs were collected in that inning as such: Moore and Melton both got 2, and Young, Danning, Ott, and Cuccinello each got one.

Secondly, as far as I can tell,

**no plate appearance counts for two outs.**In order for Whitehead to have gotten 6 at-bats, there must have been at least 46 plate appearances by the Giants -- 5 times around the order is 45, and thus his 6th at-bat was a 46th. Well, in 8 innings the Giants were put out 24 times, plus they got 17 hits, plus there was one error, plus there were 4 walks (2 by Mulcahy, 2 by Brown) given them. If you add up 24 + 17 + 1 + 4, you actually get EXACTLY 46. Meaning that the very last at-bat of the 8th inning was Whitehead and he made an out somehow. (He couldn't get a hit then because the double in the 6th inning was described as "his third blow of the day" and the box score shows he only got 3 hits.) They DO list Hit-by-Pitch and Double Plays AND sacrifices and such generally in these box scores, so there just

**weren't any HBP, Sacs, etc**.

Taking that, you know that

**the four men who walked were Rucker, Ott, Cuccinello, and Witek**, because they don't have 5 at-bats each. (Ken O'Dea came in to replace Harry Danning at the plate during the seventh inning or so and managed to get an at-bat.)

Now, let's piece together the first inning to figure out who led off the second inning. Now, here's something interesting. If you make a grid and start filling in frames like a scorecard, you'll see that Moore had to be the batter driven in on Young's two-run homer in the first inning. Why? Because he scored two runs during the game, and there's no way the No. 1 hitter Whitehead could have driven him in during the 4th or 6th inning; it's simply impossible. Therefore, he scored one in the first inning and one in the second. (He can't have scored two in the second. With eight runs scored and three outs, even with three men left on base, that's a maximum of fourteen possible at-bats, which wouldn't get all the way back around to him.)

Okay, so

**in the first inning, Whitehead made an out, Johnny Rucker made an out, Jo-Jo Moore singled, Babe Young hit a home run. Harry Danning made an out**. We know this because Whitehead and Rucker couldn't have also gotten on base or it would have been more than a two-run homer. Harry Danning also made an out -- we know this because he had exactly one hit all game, and he drove in a run -- meaning that hit HAD to come in the second inning. Therefore

**Mel Ott led off the second inning**.

**Mulcahy was taken out after 7 batters in the second inning**. We know this because he is listed as pitching 1 and a third innings, so there must have been one out credited to him. The text in the article says "two passes and four singles routed Mulcahy." Therefore he definitely had to come out before Danning's double. If Ott led off the second inning, then Mulcahy faced Ott, Cuccinello, Witek, Melton, Whitehead, Rucker, and Moore.

Now the question is... how many earned runs were charged to him? And what exactly transpired in that second inning?

The easy answer to the first part is that 8 earned runs were charged to him total. 2 for the first inning, and 6 for all of the runners in the second (since 8 runs were scored, it stands to reason that all of his runners scored). But it's possible otherwise, especially in trying to figure out how that first out happened and also when Brown's error occurred.

And this is sort of where I'm stuck right now. I can't quite reconstruct a plausible second inning. I'm close, but I don't think it's quite right.

I mean, what we know is that in the second inning, Young, Melton, Moore, Danning, Ott, and Cuccinello had RBIs (and also importantly, Witek and Whitehead and Rucker did NOT). And we can also deduce who HAD to score in the second inning:

-- Whitehead, because he is credited with a run but could not possibly score in another inning (he batted in all the runs after the 2nd without a homer -- and he could not have scored on a wild pitch because all the runs are accounted for with RBIs)

-- Rucker, for the same reason. Batting AFTER Whitehead, he could not be batted in during a later inning, and is credited with a run, so it had to come here

-- Moore, same reason as Rucker but credited with 2 runs, one of which happened in the first inning

-- Young, same reason as Moore

-- Witek, because he scored 3 runs, meaning he was batted in this inning and twice by Whitehead's later hits

-- Ott, credited with two runs, could not have scored both of them behind Whitehead's triple and double (do the math, with Cucc, Witek, and Melton scoring 7 runs between them total but only 5 runs batted in by Whitehead in those later innings, even if you gave them all runs in the 2nd that still accounts for 4 out of the 5 runs Whitehead batted in, so only that fifth could have been taken by Ott)

Also, curiously, Danning did NOT score in the second inning, according to the box score. I wonder if the box score was just wrong -- because THAT is the trickiest wrench to deduce.

So, here's the sequence I'm working with right now:

Ott - out

Cuccinello - walk

Witek - walk, Cuccinello to second

Melton - single, batted in Cuccinello and Witek (2 runs so far)

Whitehead - single, Melton to second

Rucker - single, Whitehead to second, Melton to third

Moore - single, batted in Whitehead and Melton, Rucker to second (4 runs)

**Pitching change : Lloyd Brown replaces Hugh Mulcahy.**

Young - single, batted in Rucker, Moore to second (5 runs)

Danning - double, batted in Moore, Young to third (6 runs)

This works out fine so far -- Moore was Mulcahy's last batter and he's scored. Great. Now here's where I run into problems. Danning somehow has to get out before crossing the plate, but Cuccinello has to get an RBI, as does Ott -- but DANNING CANNOT SCORE. So I *think* the following is possible, assuming Ott would get an RBI for a fielder's choice. This also assumes the error didn't actually lead to a run being scored.

Ott - Fielder's choice, Danning out at third, Young scores, Ott to second on the throw home. (7 runs)

Cuccinello - singles, Ott scores. (8 runs)

Witek - reaches base on error, Cuccinello to second.

Melton - makes an out. Inning over.

I think this works for the other innings --

Third inning - Whitehead, out 1. Rucker, walked. Moore, out 2. Young, out 3.

Fourth inning - Danning, out 1. Ott, singles. Cuccinello, singles, Ott to second. Witek, singles, Ott to third, Cuccinello to second. Melton, out 2. Whitehead, triples, bats in Ott, Cuccinello, Witek. Rucker, out 3.

Fifth inning - Moore, out 1. Young, out 2. Danning, out 3.

Sixth inning - Ott, out 1. Cuccinello, out 2. Witek, singles. Melton, singles, Witek to second. Whitehead, doubles, bats in Witek and Melton. Rucker, out 3.

Seventh inning - Moore, out 1. Young, out 2. O'Dea, out 3.

Eighth inning - Ott, walked. Cuccinello, out 1. Witek, out 2. Melton singles, Ott to second. Whitehead, out 3.

To sum up:

Whitehead - 1st: out. 2nd: single, run. 3rd: out. 4th: 3-RBI triple. 6th: 2-RBI double. 8th: out. 6 AB, 1 R, 3 H, 5 RBI

Rucker - 1st: out. 2nd: single, run. 3rd: walk. 4th: out. 6th: out. 4 AB, 1 R, 1 H, 0 RBI

Moore - 1st: single, run. 2nd: 2-RBI single, run. 3rd: out. 5th: out. 7th: out. 5 AB, 2 H, 2 R, 2 RBI.

Young - 1st: 2-RBI home run. 2nd: RBI single, run. 3rd: out. 5th: out. 7th: out. 5 AB, 2 H, 2 R, 3 RBI.

Danning - 1st: out. 2nd: RBI double. 4th: out. 5th: out. 4 AB, 0 R, 1 H, 1 RBI.

O'Dea - 7th: out. 1 AB, 0 anything.

Ott - 2nd: out. 2nd: RBI FC, run. 4th: single, run. 6th: out. 8th: walk. 4 AB, 2 R, 1 H, 1 RBI.

Cuccinello - 2nd: walk, run. 2nd: RBI single. 4th: single, run. 6th: out. 8th: out. 4 AB, 2 R, 2 H, 1 RBI.

Witek - 2nd: walk, run. 2nd: Error. 4th: single, run. 6th: single, run. 8th: out. 4 AB, 3 R, 2 H, 0 RBI.

Melton: 2nd: 2-RBI single, run. 2nd: out. 4th: out. 6th: single, run. 8th: single. 5 AB, 2 R, 3 H, 2 RBI.

Mulcahy 1.1 IP, 6 H, 8 R, 8 ER, 2 BB, 0 K, 1 HR.

Brown 6.2 IP, 11 H, 7 R, 7 ER, 2 BB, 4 K, 0 HR.

So, um, if you happen to have access to play-by-play data from this game and want to back me up on my reconstruction of the game, [Lumbergh]that'd be greeeeeeeeeeat[/Lumbergh]. For now, I'm going to sleep, because I've been thinking about this too much. I may or may not edit this down in the morning; I really just wanted to do a brain dump of it all, because dang, my brain's about to explode.

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