## Math Quiz: NYT Learning Network

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:

This question is based on the the recent historic presidential elections in Egypt. How many more votes did the winner receive?

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## Math Quiz: NYT Learning Network

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:

This question deals with the high number of adults in prison in Louisiana. Of Louisiana’s 4.5 million residents, how many are in jail?

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## Math Quiz: NYT Learning Network

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:

This question focuses on the increasing number of Americans who are collecting Social Security early. What hourly wage is equivalent to collecting social security benefits?

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## Math Quiz: NYT Learning Network

**Test Yourself** quiz-question, can be found here:

This question is built around the recent $2 billion loss posted by the bank JPMorgan. How many yearly salaries is that loss equivalent to?

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## NBA Draft Math: Strength of Draft Class

After creating a simple metric to evaluate the success of an NBA draft pick, I realized that the same approach could be used to evaluate the overall strength of a draft class.

To quantify the success of an individual draft pick I’m looking at the *total minutes played* by a player during the first two years of his contract. As far as simple evaluations are concerned, I think minutes played is as good a measure as any of a player’s value to a team, and I’m only looking at the first two years as those are the only guaranteed years on a rookie’s contract. This is by no means a thorough measure of value–it’s meant to be simple while still being relevant.

After using this measure to compare the performance of individual draft picks, I used the same strategy to evaluate the entire “Draft class”. I computed the average *total minutes per player* for the entire first round (picks 1 through 30, in most cases) of each draft from 2000 to 2009. Here are the results.

There doesn’t seem to be much variation among the draft classes, but the 2006 draft certainly looks weak by this measure. Upon closer inspection, that year does seem like a weak draft: the best players being **LeMarcus Aldridge** (2), **Brandon Roy** (6), and **Rajon Rondo** (21). The weakness of the 2000 draft also seems reasonable upon closer inspection at basketball-reference.com.

Another approach would be to somehow aggregate the career stats of each player in a draft, rather than looking at only the first two years, but that would make it difficult to compare younger and older players.

Are there any other suggestions for rating the overall strength of an NBA draft class?

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## NBA Draft Math, Part I

Having put some thought into the mathematics of the **NFL draft**, I decided to turn my attention to basketball. From an anecdotal perspective, the NBA draft seems to be more hit-or-miss than the NFL draft: teams occasionally have success and draft a great player, but it seems more common that a draft pick doesn’t achieve success in the league.

In an attempt to quantify the “success” of an NBA draft pick, I researched some data and ending with choosing a very simple data point: the total minutes played by the draft pick in their first two seasons.

**Total minutes played** seems like a reasonable measure of the value a player provides a team: if a player is on the floor, then that player is providing value, and the more time on the floor, the more value. I looked only at the first two seasons because rookie contracts are guaranteed for two years; after that, the player could be cut although most are re-signed. In any event, it creates a standard window in which to compare.

There are plenty of shortcomings of this analysis, but I tried to strike a balance between simplicity and relevance with these choices.

I looked at data from the first round of the NBA draft between 2000 and 2009. For each pick, I computed their total minutes played in their first two years. I then found the average **total minutes played** **per pick** over those ten drafts.

Not surprisingly, the **average total minutes played** generally drops as the draft position increases. If better players are drafted earlier, then they’ll probably play more. In addition, weaker teams tend to draft higher, and weak teams likely have lots of minutes to give to new players. A stronger team picks later in the draft, in theory drafts a weaker player, and probably has fewer minutes to offer that player.

However, when I looked at the **standard deviation** of the above data, I found something more interesting. **Standard deviation** is a measure of dispersion of data: the higher the deviation, the farther a typical data point is from the **mean **of that data.

Notice that the **deviation**, although jagged**, **seems to bounce around a horizontal line. In short, the deviation **doesn’t decrease** as the **average **(above in blue) decreases.

If the total number of minutes played decreases with draft position, we would expect the data to tighten up a bit around that number. The fact that it isn’t tightening up suggests that there are lots of lower picks who play big minutes for their teams. This might be an indication that value in the draft, rather than heavily weighted at the top, is distributed more evenly than one might think

This rudimentary analysis has its shortcomings, to be sure, but it does suggest some interesting questions for further investigation.

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## Math Quiz: NYT Learning Network

**Test Yourself** quiz-question, can be found here:

This question is based on the complex methods companies like Apple use to reduce their tax bills. How much more would Apple have to pay if it were taxed like an individual?

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