Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here:
https://learning.blogs.nytimes.com/2012/04/30/test-yourself-math-april-30-2012/
This question is based on rapid population growth in African countries. How long will it take Nigeria’s population to quadruple?
Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here:
https://learning.blogs.nytimes.com/2012/04/25/test-yourself-math-april-25-2012/
This question is based on the increasing number of Chinese tourists visiting the United States each year. Just how much are they spending?
It’s almost time for the 2012 NFL Draft, and I thoroughly enjoy the many quantitative aspects of this event. The NFL Draft offers a complicated optimization problem with 32 actors all trying to maximize their gains.
To begin, teams and scouts evaluate the draft-eligible players and attempt to quantify their value. In doing so, they consider not just the player’s skill and athletic ability, but also the importance of the position. For example, generally speaking a left tackle is seen as providing more long-term value than, say, a cornerback.
But quantifying player value is just one part of a complicated equation. Teams need to balance player value with team need; if the best player available doesn’t fit with what the team needs, selecting that particular player may not be the best use of that pick. However, if that player is coveted by others, the team can try to extract more value by trading the pick for other picks or assets.
In order to facilitate deals, a trade value chart exists which allows teams to compare the values of different picks in the draft, almost like a currency conversion chart. It is interesting that the perceived value of picks seems to decline exponentially. And as teams package picks to move up in the draft, they may end up paying more than market value.
Further complicating matters is how player contracts play an increasing role in draft evaluation. Highly drafted players earn large guaranteed salaries, but certain positions may not be seen as worthy of such payouts. Would $10 million be better spent on an above average lineman, or an outstanding safety?
There’s a lot of math in the NFL draft, so if you like football and mathematics, sit back and enjoy! We’ve already got one great question to keep an eye on this season: will Robert Griffin III prove to be worth the high price the Redskins paid to draft him?
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During last night’s Yankees-Twins baseball game, the commentators were discussing the Yankees’ increased use of defensive shifts.
A “shift” is a defensive realignment of the infield to guard against a particular player’s hitting tendencies. For example, if a player is much more likely to hit the ball to the right side of the infield (as, say, a strong left-handed hitter might be), a team may move an infielder from the left side to the right side to increase the chance of defensive success.
Dramatic infield shifting was once a rarity in the game, employed against only a few hitters in the league. It is now being used with increasing frequency. “All the data is out there,” said the announcers when discussing Yankees’ manager Joe Girardi’s explanation of why he was using it more. (Which sounded remarkably like what Rays’ manager Joe Maddon, a pioneer in increased defensive shifting, had to say when asked about it some time ago).
The essential idea is that, given the reams of data now recorded on player performance, teams have a much more refined understanding of what a player will do. No longer is the projection “The player has a 30% of getting a hit”; now, it’s “The player pulls 83% of ground balls to the left side of the infield”. Naturally, teams try to use such information to their advantage.
It’s good that Joe Girardi is demonstrating an increased appreciation for, and understanding of, probability. But as last night’s game suggests, he may need to learn more about the principle of expected value.
Early in the game, the bases were loaded with two outs, and a left-handed batter came to the plate. Girardi put the defensive shift on, responding to data on this player that suggested he was extremely likely to ground out to the right side of the infield. But probability considerations should be only one part of the analysis. By leaving so much of the left side of the infield undefended, a situation was created where a weakly hit ground ball that would usually be an easy out actually produced two runs for the Twins.
In short, although the probability of that event (ground ball to the left side) was low, the risk (giving up two runs) was high. Considering both the probability and the payoff is essential to long-term success.
I’d be surprised if the Yankees’ employ the shift again in that situation. And if the Yankees need a special quantitative consultant, I am available during the summer.
Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here:
https://learning.blogs.nytimes.com/2012/04/16/test-yourself-math-april-16-2012/
This question is based on the current oil-export capacity of Iran. How long would it take Iran to export a billion dollars’ worth of oil?