Visually, we see that until 2011 the Giants preferred to run on first and second down. Third down is usually a do-or-die down so passes will dominate on third-and-long. The grey vertical lines mark Super Bowls XLII and XLVI.
A friend of mine has told me on numerous occasions that since 1960 the Yankees have not won a World Series while a Republican was President. Upon hearing this my Republican friends (both Yankee and Red Sox fans) turn incredulous and say that this is ridiculous. So I decided to investigate. To be clear this is in no way shows causality, but just checks the numbers.
The plot above shows every Yankee win (and loss) since 1960 and the party of the President at the time. It is clear to see that all nine Yankees World Series wins came while a Democrat inhabited the White House. The fluctuation plot below shows Yankee wins both before and after 1960 and the complete lack of a block for Republican/Post-1960 simply makes the case.
There are similar plots for the American League after the jump.
Shortly after the Giantsfantasticdefeat of the Patriots in Super Bowl XLVI (I was a little disappointed that Eli, Coughlin and the Vince Lombardi Trophy all got off the parade route early and the views of City Hall were obstructed by construction trailers, but Steve Weatherford was awesome as always) a friend asked me to settle a debate amongst some people in a Super Bowl pool.
We have 10 participants in a superbowl pool. The pool is a “pick the player who scores first” type pool. In a hat, there are 10 Giants players. Each participant picks 1 player out of the hat (in no particular order) until the hat is emptied. Then 10 Patriots players go in the hat and each participant picks again.
In the end, each of the 10 participants has 1 Giants player and 1 Patriots player. No one has any duplicate players as 10 different players from each team were selected. Pool looks as follows:
Winners = First Player to score wins half the pot. First player to score in 2nd half wins the remaining half of the pot.
The question is, what are the odds that someone wins Both the 1st and 2nd half. Remember, the picks were random.
Before anyone asks about the safety, one of the slots was for Special Teams/Defense.
There are two probabilistic ways of thinking about this. Both hinge on the fact that whoever scores first in each half is both independent and not mutually exclusive.
First, let’s look at the two halves individually. In a given half any of 20 players can score first (10 from the Giants and 10 from the Patriots) and an individual participant can win with two of those. So a participant has a 2/20 = 1/10 chance of winning a half. Thus that participant has a (1/10) * (1/10) = 1/100 chance of winning both halves. Since there are 10 participants there is an overall probability of 10 * (1/100) = 1/10 of any single participant winning both halves.
The other way is to think a little more combinatorically. There are 20 * 20 = 400 different combinations of players scoring first in each half. A participant has two players which are each valid for each half giving them four of the possible combinations leading to a 4 / 400 = 1/100 probability that a single participant will win both halves. Again, there are 10 participants giving an overall 10% chance of any one participant winning both halves.
Since both methods agreed I am pretty confidant in the results, but just in case I ran some simulations in R which you can find after the break.
With the Super Bowl only hours away now is your last chance to buy your boxes. Assuming the last digits are not assigned randomly you can maximize your chances with a little analysis. While I’ve seen plenty of sites giving the raw numbers, I thought a little visualization was in order.
In the graph above (made using ggplot2 in R, of course) the bigger squares represent greater frequency. The axes are labelled “Home” and “Away” for orientation, but in the Super Bowl that probably doesn’t matter too much, especially considering that Indianapolis is (Peyton) Manning territory so the locals will most likely be rooting for the Giants. Further, I believe Super Bowl XLII, featuring the same two teams, had a disproportionate number of Giants fans. Bias disclaimer: GO BIG BLUE!!!
Below is the same graph broken down by year to see how the distribution has changed over the past 20 years.
As mentioned earlier, yesterday was Pi Day so a bunch of statisticians and other such nerds celebrated at the new(ish) Artichoke Basille near the High Line. We had three pies: the signature Artichoke, the Margherita and the Anchovy, which was delicious but only some of us ate. And of course we had our custom cake from Chrissie Cook.