Challenge Questions

The question as written is nonsense - so I'm giving you a GA for your correct answer to a reasonable* guess at what was meant (other than the "85" mistype).
*The only other "close" guess that I can find would be 0.667% (rounded), which would be too easy.

The Red Sox. They could have won 83 of 125, 85 of 128, 87 of131, 89 of 134, 91 of 137, 93 of 140, 95 of 143, 97 of 146, 99 of 149, 101 of 152, 103 of 155, 105 of 158, or 107 of 161 to have a three digit percentage of 0.664. These all are greater than 70.

Thanks,

Jim

Please disregard my previous post. Again I found an error in my analysis.

I agree that 83 of 125 games is the only combination that gives exactly 0.664 winning fraction. However, winning fractions and batting averages are usually given to just three significant digits so other combinations would likely be reported as 0.664. The lowest number of wins for this is 75 of 113 or a winning fraction of 0.663717... which rounds to 0.664. There are twelve other combination below 162 total games have wins of 77, 79, 81, 85, 87, 89, 91, 93, 95, 97, 99, and 101 wins.

I missed a couple more. 71/107 is 0.663551... which rounds to 0.664. Red Sox still ahead.

Thanks,

Jim

GA. I believe this is indeed the smallest pair that validly approximates to 0.664 (alternate smaller numbers can create 0.6666... and subtracting one from each creates the closest local number below that)

Reading around the rules for tied games, and without proper knowledge of how Baseball league positions are accounted:
Unless Yankees had two or more games abandoned due to weather conditions, in which case the answer is undecidable.

GA

Unfortunately there are no combinations that give a 0.664% winning percentage. Must be a trick question.

Jim

The shortest series for which this could be an exact percentage is 12,500 games. Even if we assume a number between 0.6635 and 0.6645% there is no possible number of games that is less than 163. So I think we have to assume the challenge meant 66.4%.

I'm giving a G.A. to ddk (even though he simply assumed "the most reasonable misinterpretation" without actually saying so, and typed 85 when he meant 83).

thanks for catching my typo

Is there an elegant way to solve this problem? I did it the brute force method on an excel spreadsheet.

It's not particularly elegant, but the best you can do is write in standard form (numerator and denominator co-prime):

0.664 = 64/1000 = 83/125

The problem can be framed as: Number of games played GE 70 AND LT 162 AND winning ratio = 0.664. Critical number of games is 105 (70/.664). More than 105 and .664 beats 70 games i.e. Boston is ahead. There are no number of games below 105 (and wins below 70) which give winning ratio of exactly 0.664 (0.663, yes several). Therefore, Boston is ahead. It turns out that 113 games with Boston winning 75 gives winning ratio of 0.664 as does 83/125 pointed out before and 85/128 etc. So, the answer is NOT unique, BUT Boston is ahead in all case above 125 games. A lot of discussion over a trivial badly worded question.

You are, of course, absolutely correct! Why don't you register so you can get the credit you deserve?

Thank you, "Guest",

I was a little amazed to see so many hits on this question by folks who really did not "read the fine print".

Helo All,

I simply believe that this is the microcosm of Engineering that we must deal with. 0.664 % is a non-sensical description, as previously posted. While the math is relatively straight-forward (and as we engineers must do, it takes a little creativity to discern what Marketing/Management/BOD was trying to express) the process is fraught with uncertainty (non-Occum).

Once again, we need to educate M/M/BOD to express their requirements concisely and ACCURATELY.

Sorry Guys and Gals, a particularly bad day: Jousting with a 25 YO MBA from the Wharton School of Business who will NOT listen.... ... Retirement is looking very good about now.

Said 'Pappy : "When engaged in a battle of wits, always ensure that your opponent is armed"

GB

Firstly there is typo in the question - it should read ..... 66.4% and not 0.664%

by looking for a number between 1 & 162 that 66.4% of that number is a whole number is the way to find the number of games the Sox played. (Used Excel)

They played 125 games and won 83 (66.4% of 125) therefore more than the Yankees

0.664% seems like a misprint.

Red Sox must have won at least one game. That means playing 151 games to get this score. The Yankies having won 70 would be ahead - even if Red Sox won the next 11 games.

Solve this problem, you cannot. Number of games that have been played, you must know.

Clearly the question is flawed (mistyped percentage, not enough information to solve)? Can we find out who submitted the question (or better yet who chose to run it as 'this week's challenge')? And can we ban them from the blog for a day (or some other suitable punishment for sounding like the marketing department)?

Really, who cares, it is Boston and the Yankees.

If this gets rolled up to 'Specs & Techs' the poster could be INfamous.

On the other hand, if this was not a mis-print but instead the gimmick to be addressed, then the Red Sox had won 1 game and were 7.568% into a winning game at the moment of the "one point" designated in the challenge question. Second inning, first batter is up 2-1.

One has to wonder, since this typo was glaringly obvious to all of us upon reading the question, if dealing with the typo is not the actual challenge?

What typo? I have just about figured this one out. I'm stuck.

Anyone have an idea what I'm leaving out?

I don't know if the typo was intentional or not but it is reflective of how problems are some times presented in the real world. In school, we were taught how to solve problems. When I got into the real world, I found out I had to figure out what the problem was first. Often times communication is the hard part. We all have our own unique understanding of the meanings of words. I for one had no particular problem in interpreting the the 0.664% to mean 66.4% or a winning fraction of 0.664. When we say someone is batting three hundred we mean 30 percent or the fraction 0.300. While technically not correct, the challenge does present the same type of situation that often needs to be addressed in the real world. I think everyone has a right to criticize the challenge question as long as they have submitted an elegant challenge question that was error free.

Thanks,

Jim

Didn't happen:

8/23/08 Yankee's won their 69^th game, 69 wins/60 losses (.535). Red Sox 74/55 (.574), game's played for both teams = 129

8/24/08 Yankee's won their 70^th game, 70/60 (.538). Red Sox won, 75/55 (.577), GP = 130

8/25/08 Yankee's did not play, 70/60 (.538). Red Sox did not play, 75/55 (.577), GP = 130

8/26/08 Yankee's lost to Boston: Yankee's 70/61 (.534). Red Sox 76/55 (.580), GP = 131

8/27/08 Yankee's lost to Boston: Yankee's 70/62 (.530), Red Sox 77/55 (.583), GP = 132

8/28/08 Yankee's beat Boston: Yankee's 71/62 (.534), Red Sox 77/56 (.579), GP = 133

For this to have been true, our hypothetical Red Sox would have had a record of 86/44 (.662) on 8/25/08.

Then, when they beat the Red Sox on 8/26/08, they would have had a record of 87/44 (.664).

Once again, it didn't happen.

At game 22, the Red Sox were 15W/7L (0.682). After that game, they never got above 0.652 for the rest of the season and thus never hit 0.664 at any point, so it's truly a hypothetical question.

Yup... can't mix historical & hypothetical statistical analysis. If you do... You wind up with one hell of a hangover. . I later analyzed all the possibilities. and you were correct. 16 total possibilities, in the hypothetical.

Actually with just a little modification, this could have been much more challenging:

"At one point during the last baseball season, the Red Sox had won 0.664% of their games a 0.587 win percentage while the Yankees had already won 70 games. Assuming that both teams had played the same number of games as part of the 162 game season, which of the two teams was ahead?"

Unless you are have the 2008 season's chronological results for both teams in front of you (yawn), we have no way of knowing. Theoretical Red Sox scores would be 44/75, 54/92, 61/104, 71/121, 81/138 and 88/150.

There actually is a singular point in last year's season when this occurred - the challenge is to figure out when it was.

Given the possibilities I've described, we only need to know the timings and results of both teams games.

But it does point to the same possibility for the original question - that it actually refers to last season and the Yankees could have won more than 70 games at that point (that last possibility is not addressed elsewhere in the thread, SFIK). But manual searches are not my thing unless they have real consequences - so I'm out of this.

I just cut & pasted the season results from both teams into Excel and crunched away

The problem with the original problem statement is that the Red Sox never actually hit the stated 0.664 win percentage (or even 0.664%) at any point in the 2008 season, so it has to be theoritical. I was just trying to relate the challenge to real-life data, instead of it being a pure math exercise.

I'm guessing on 9/2/08. Boston's record was 81/57 (.587) and the Yankees were 74/64 (.536). So the Red Sox's were ahead. and remained ahead for the rest of the season. The Yank's didn't make the post season, Tampa, took the division, and the City of Brothery Love, won it all.

You got it! Of course, the simplest and easiest answer to the original question (no matter what the statistics) is 'the Red Sox were ahead', because after game 16 the Yankees were behind and never caught up. It would be more interesting if the two teams actually see-sawed for the lead.

The Red Sox have a record of 81 wins and 41 losses. The Yankees would have a record of 70 wins and 52 losses. The Red Sox lead by 11 games.

I think somebody's been hanging around the wrong places. Sports bookies often refer to .546 as a "percentage" or as "%".

Assuming .6635 rounds up to .664 as it does in all baseball statistics, and knowing that baseball schedules have all teams playing roughly the same amount of games at any one time in a baseball season, then the Sox would have won 69 out of 104 games while the Yanks would have won 70 out of 104 games.

Therefore the Yanks would have been 1 game ahead in the standings.

Exactly .6635 would round up. But 69/104 is 0.6634615. That should round down.

For what it's worth:

From Wikipedia

"In sports, a winning percentage is the fraction of games or matches a team or individual has won. It is equal to wins divided by wins plus losses. Winning percentage is one way to compare the record of two teams; however, another standard method most frequently used in baseball and professional basketball standings is games behind.

Ties count as a game and should be calculated as neither a loss nor a tie.

In baseball, pitchers are assessed wins and losses as an individual statistic and thus have their own winning percentage (see Win (baseball)). A pitcher's winning percentage is commonly expressed to three digits.

The name "winning percentage" is actually a misnomer, since a winning percentage, such as 0.536, is commonly not expressed as a percentage. The same value expressed as a percentage would be 53.6%. With points on ties and overtime losses, it's possible to have a winning percentage above 0.500 (50%) despite losing more than half of the games played."

Thanks,

Jim

Everybody seems to have missed this one. Back when I was in 5th grade, I learned that 0.664% < 1.0% The Red Sox have won 1 game at best, 1/162 = 0.00617, x 100 to convert to % = 0.617% They have played 151 games of the 162, 1/.00664 = 150.6. No pennant this year.

Another question where one wonders, "What on earth did the question writer have in mind?" If we take .664% as meaning less than one out of a hundred, we can conclude that the Red Sox are having a really bad season.

Check your math!! 0.664 % is lessthan 1 %!

We all know this was an easy one... Maybe the question should have been...

Using the current MLB standings, the 2009 schedule, and the win/loss records against each scheduled opponent.

1. Which team is most liklely to win 70 games first this season, the Yankees or the Red Sox's?

2. Which team is most likely to win their division?

In order to atain an average of 0.664 (I assumed you meant to use conventional baseball statistics, not 0.664% which would actually be 0.00664, in which case the Yankees were easily in the lead), Boston would have needed to have won at least 71 games, else the closest ratios for less than 71 games won would be 0.662 and 0.667. Therefore, Boston had the lead with at least 71 games won. You must be a Boston fan...

That is 71 Wins in 107 games = 0.6635514..., rounded to 3 decimals is 0.664. The smallest number of wins possible to attain a 0.664 average, by my calculations. Contradictory to the 75 minimum previously reported.

Yankees ' Yankees had already won 70 games'.

Why does it say that the answer will be posted on 21 July - the "launch" date of this challenge, although it was actually posted on 19 July ???

And today (27 July) the answer still hasn't been posted.

not that I'm particularly bothered...I only read through the answers ot make sure the 0.664% mistake had been picked up. Who cares about baseball anyway...a World Series in which only one country plays ??

id they have won 0.664% then they have won 7 games! % is one of hundred!

Sorry, not 7 just .7 or nearly one game won!