Don't Be a Tool

With draft season almost upon us, I thought I’d share a handy statistic I’ve been tinkering with. This number, which I’ve coined “minimum expected value” (statisticians probably have another name), can be found by subtracting the standard deviation from the mean. What the hell does that [ahem] mean? Let me explain…

Standard Deviation
Last year in my article on the Magic Formula, I described standard deviation. It’s the amount one thing differs, on average, from another. For our purposes here, think of it as the “plus or minus.” We’ve all heard someone say, “He scores an average of 30 points, plus or minus 5.” That plus or minus is the standard deviation. If you’re a masochist, go ahead and read the Wikipedia entry. As for understanding it completely, don’t worry; what’s important to know is that it measures consistency. From a fantasy perspective, “consistency” refers to how widely varying a player’s point total will be from week to week. The smaller the point swing, the smaller the standard deviation, and thusly the more consistent a player is.

For the 2007 season, who was the best fantasy QB? Tom Brady, of course. But what if I asked you this: Who was the most consistent QB? Tom Brady? Nope. It was David Garrard. To help you understand what I’m talking about, let’s take a look at the top five fantasy QBs. [For more players and positions, download my Excel spreadsheet.]

Now compare that to a list of the most consistent QBs, those with the lowest standard deviation.

As you can see, this is a very different list. Some of the QBs’ point totals here are actually quite low. Standard deviation, remember, can only tell us how consistent a player is. So in the case of Tarvaris Jackson, for example, the standard deviation alone does us no good because Jackson is consistently bad. On that basis, standard deviation alone is basically a useless stat in fantasy football. However, if we take a player’s standard deviation and subtract it from his weekly scoring output, we end up with an incredibly useful number, his minimum expected value.

Minimum expected value (MEV) is best defined as the lowest total points per week you can expect from any given player. By knowing this number, you can predict a player’s relative value. David Garrard, for example, can reasonably be expected to score at least 12.07 points each week (his average, 18 points, minus his standard deviation, 5.93 points). Take a look at the top five QBs by MEV.

Each week, we can expect Tom Brady to put up at least 18.73 points. No, he won’t do it every week, but he’s likely to do it much more often than not, and more importantly, he’s likely to do it way more often than anyone else. So there, that proves it: Tom Brady is the top fantasy QB. Duh. No, the real benefit of MEV is that it highlights guys like David Garrard and Big Ben, too. In fact, on a weekly basis, we can expect Garrard to outscore every QB in the NFL besides Brady. The math doesn’t lie, and if you subscribe to the theory that consistency is king, MEV can be an invaluable compass come draft day, especially as you hunt for value in the middle rounds, where championship seasons are truly built. Where did Garrard, Hasselbeck, and Big Ben go in your draft last year? I bet it wasn’t in the first five rounds.

The best part about MEV is that it’s universal. It works across players, teams, sports…you name it. Check the spreadsheet again where I detail QBs, RBs, WRs, and TEs. Just a quick glance and you’ll see why guys like Garrard, Ronnie Brown, and Andre Johnson could be the key to your season.

Discussion
After this article was posted, TFFG forum member 7grain pointed out an important fact about SD and MEV on the comments thread: “One Standard Deviation, by definition, encompasses 68% of occurrances. (34% above the average, and 34% below the average). Beyond one STD is 32% of occurrences: 16% above 1 STD and 16% below 1 STD. So you could “geek it up” a little bit more, but not scare people away, by saying that a player beat their MEV 84% of the time. And that’s 11 games out of a 13 game season.” If it seems like too much, just know this: He is absolutely right. Any player should beat their MEV 84% of the time.

This entry was posted on Monday, June 30th, 2008 at 9:03 am and is filed under Lyle's Lounge. You can follow any responses to this entry through the RSS 2.0 feed. Responses are currently closed, but you can trackback from your own site.