Archive of posts filed under the Sports category.

## 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.

www.MrHonner.com

## 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:

http://goo.gl/cnMwj

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?

Click here to see more in Challenge.

www.MrHonner.com

## 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:

http://goo.gl/dCBy2

This question is based on rapid population growth in African countries.  How long will it take Nigeria’s population to quadruple?

Click here to see more in Challenge.

www.MrHonner.com

## 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:

http://goo.gl/ZNTL3

This question is based on the increasing number of Chinese tourists visiting the United States each year.  Just how much are they spending?

Click here to see more in Challenge.

www.MrHonner.com

## NFL Draft Math: 2012

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 exponetntially.  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?