Comments on: Home team winning percentage This and that about baseball stats. Tue, 16 Jul 2013 17:01:55 +0000 hourly 1 By: Tmckelv Tue, 15 Feb 2011 17:44:09 +0000 @19

"...tossing a coin say 1000 times ALL heads is IMPOSSIBLE, not very, very, very, very unlikely, but infact IMPOSSIBLE. Most people will not believe you even though it is a mathematical fact of the universe."

What is the exact number of coin flips that the "Universe" deems an outcome of all heads being "impossible" as "mathematical fact".

It has to be somewhere between 1 flip and 1000 flips. Is it 10 flips, 20 flips, 100 flips? I am completely intrigued.

So for example, if I get to the cutoff number of flips (we will call it N) with all heads, then you are saying the next flip (N+1) has 0 probability of being heads, instead of .5?

I am truly interested in how that can be. Seriously. Even if it takes a lengthy explanation of the law of large numbers.

By: DavidS Tue, 15 Feb 2011 13:47:15 +0000 I'm confused as to why Topper thinks 10^-301 is incorrect. I think we can all agree this number is ridiculously small and most calculators probably would give 0. However, surely we can agree upon the following:

1) Each sequence for a fair coin is equally likely, from TT...TT to TT...TH all the way to HH...HH. Not the total result (e.g. 500 H and 500 T), but the 1000-flip string. For the 3-flip example - TTT,TTH,THT,THH,HTT,HTH,HHT,HHH all have probability 1/8.

2) The total number of these strings is 2^1000 (approx 10^301)

3) The sum of the probabilities of all strings = 1

Therefore each string, including 1000 tails, has a probablity of 2^-1000 (or 10^-301)

By: dukeofflatbush Sun, 13 Feb 2011 18:17:01 +0000 Nobody here has discussed the emergence of mercenary free agents and their correlation to fans and fan base. A fifteen year old kid can remember the Yankees as the Tino Martinez or the Giambi or now the Teixiera era.
I think when teams virtually do not have a single player stay more than 7 years with their club, it is hard for fans to relate to a new group of faces every year. They are rooting for clubs, not players, where in the past, fans liked the uniform and the player in the uniform.

By: DavidRF Sun, 13 Feb 2011 00:28:55 +0000 @28
I understand what you are saying, but an 8th grader can calculate 0.5^1000 and its about 10^-301. I think the point of the strong law is how fast this process is converging. A thousand flips is really not that many... I think perhaps its not obvious how unfathomably small 10^-301 actually is.

But Barkie's a bit of an anti-intellectual, so the more we try to explain things the less he's going to listen. 🙂

By: topper009 Sat, 12 Feb 2011 23:38:20 +0000 Not to get into it but the strong law of large numbers says that the probability of 1000 heads in 1000 tosses = 0, not = 10^-301. It is not very, very, very unlikely for all intents and purposes, it is impossible.

By: DavidRF Sat, 12 Feb 2011 16:25:54 +0000 @23
Its just a semantic question of at what point "extremely remote" becomes "impossible". The odds of 1000 coin-flips coming up all heads is 1 in 1.07 * 10^301. That's 301 zeros. No number of things in all the history of the universe even remotely approaches a number that large. So for all intents and purposes you can call it "impossible". I don't know how useful this tangent is to the discussion but that's basically the point of that anecdote.

In the real world, you can 1000 coin flips isn't even that much. Imagine atoms or molecules. So, the remoteness of all the air in the room randomly migrating to the far corner and suffocating you is even more extreme than the coin flip example above.

r-squared measures correlation. It ranges between 0 and 1. A number near 1 means very correlated. A number near 0 means no correlation... not even anti-correlation. Basically random. The number Andy got was 0.02. Which means he didn't find a link between offense levels and home-field advantage.

By: barkie Sat, 12 Feb 2011 14:41:51 +0000 I was waiting for the coin flip explanation too

By: Soundbounder Sat, 12 Feb 2011 12:01:35 +0000 Surprised I haven't seen this mentioned yet. The pitchers mound often accommodates the home pitcher. Greg Maddux has discussed this issue. There were some mounds that he hated, and it impacted his effectiveness. I think Arizona was one of them.

By: Jason W Sat, 12 Feb 2011 02:50:21 +0000 @19: I'd like for you to explain your coin flip example to me. I've never heard of that.

By: Albert7 Sat, 12 Feb 2011 02:14:39 +0000 @johnautin

"That's a bit too simplistic, no? "


If you'd read the rest of it, you'd see I make a point of saying "seemingly".


"Its not the number of fans its their involvement. Just because the Dodgers have high attendance doesnt matter when half the fans are there between the 3rd and 6th innigns.

Naturally there are going to be exceptions. That's what makes this and other sports impossible to completely understand using stats alone. It's not a closed door lab situation.