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GripHoldOn · Posted: Mon Sep 05, 2005 8:17 pm Post subject: Tricky Math Question

A baseball player named Tony is fortunate enough to be the starting first baseman for a team that advanced to the World Series. Tony had a better batting average than the backup first baseman, Elmer, throughout the regular season. So for that reason Tony assumed he'd be starting over Elmer in game 1 of the World Series. He goes too look at the starting lineup, and sees that Elmer is starting game 1. Feeling a little upset, Tony goes to the manager and asks him why he isn't starting. The manager says, "We are facing a lefty in game 1, and Elmer had a better batting average against lefties than you did during the regular season."
This seemed fair to Tony. After all, Baseball is a game of averages. Tony knew that in a righty was scheduled to start game 2 for the opposing team, so he assumed that if he didn't start game 1, he would definitely be starting game 2. He looked at the starting lineup card, and again he saw Elmer's name in place of his. Again he went to the manager and asked why he isn't slated to s tart game 2. The manager replied, "Elmer had a better average against righties than you during the regular season, so we're starting him against the righty."

Now Tony was a little confused. Is this situation possible? Can you help him out?

capt midnight · Full House Joined: 24 Aug 2005 Posts: 179

i dont think so

Zuchov · Royal Flush Joined: 29 Jun 2005 Posts: 646

Sidearm pitchers? Or is the manager including the other guy's post season averages too?

TribeLife05 · Three of a Kind Joined: 31 Aug 2005 Posts: 77

yea tony obvisously either didnt play in the regular season or played very few games and did at least halfway decent those few games... batting maybe .350.... while Elmer played most of the time and was just average batting around .300

TribeLife05 · Three of a Kind Joined: 31 Aug 2005 Posts: 77

tony may have been out for some time because of injury also

BLS99 · Straight Joined: 28 Aug 2005 Posts: 108 Location: MA

This is a good one Grip. Can you tell me if the trick is in the wording of the question or in the math? I have yet to find a way that Elmer could be better than Tony against RHP and LHP and still have a lower average than Tony on the season. There has to be a trick to the calculations. I know that you would not average the averages, but rather add all hits and divide by at-bats. The trick might be in that baseball has some unusual ways of scoring and keeping stats...like a walk is not an official at-bat. I'm getting nowhere...anybody have a clue?

Zuchov · Royal Flush Joined: 29 Jun 2005 Posts: 646

Well, for those of you who need a clue, try this... I'll just give you the answer. Highlight the stuff between the spoiler tags to make it resonably readable, or see the end for hints. (9 edits later, I finally found the same color as the background. W00T!)

[spoiler]

Player A has 100 at bats vs righties and ten at bats vs lefties during the regular season. He hits on 36 of each.

Player A's avg: .360 vs righties, .360 vs lefties.

Player B has 20 at bats vs righties and ten at bats vs lefties during the regular season. He hits on 7 of each.

Player B's avg: .350 vs righties, .350 vs lefties.

Player A is then caught having sex with the manager's wife before the post season and gets benched for the first playoff series.

Player B does not get caught having sex with the manager's wife before the post season and gets to play. He has has 5 at bats vs righties, and 5 vs lefties. Because he's not worried about getting caught banging the manager's wife, his mind is focused on the game, and he gets a hit on 6 of those at bats (3 vs lefties, 3 vs righties).

Player B's new totals:

25 at bats vs righties, 10 hits. AVG: .400
25 at bats vs lefties, 10 hits. AVG: .400

[/spoiler]

So, what's the message in this little mathematical problem?

A) Don't dip your pen in the company ink.
B) Variance... more important than you think.

Honest_Rob · Posted: Tue Sep 06, 2005 12:23 am Post subject:

This is how i see it. Elmer must have had a limited number of at bats vs. either a lefty or righty. See example:
ELMER
LH: 1for1=1.0 average
RH: 50for150=.333 average
Elmer's total batting average=.337

TONY
LH: 49for50=.98 average
RH: 49/150=.326 average
Tony's total batting average=.490

Tony's .490 is higher than Elmer's .337 but
Elmer's LH average of 1.0 is higher than Tony's LH average of .98
Elmer's RH average of .333 is higher than Tony's RH average of .326

TribeLife05 · Three of a Kind Joined: 31 Aug 2005 Posts: 77

that doesnt fit the problem rob

Jaconda78 · Message Board Junkie Joined: 06 Jul 2005 Posts: 4177

How does i tnot fit the problem? Seems reasonable to me...

claw1980 · Pair Joined: 23 Jun 2005 Posts: 49

Honest_Rob's scenario definitely works, Elmer had very few ABs against whichever group of pitchers Tony hit best against, and he produced in those few ABs.. like 1 for 1 or 1 for

GripHoldOn · Posted: Tue Sep 06, 2005 8:22 pm Post subject:

Honest Rob's solution works perfectly. Here's another possible solution that may allow you to see the reasoning behind the answer a little more clearly:

Tony:

vs RHP: 199/200 .990
vs LHP: 30/100 .300
Overall: 229/300 .763

Elmer:

vs RHP: 1/1 1.000
vs LHP: 5/15 .333
Overall: 6/16 .375

Elmer is better against each individual type of pitcher but Tony's batting average is more than twice as big as Elmer's.

KGBlovesOreos · Moderator Joined: 28 Jun 2005 Posts: 5319 Location: VA

lol, i like this post... had me thinking for a while... any others grip?

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