At this article: Fox Sports expects at least 1.5 teams to win the World Series this year.
No, I'm not making this up.
They give odds for fifteen Major League Baseball teams to win the World Series, ranging from the Marlins at 40 to 1 to the Angels at 5 to 2. I'll just give the top five teams here: Angels 5:2, Yankees 3:1, Cubs 7:2, Red Sox 4:1, Mets 8:1. So they figure that the Angels has probability 2/7 of winning the World Series, the Yankees 1/4, and so on.
Add up their probabilities for the top five teams: 2/7 + 1/4 + 2/9 + 1/5 + 1/9 = 449/420, which is greater than one. If you add up the probabilities for the fifteen teams they give probabilities for, you get about 1.506.
I'm not arguing with their ranking of the teams. (There might be things to argue with, but contrary to what you might come to believe in the next two months, or to what longtime readers might remember from last August and September, this isn't a baseball blog.) But a bookie that offered these odds would be broke pretty quickly.
Also, about the Phillies (to whom they give 16 to 1 odds to win at all), we're told that "Odds say they can't mash their way in two years in a row." Okay, it may be true that they can't rely on just their offense. But the fact that they did it last year really has no bearing on whether they can do it this year. If anything, the fact that they did make the playoffs last year is evidence that their offense is enough.
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24 comments:
Regarding the statement, "Odds say they can't mash their way in two years in a row," they really mean that few teams win the World Series two seasons in a row. So they're correct in a historical statistical sense, but not in the sense that each season is an independent trial.
Actually I'd think the influence would go the other way.. How does the probability that a team wins the series given that they did last year compare to the probability that they win given that they didn't last year?
Wouldn't a bookie who offered those odds actually make more money in the long run than one who offered odds adding up to 1?
I see jonah has beaten me to it, but bookies offer shorter, (not longer) odds than yield an overall implied probability of 1, so if you add the probabilities implied by bookies' odds they come out to more than 1 (the excess corresponds to profit).
The longer the odds (the lower the implied probabilities) the less money they make. Fox Sports' numbers possibly came from a bookie (maybe one who wants to make his offered odds look good, since they seem a tiny bit short overall even for bookie odds).
Isabel is right. With those odds, if I bet a dollar on the whole field, I'll win, on average, $1.50.
David, I have a deal for you. I'll pick a random number between one and a million, and you try to guess it on your first try. If you're correct, you get $1000, but if not, you give me $1000. Since I'm giving you 1:1 odds (50/50) on each of the million choices, you should expect to make five hundred million dollars on average.
Oh, you're right Jonah. I miscalculated, If you bet a dollar on each team in the field, you would expect to win $2 for each one you bet.
Just so we are clear how I got this:
LAA -> -$11.5
NYY -> -11
CHC -> -10.5
BOS -> -10
NYM -> -6
CHW -> -4
ARI -> -2
MIL -> 1
PHL -> 2
TPB -> 4
LAD -> 6
DET -> 11
STL -> 16
MIN -> 19
For a total expectation of +$30 [which, when you divide by 15 $1 bets ...].
I'll gamble with you all day and twice on Sunday.
I went to baseball game yesterday, phillies vs. cardinals. Turns out that ryan howard guy is pretty good huh?
Ok now to my random question for the day. Is all human knowledge based on Pi? This just occurred to me the other day, if knowledge is based on measurement and the only objective form of measurement we have is the ratio between a circle's circumference and diameter then is all knowledge really based on Pi? (of course we can debate what actually constitutes knowledge)
Kurt, that all falls apart when you realize that space is never perfectly flat, so even if you had perfect measurement devices (which you don't) you still won't get π from any measurement of any circle.
David, you're assuming that each team has an equal probability of winning. This is most definitely not the case.
If, however, it is true that each team has an equal chance at winning, then you're right: this is a bad deal for the bookie. However, it's not for the reason Isabel cited. The reason the bookie loses money in your calculations is that it severely underestimates the likelihood that certain teams would win. On the contrary, Isabel (and, I assume, yourself) are criticizing the Fox numbers for overestimating the likelihood that some teams will win, since certainly the probabilities add up to more than 1.
Think about it this way: if you wanted to correct the odds given by Fox Sports so that the probabilities did sum to 1, you'd want to increase the denominators for some of the fractions, which means increasing the payouts of some of the bets. Do you really think that by increasing payouts, a bookie stands to gain more money per bet?
Another reason teams don't usually win two years in a row is that the players' market value increases after a championship, so teams often can't afford to pay their best players and have to trade them away, making the team worse.
unapologetic:
Not at all. The fact that measurements differ from what they would be if space were flat is knowledge. It tell us very important things and gives us a starting point to measure the deviation from what it is we would expect to see. As for measurement, of course we could go down the path of mr. heisenberg's principal, but since probability density functions are also based on pi, can we not skip that step?
Kurt: earlier you claimed that the ratio was a measurement, and now you claim that π is just an idealization. You're jumping around, saying whatever occurs to you at the moment, and there's no rigor whatsoever to anything you say. It's all just so much numerology.
The short answer is, "no, and you're acting like a crackpot".
unapologetic:
perhaps, i am a crack pot, i certainly don't know this is the case that's why i posed it as a question.And, there's certainly no rigor.
But these thing had actually occurred to me already. Certainly knowing something is not where the theory dictates it would be is knowledge! The ratio would still be acting of unit of measure even if things do not measure what you predicted.
After all this is how Urbain Le Verrier discovered Pluto, Neptune wasn't where theory dictated it should be. And, from my limited understanding, this is how most of planetary motion was discovered from deviation from our predictions.
It seems to me most scientific discovery comes from things not doing what they're predicted to do. But first you need a prediction, and for that you need an objective unit of measure, which brought me to my question about Pi.
Am I completely misguided?
kurt: that certainly is the fairy tale about the discovery of Pluto. However, the truth is that the discrepancies in Neptune's orbit were due to experimental error, and Le Verrier happened to be looking in the right place at the right time.
But that's all as maybe. It's certainly not the case that "all human knowledge [is] based on [π]". There was plenty of knowledge around before humans ever thought of π. And if you're taking the position that it has always been around behind the scenes, you could take almost any concept and spin the same fundamentalist nonsense around it. Try the Cabibbo angle -- it at least has something to do with the real world instead of being a purely independent idealization.
Ok unapologetic i take your word for it. But what knowledge specifically are we talking about existing before pi? I certainly don't consider history to be knowledge as you just pointed out with the Le Verrier example.
I don't think most species know things at all, so i wonder what it is we first knew and when we knew it. if not Pi (and i'm including all distances here) then what?
if knowledge is based on measurement and the only objective form of measurement we have is the ratio between a circle's circumference and diameter then is all knowledge really based on Pi
Pi (and i'm including all distances here)
First you're talking about the actual ratio π. Then you're talking about all distance measurements. There's at least two cardinal sins right here.
First, you're changing the terms on a whim. You can never just be wrong, since you never actually take a stand on anything. If I show that one position is untenable, you just claim to have actually been taking a different one.
Secondly, you're now begging your own question. You take as an article of faith that "knowledge is based on measurement", and now you're somehow using the term "Pi" to refer to "all distances". So you've assumed what you wanted to show: that "all knowledge is based on [what you call] Pi".
It's all mush. Maybe this sort of sloppiness passes muster in a philosophy department, but mathematicians won't stand for it.
Unapologetic:
I haven't changed anything, here's my original comment:
"I went to baseball game yesterday, phillies vs. cardinals. Turns out that ryan howard guy is pretty good huh?
Ok now to my random question for the day. Is all human knowledge based on Pi? This just occurred to me the other day, if knowledge is based on measurement and the only objective form of measurement we have is the ratio between a circle's circumference and diameter then is all knowledge really based on Pi? (of course we can debate what actually constitutes knowledge)"
I am not presupposing the knowledge is based on measurement, i am submitting that as the statement to be tested.
Please demonstrate to me some form of knowledge that is not based on measurement! so far you have only said "There was plenty of knowledge around before humans ever thought of π" But you haven't told me what this knowledge was.
Now granted I am imposing a rather strict definition on knowledge, as something that has been definitively proven. Which may consequently restrict knowledge to math, but hey isn't that what you mathematicians have been saying all along?
I am also submitting as a statement to be tested that all distance measurements (and therefore measurement that can be expressed as distance, such as mass on a scale) are based on pi.
I suppose the easiest test here, would be to show that the Pythagorean theorem is independent of Pi.
All of this was part of my original question. I don't have a have a stake in it being right or wrong. Its just that you've only brought up things that i'd already thought of before I posed the question in the first place. Maybe I should have stated things more clearly, but i didn't want to go on, like i usually do.
I want to chime in agreeing that these odds are how the bookies make money, not lose money. The odds of winning are overestimated so the payouts are lower.
I also want to agree that this "all knowledge is based on pi" seems like a fruitless direction to pursue.
And I want to point out that Percival Lowell and Clyde Tombaugh were the folks involved in discovering Pluto. Leverrier et al were involved in the discovery of Neptune based on discrepancies in Uranus's orbit. http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/Neptune_and_Pluto.html has a pretty good rundown of the history of it all, going all the way back to Galileo's (!) observations of Neptune.
Of course you're right, Josh.. it was L&T. Serves me right for not checking that part of the nonsense too.
As further support for my position:
http://en.wikipedia.org/wiki/Odds#Gambling_odds_versus_probabilities
where in the example, "fair" odds have probabilities that total 100%, but the bookmaker shortens the odds (in order to make a profit), making the total implied probability 130%.
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