[Guest]

In Littleton, Little League baseball is huge. Everyone is turning out for the cross town rivalry. Tonight will be the first time that these two teams meet this year. This year is special. Both teams are winners at 9 and 2, with the Bruisers being only slightly better statistically than the Boxers. The Bruisers have played 9 home games, winning all 9 and have lost 2 away games. The Boxers have played only 4 home games, which they won, and have won 5 of 7 away games. The Bruisers are the home team tonight. The Bruisers have a team ERA of 1.20. The Boxers have a team ERA of 1.17.

Bonanova is craving some action and wants to put $1000 on this game with a local bookie. He's studied the two teams and has noticed something odd. The Bruisers score one run EXACTLY every 3.1 innings regardless of the opponent's ERA, with every third point being a home run. The Boxers score one run EXACTLY every 3.2 innings, regardless of the opposing ERA, with every second score being a home run. What's more, neither team has ever scored more than one run in an inning.

Bonanova analyzes the win/loss records, the home/away records and both teams' ERA's. (Earned Run Averages). He knows that little league games go seven innings, unless they are tied, and then they go until they are won. Normal baseball rules apply, in that the home team always bats last, unless the home team is ahead in the 7th inning. He figures he can't lose.

He better not lose. If he does lose, the local bookie is going to break his legs. Bonanova places his bet.

The next week, you see Bonanova and he's all smiles. He obviously won his bet. Who did he bet on and why?

(assume all statistics hold as true in this game)

[Guest]

Clarification: Neither team has played an extra inning game so far this year. OP was edited slightly to fix some typo numbers that didn't add up. Sorry if any of you read it before the edit.

[Guest]

Man, I wish I didn't wait until lunch was over to read this ... my gut feeling is those poor little tikes are gonna have a long game ahead of them.

When I played in Little League, our coach made it clear that we were winners as long as tried our best, regardless of our record. That was good, because I think we won about 1 out of 3.

[Guest]

3.1 innings really equals 3 1/3 innings and 3.2 innings really equals 3 2/3 innings.

Since the game is 7 innings long, the Bruisers would be able to score 2 runs as 3 1/3 + 3 1/3 = 6 2/3 or scoring with 2 outs in the 7th inning. The Boxers wont be able to score 2 runs until the 8th inning as 3 2/3 + 3 2/3 = 7 1/3. And since the game is 7 innings long, the Bruisers would win 2-1.

[Guest]

Good try Riddle Solver, but you are incorrect in your analysis. Keep trying (and use spoilers!)

[Guest]

To clarify: I assume you do mean that 3.1 innings is 3 and 1/3 innings equaivalent to 3 innings and 1 out in the 4th inning? And that 3.2 innings is 3 and 2/3 innings?

[Guest]

In Littleton, Little League baseball is huge. Everyone is turning out for the cross town rivalry. Tonight will be the first time that these two teams meet this year. This year is special. Both teams are winners at 9 and 2, with the Bruisers being only slightly better statistically than the Boxers. The Bruisers have played 9 home games, winning all 9 and have lost 2 away games. The Boxers have played only 4 home games, which they won, and have won 5 of 7 away games. The Bruisers are the home team tonight. The Bruisers have a team ERA of 1.20. The Boxers have a team ERA of 1.17.

Bonanova is craving some action and wants to put $1000 on this game with a local bookie. He's studied the two teams and has noticed something odd. The Bruisers score one run EXACTLY every 3.1 innings regardless of the opponent's ERA, with every third point being a home run. The Boxers score one run EXACTLY every 3.2 innings, regardless of the opposing ERA, with every second score being a home run. What's more, neither team has ever scored more than one run in an inning.

Bonanova analyzes the win/loss records, the home/away records and both teams' ERA's. (Earned Run Averages). He knows that little league games go seven innings, unless they are tied, and then they go until they are won. Normal baseball rules apply, in that the home team always bats last, unless the home team is ahead in the 7th inning. He figures he can't lose.

He better not lose. If he does lose, the local bookie is going to break his legs. Bonanova places his bet.

The next week, you see Bonanova and he's all smiles. He obviously won his bet. Who did he bet on and why?

(assume all statistics hold as true in this game)

Perhaps it's also up to chance what the teams did at the end of their last game. For instance, if the Bruisers score exactly 1 run every 3.1 innings, perhaps they scored 1 run to start the 5th inning (with 0 outs) and then recorded 9 straight outs to end the game (3 innings worth of outs), meaning that the next game they would record 1 out to account for the remaining .1 inning before scoring a run. In this way, the scores can vary more:

Bruisers:

----> MIN: 3.1 Inn, Run, 3.1 Inn, Run, .1 Inn = 2 Runs

----> MAX: Run, 3.1 Inn, Run, 3.1 Inn, Run, .1 Inn = 3 Runs

Boxers:

----> MIN: 3.2 Inn, Run, 3.2 Inn = 1 Run

----> MAX: Run, 3.2 Inn, Run, 3.2 Inn = 2 Run (but if it goes to extra innings tied at 2, the Boxers will score in the 8th and the Bruisers will not)

So it seems either team has a shot at winning. I was thinking that perhaps if this whole trend is true, they have both been following it the entire season. They have both played 11 games (with no extra innings), which you would think is a total of 77 innings, but it isn't. Because the home team won't bat if they're leading going into the bottom of the 7th, this number could get messed up. Additionally, you can't assume that the home teams never went to bat in the 7th if they won the game, since the bottom of the 7th could easily have began with the home team behind or tied with the visitor, ending with a walk-off win for the home team (and in this case, they could have batted for 6.0, 6.1, or 6.2 innings worth of outs). So, I'm a little confused as to where to go from here.

It seems that it may be possible to calculate the scores in the games to come close to where in the 3.1 or 3.2 inning cycles these teams are using their records and ERAs, but this may be too complicated as you don't know how many runs you win or lose by, and (maybe too technical for this problem) you can lose by giving up only unearned runs having, no effect on your ERA.

Help?

[Guest]

Also to clarify. The ERA is calculated as runs per inning times 9 and not 7 (despite playing 7 inning games), correct? I'll go on this assumption unless corrected.

[Guest]

[spoiler=,,,..]Im going for the bruisers

because they so far have won every home game. I am rather bad at math. I think all the numbers are just there to confuse me.

[Guest]

Sorry for the confusion. Yes - 3.1 means 3 innings 1 out, not three and one tenth innings. My bad on not clarifying that. Also, ERA is earned runs per 9 innings, even though they only play 7 per game.

[Guest]

Good try painter, but that's not the correct analysis.

[Guest]

You are on the right track, but read my second post clarification and the last sentence of the second paragraph in the OP.

[Guest]

The Bruisers

I made some assumptions, but I think (I hope) they hold true even in slightly differing scenarios.

The Bruisers ERA is 1.20. Note that they have to play 7 innings of defense in the 9 games they win (9*7=63) and they might not have played 7 innings of defense in the 2 away losses. This leaves a few possibilities for defensive innings played, but the scenarios in which they lose the game in the bottom of the 7th are really unknowns since we can't know how many outs there were when the game ended, just that it definitely wasn't a full inning. It wouldn't be nice of Writersblock to put an unknown in the problem, so let's assume that they played only 6 innings of defense in those 2 games. If we make that assumption, then they played 75 innings of defense and gave up exactly 10 runs. 10 runs per 75 innings times 9 innings is an ERA of exactly 1.20. If they never score more than 1 run an inning, then in those losses they score 2 runs and I'll assume lost each game 3-2, leaving 4 runs for the opponents to score in the remaining 9 games.

They haven't played any extra inning games, and they can't score more than 2 runs a game except under specific circumstances (which we'll get to) so they have won 4 games 2-1 and 5 games either 2-0 or 1-0. In those 4 2-1 games, they (almost certainly) had to play the bottom of the 7th inning, but in the 2-0 or 1-0 games, they definitely didn't play the bottom of the 7th.

Anyhow, if I counted correctly then the Bruisers will lead of the game against the Boxers with a Home Run, and it will be the only game they've played so far in which they've score in the 1st inning. They'll score again in the 4th and again in the bottom of the 7th to win the game.

I didn't really do any calculating for the Boxers. Note that even if they lead off the game with a home run, they will only score 2 runs in 7 innings, and it's possible that they'll score only 1 run in 7 innings (making the bottom of the 7th unnecessary).

Though if the assumptions I made were not founded properly, then I could be wrong. I've got to go in a minute, so I can't figure it out, but

that even if the boxers lead of the game with a home run, the bruisers will still score a second run in the bottom of the 7th, tying the game, and then winning in extra innings eventually.

[Guest]

Very nice try ChuckJerry, but keep a lookout for thugs wanting to take out your kneecaps.

[Guest]

Looks like very little interest in this one besides ChuckJerry. Should I give the answer?

[Guest]

I'd like to know.

[Guest]

I made an attempt however I do not know alot about baseball:

I used the assumption for the bruisers that every home game they had six innings then using the 3.1 thingy I worked out how far through they were to scoring their next run.

I did the same thing with the Boxers.

I came out that at the end of the 7th innings both teams would have 2 runs, however in the next innings the bruisers score while the boxers do not.

Bruisers win and my kneecaps stay intact... I hope

[Guest]

Here I am with broken kneecaps and I don't even know why.

[Guest]

Looks like very little interest in this one besides ChuckJerry. Should I give the answer?

I'm surprised this one is still unanswered. I haven't had time the past few days, but I'll take a quick stab at it ...

If I understand how the "one run every 3.1 innings" works, the Bruisers will score one run in inning 3, after one out, and will score again in inning 6, after two outs, right? If so, then ...

The Bruisers will win 3-2 in the bottom of the 10th.

Boxers will score like so:

3rd inning, after 2 outs

7th inning, after 1 out

Bruises will score:

3rd inning, after 1 out

6th inning, after 2 outs

10th inning, after 1 out, for the win

And the ERA's, knowing which runs are HR's, and insight into Bonanova's gambling addiction are all just red herrings.

[Guest]

just a bump I really wanna know if I is correct

[Guest]

Another bump

[Guest]

just a bump I really wanna know if I is correct

No worries Lortek. Writersblock didn't get to VIP status by forgetting to reply to his own threads; he just hasn't been on for a few days. Nothing wrong with bumping, but in this case, we just need a bit of patience.

[bonanova]

How cow! .. he said, using his best Phil Rizzuto impersonation ... I'm late to the game.

Wait. I bet, and I won.

Now to figure out why. Gimme a minute.

Duh Puck - my gambling addiction is no red herring.

WritersBlock and I attend GA faithfully, every Tuesday, if there's no action at the track.

I'm betting

that the W/L, H/A and ERA info - along with the assumption that the 3.1 and 3.2 innings start with 3 scoreless innings at the opening of the season and proceed like clockwork leads to the initial conditions for tonight's game. In other words, no red herrings IMO.

Given the place each team is in its cycle, tonight's scoring, and the winner of the game, is determined.

Hats off to WB for yet another fine puzzle!

And hats off to me, as well, for apparently figuring this all out.

... altho I haven't, actually.

I think I just got lucky.

[Guest]

No red herrings IMO.

Not sure why I didn't think about how the whole season would factor into the starting conditions of the final game. Makes sense.

Since there is never more than one run in an inning, however, I really don't understand how knowing which runs are home-runs could figure in. What am I missing?

Everything else seems relevant.

[Guest]

Not sure why I didn't think about how the whole season would factor into the starting conditions of the final game. Makes sense.

Since there is never more than one run in an inning, however, I really don't understand how knowing which runs are home-runs could figure in. What am I missing?

Everything else seems relevant.

I think (however I know little about baseball) that all runs scored would be home runs because if one of the bases was occupied then 2 runs would be scored thus voiding the observation they score every 3.1 innings

[bonanova]

Not sure why I didn't think about how the whole season would factor into the starting conditions of the final game. Makes sense.

Since there is never more than one run in an inning, however, I really don't understand how knowing which runs are home-runs could figure in. What am I missing?

Everything else seems relevant.

I don't get the home run thing either.

Why would a walk and three stolen bases make anything different?

Still betting it figures in tho.