Calculus Anyone?

[Rask0lnik0v]

I haven't studied any math in 7 or 8 years, so it may not even be calculus. I am watching the home run derby tonight, and a question occurred to me. I wonder if any mathematicians can help me solve it. After the first round, 4 players advanced to the second round. Wright had 16 home runs, Ortiz had 10 home runs, Cabrera had 9 home runs, and Howard had 8 home runs. I wondered what the odds were each player would advance to the next round. Each player starts the second round from their first round total, so if I assume the players will hit home runs at the same basic rate (say 50% per swing) what are the odds for each player to advance? A player compiles home runs until they reach 10 outs, and that is their total. Every swing results in either a home run or an out.

To make my question as precise as possible. What are the odds Ortiz will advance to the next round if each player has a 50% chance of hitting a home run in each swing he takes?
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Obviously, we see that Wright has a major advantage starting with 16 home runs. Ortiz has a slight advantage on the other two players, but the other two players combined probably have a better chance than Ortiz does to advance. I estimate Ortiz has a 41% chance of advancing.

The question comes down to flipping a coin until you get 10 tails. How many heads do you get before you get 10 tails. We would have to do this 4 times to estimate the total for each player for the second round, and then we would add to his first round total to determine the two players with the highest scores. What are the odds Ortiz advances to the second round?
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I figure we would have to plug a rate of change in there somewhere. Sounds like calculus to me, but I forget how to do my integrals. Can anyone explain how we could establish a function to estimate the number of home runs of each player?

I know there used to be some math people here, so let's see if any of you really are good?

[R. Steven Coyle]

I would, but I haven't learned calculus yet.

It also reminds me of waking up at 6 am to take the SATs.

[DHodges]

I haven't studied any math in 7 or 8 years, so it may not even be calculus.

You are correct, this is not a calculus problem. It's a problem in probability, or statistics.

The answers to your question can be found in the Binomial Distribution.

[Rask0lnik0v]

Those equations you directed me to sure look a lot like the ones I remember from Calculus 2. Maybe not technically "calculus" but they were taught in Calc 2. Incidentally, that was my last year of math. Perhaps that was an introduction to the upper level Stats courses.

So, I may or may not take the time to figure it out on my own. I would appreciate it if you would walk me through it, if you are comfortable with this type of problem.

I had to look you up on your profile from before, because I thought you were the Rambo guy, but I didn't see your picture next to your post. Sure enough, I remembered right. You are Rambo. So you are an actuary, you should be able to calculate this without too much difficulty..

[DHodges]

So, I may or may not take the time to figure it out on my own. I would appreciate it if you would walk me through it, if you are comfortable with this type of problem.

No, I'm not going to walk you through it. If you decide to go through it on your own, I may be able to help you along the way if you have questions.

[Rask0lnik0v]

lol. yea I figured you wouldn't be able to do it. It's probably more complicated than giving me a link to wikipedia to solve it based on some equations which aren't directly related to the problem at hand. The problem is simple, yet complicated, and probably well beyond what you are capable of answering.

I have lost interest in the question anyway, now that the home run derby is over with.

[DHodges]

lol. yea I figured you wouldn't be able to do it.

Your attempts to goad or manipulate me into doing it for you say something about your personality - but nothing new. You are still the same old Rask.

I have lost interest in the question anyway

Exactly. If you had some real interest, it would be a different matter entirely.

[Rask0lnik0v]

No, I honestly do not believe you are capable of answering it. You probably crunch numbers for a living, but you only crunch the same numbers over and over again, so you don't know how to calculate anything except insurance figures. Is he a smoker? There, you add 10%. That's simple arithmetic.

Just going to say, if you actually could answer it, that would be impressive. It's a difficult problem, but hey no need to prove anything here. We will all just maintain our assumptions, and this is what I assume about you. You can't do it. It's not that you won't, but you can't. Thank you for your time.

[DHodges]

No, I honestly do not believe you are capable of answering it.

I don't care what you think of me, Rask.

[Rask0lnik0v]

Well, it seems pretty obvious you don't know the answer, just trying to be honest about the facts of the matter here. If you knew how to do it, you would have said something because it would have taken very little time to answer if you did know. Next time, don't talk all big about knowing how to do it, and then refuse to come through with any indication that you can actually answer the question.

[Tomas]

Home Run Derby...

Ah, yes!

Don't watch hardly any TV. Was at work for the All-Star game. I'd rather they played a doubleheader so all the selection could have a go at it. Make an inning or so appearance. Play 80+ games to be showcased in a 3 hour package. What a waste. Should have taped it.

BTW - Who DID win the home run hitting contest?

........


Warm and Fuzzy Regards

Tomas (the tank)
VietNam veteran - 1971
'A former wanna-be' major league aspirant - other stuff got in the way :-(


life is what happens to you while you're busy making other plans...












,

[Rask0lnik0v]

Ryan Howard won the Home Run Derby. He defied the odds of probability by coming out of last place to win it. He beat Wright in the finals 5-4. And the American League won the All Star Game, so Boston is going to have home field advantage in the World Series.

[Tomas]

Boston's gonna have home field advantage in The Series hahahahah

Yeah right ... _perhaps_ the Cardinals will have their act together this year and "sweep" the Sox.

I must tell you that turning age-53 in a few days ... the sports years blur one into another.

You mentioned a Ryan Howard.

I go back to Frank Howard of the old Washington Senators. Now, that boy could blast it a ways. Are these two fellows related?

Willie Mays is my all-time favorite player. I have gone out of my way many-many times to have several autographs (gloves, bats, balls etc.) personally signed by that dude. Gracious fellow.

You mentioned the Red Sox- I've a few items signed by Ted Williams, he was always a bit peculiar in his approach to signing stuff tho.

Anyways, Go Cards!!


Tomas (the tank)
VietNam veteran - 1971

[Rask0lnik0v]

I don't know anything about Frank Howard, but Ryan Howard is a 2nd year player for the Phillies. He's one of the top sluggers these days. Willie Mays is quite the icon. Why not sell those autographs, along with the Ted Williams memorabilia? So, Red Sox vs. Cardinals World Series this year. We'll just have to hope both teams can keep it together into the playoffs. I don't mind the Cardinals. As you eluded to, the Red Sox broke the Curse of the Bambino against the Cards, so I gotta like those guys.

[Tomas]

A peek at Ryan Howard
http://msn.foxsports.com/mlb/player/223779

Ryan was born in St. Louis, Missouri. Probably a Cards fan growing up :-)

No relation to Frank Howard. Ryan would appear to be a black man ... as Frank is a whitey...


Both play(ed) first base tho.

The link above has Ryan's 'projected stats' for this year, barring any longterm injury :-(


Not selling any autographs and other memory lane goodies, the grandkids already have it nearly in their clutches.

Tomas (the tank)
VietNam veteran - 1971


.

[Rask0lnik0v]

Sounds like a good thing to pass on to the next generation. Personally, I don't have any interest in autographs and the like, but I still haven't thrown away all my old baseball cards. I looked up Frank. He had 48 home runs in 1969, and some other pretty big seasons. Based on that, I was surprised I hadn't heard of him. I was born in 1980, so some of those old timers are bound to slip through the cracks. I don't think Frank is a Hall or Famer. Howard is projected to hit 52 home runs. I would like to see somebody hit 60 home runs this season, hopefully Ortiz. Ortiz is on pace to hit 58, based on that same link you provided, so he has a chance. My best guess is your man Pujols has the best chance to hit 60 this year, if he can get back on track after that injury he sustained a few weeks ago. He's the heart and soul of the Cards, I would say. I actually went to a Cardinals game a few years ago. I forget the name of your stadium, but we had a good time there. I was visiting friends in Charleston, Illinois at the time. We had to drive across the whole state to get there, but it was worth it for the game. Other than that I have been to Fenway, Skydome, Comiskey, and the Phillies stadium, but I haven't been to a big league game in years. Thinking about getting down to Fenway sometime this summer, but not sure if I will pull it off or not. I'm a big baseball fan these day. Watching the Red Sox in about 5 minutes, so I guess I will tune out, and tune into NESN. I think Beckett is pitching tonight, so we should be able to pull out a win, but my boys have been slumping lately, I'm afraid to say.

[Tomas]

Frank Howard won a couple World Series while with his first team, the Dodgers.

I now live in California, about a 100+ miles south and some west of San Francisco. So, the only times mostly to see the Cards is when they visit the Giants. Seen a lot of Barry Bonds homers over the years. Never caught one of his, the closest being two seats behind me. Didn't bother for a leaping grab as i didn't have the glove handy.

Barry's godfather is none other than Willie.


Be well.


Tomas (the tank)
VietNam veteran - 1971

[Rask0lnik0v]

I heard Willie spoke out against Barry due to the steroid scandal. I personally hope Bonds breaks Aaron's record, even though Bonds does seem guilty. I think it would be neat to see that record go down. I am sure you were a fan when Aaron broke Ruth's record. I never caught a baseball period. I always wanted to catch a Red Sox homerun at Fenway, and then throw it back because I thought it would get me on Sports Center. Of course, I never came close to catching one, but my friends and I always used to joke about that scenario.

[R. Steven Coyle]

DHodges:

I've been doing some physics reading, and was wondering if you could help me out with a few math principles:

When an exponent is squared in an equation, what does it represent in regards to physics? (i.e. e=mc_2)

When a square root is placed beneath the division bar, in conjunction with squared exponents, is that to simplify and contain the denominator?

[DHodges]

I'm not sure I understand your questions...

When an exponent is squared in an equation, what does it represent in regards to physics? (i.e. e=mc_2)

In the famous equation E = m * c ^ 2, the two is the exponent. c is a constant (here, the speed of light), which is getting squared.

Are you asking why c gets squared here?

When a square root is placed beneath the division bar, in conjunction with squared exponents, is that to simplify and contain the denominator?

I'm not sure what you mean here - maybe an example would clarify it. One over the square root of x could be written as:

1/[(x)^(1/2)]

or as

(x)^(-1/2)

The "^" is a fairly standard way to write exponents (raising to a power). There are (at times) different ways to write things out, and one might be simpler, or easier to understand, in a given context.

[Rask0lnik0v]

DHodges, you should change your name to MrAlgebra1. I notice how you are gobbling up these junior high math problems for lunch. You might even score above the 50% line if you were to reenroll in fourth grade, and take the CAT examinations again. I must say, I am highly impressed with what you have shown us here.

[R. Steven Coyle]

Steven: When an exponent is squared in an equation, what does it represent in regards to physics? (i.e. e=mc_2)

Dave: In the famous equation E = m * c ^ 2, the two is the exponent. c is a constant (here, the speed of light), which is getting squared.

Are you asking why c gets squared here?

Indeed.

--

Also,

Why isn't m divided into c? - the limit?

Is it because it represents the overall capacity of a system? - it's energy?

Which would abstractly require multiplication?

As stupid as it sounds, I've never grasped the essence of multiplication. I was educated with times tables, never realizing the underlying application.

Steven: When a square root is placed beneath the division bar, in conjunction with squared exponents, is that to simplify and contain the denominator?

Dave: I'm not sure what you mean here - maybe an example would clarify it. One over the square root of x could be written as:

1/[(x)^(1/2)]

or as

(x)^(-1/2)

The "^" is a fairly standard way to write exponents (raising to a power). There are (at times) different ways to write things out, and one might be simpler, or easier to understand, in a given context.

1 / [1 - (x^2)(c^2)]

Why is there a one in the denominator? What does it express?

Why is the variable and constant squared when there is a square root sign?

[Trevor Salyzyn]

rasko

DHodges, you should change your name to MrAlgebra1. I notice how you are gobbling up these junior high math problems for lunch.

Come on, no need to be sarcastic. These are high school physics questions.

steven

When an exponent is squared in an equation, what does it represent in regards to physics? (i.e. e=mc_2)

Where an exponent affects a variable, the exponent represents the rate of change of the slope of a graph of the equation. For example, f(x)=ax increases in magnitude at a slower rate than f(x)=ax^2 for all values of x greater than 1.

In your example, however, since c is a constant, c^2 is simply another constant. You would have to look at the specific formulas that Einstein joined together to see why the speed of light is squared here, but I don't think that is especially important to understanding the content of the theory.

However, it will balance the units.

mass * speed * speed =
kgm^2/s^2 =
Nm =
J

As stupid as it sounds, I've never grasped the essence of multiplication. I was educated with times tables, never realizing the underlying application.

Multiplication is simply repeated addition. It's nothing more than an abbreviation. Learning multiplication is one of the rare cases where boring, mindless, memorization doesn't really do any harm.

1 / [1 - (x^2)(c^2)]

Why is there a one in the denominator? What does it express?

Why is the variable and constant squared when there is a square root sign?

I think you typed that equation wrong. For one thing, there is no square root (exponent 1/2). For another, the one in the denominator doesn't make much sense unless x^2 is divided by c^2. You wouldn't want that part of the equation to be any bigger than 1, or else you'd get nonsensical negative values.

(I say nonsensical, because the units work out to seconds/metre... and a mass can't rightly take less than zero seconds to travel a given distance)

[Trevor Salyzyn]

Self:

Where an exponent affects a variable, the exponent represents the rate of change of the slope of a graph of the equation.

Self, you are an idiot. That's what derivatives are for! :)

[R. Steven Coyle]

hey mooke,

However, it will balance the units.

mass * speed * speed =
kgm^2/s^2 =
Nm =
J

That makes sense.

Thanks.