Managing a fantasy football team and statistical analysis go hand-in-hand, but often fantasy owners neglect some important indicators. When analyzing statistics, many players are too focused on per game average, which goes hand-in-hand with season totals for yardage and touchdowns, as the only statistical indicator of a player's worth. This shouldn't be the case. To have a successful fantasy football team, one has to win individual games and to win individual games; a fantasy owner needs to be able to field a team of reliable performers. Averages don't tell us anything about reliability, but fortunately, the wonderful world of statistics gives us a tool with which we can monitor fantasy players for erratic behavior. It's called "standard deviation," and although most people are familiar with the term, its merits are rarely applied to fantasy football.

Standard deviation is basically a number representing how far points fall from a mean. In this context, each "point" would be one game's worth of stats and the "mean" would be the season average for that player. The larger the standard deviation, the farther from the mean most points will fall. Thus, players with a high standard deviation are more erratic performers and those with a small standard deviation post scores close to their average more consistently. In most cases, fantasy owners would be wise to stock their rosters with the players in the latter category.

Why is a high standard deviation generally bad? If a player on your team has a few huge games throughout the course of the season along with plenty of stinkers, he might not do you any good. You won't have the confidence to insert the player in your lineup and when his big game comes along that guy will be collecting dust on your bench. Worse yet, the big game inspires you to insert him into your lineup and he responds with a goose egg. These players are a headache and in most cases should be avoided. Using standard deviation to make draft and roster decisions can help to eliminate this problem.

Data Sample: Top 20 Wide Receivers in 2002
Because wide receivers are a notoriously inconsistent lot and on the surface it would seem that there are plenty of seemingly equal ones sitting around in any given fantasy draft, lets consider the top 20 fantasy wide receivers from the 2002 season, based on weekly averages. The following table enumerates these players, ranked by their per game average, and provides their standard deviation. Scoring is based on one-point per ten yards rushing or receiving and six points for each touchdown.

The Top-Heavy Pitfall
Before jumping headfirst into the numbers, it's good to consider one common pitfall of this type of analysis. It's slightly easier for players with high rankings to get higher standard deviations, so don't hold it against them as much as you would for players with significantly less statistics. For example, Terrell Owens' standard deviation is a lofty 9.44, but that's not so bad considering his per game average is nearly 15 fantasy points. It means Owens had several huge games and at 15 points per tilt, there weren't too many terrible ones in there.

On the other hand, if you run across a player of Corey Bradford's caliber that has a standard deviation above 9.00, avoid him like the plague. If a player that only gets 600-800 receiving yards in a season has a standard deviation that high it probably means he had one or two huge games that accounted for a large percentage of his stats and he's all but worthless to fantasy owners needing to choose a reliable lineup each week. In other words, compare apples to apples and oranges to oranges. Owens' 9.44 is still a bit high in comparison to his peers like Marvin Harrison, meaning you're going to get more consistent production from Harrison and have about the same per game average when it's all said and done. But by no means does it indicate that you should cross Owens off your draft board.

Analyzing the Data
Considering the table and remembering that the average standard deviation will naturally decrease as we head toward the bottom, it's easy to draw some conclusions about the players. First of all, Eric Moulds (5.10) and Joe Horn (5.23) have exceptionally low standard deviations. This tells us what many in the NFL already knew; these guys are money on a week-to-week basis. Of all the receivers in the league being worthy of a number one slot on a fantasy depth chart, owners should feel the best about having either of these receivers in their lineup on any given week. They're going to average 11 points per game for the season and that's just about what you're going to get on a weekly basis. Randy Moss gets honorable mention with a 5.99 standard deviation, which isn't bad at all for a guy people like to complain about having. He has his faults, but consistency doesn't seem to be one of them.

Aside from the aforementioned Terrell Owens, receivers Amani Toomer (8.83) and Plaxico Burress (8.87) have the highest standard deviations of any players on this list. Remember, cut them a little bit of slack because they are among the best performers in the league and that skews the standard deviation a bit higher, but it's still a red flag. Also remember to factor in special circumstances. One school of thought would be inclined to give Burress a pass knowing that his stats increased at the end of the year. On the other hand, only considering the second half of 2002, Burress' standard deviation jumps to a whopping 11.16 thanks in large part to 253-yard, two-touchdown game against the Falcons. But thinking of another pitfall (I never said this wasn't tricky business), keep in mind that eight games isn't much of a statistical sample and the game in which he racked up 37.3 fantasy points against the Falcons skews his average to the high side over that span and this affects the standard deviation. In other words, there are valid reasons to think Burress' high number is somewhat of an aberration.

A more typical case study can be seen with Koren Robinson, who had a 7.13 standard deviation for the season, but that number is cut to 6.00 if only the second half of the season is considered. Similarly, Laveranues Coles' 5.35 standard deviation is particularly impressive when you consider he was AWOL for the first three games of the season. It's always important to consider the special circumstances. The stats don't always provide a cut and dry explanation.

Another worthwhile exercise would be to eliminate the high and low scores for each player, reducing their numbers to a 14-game sample but eliminating the one wildcard at either end of the spectrum and this would bring Burress' numbers way down to earth at the cost of a slight reduction to the sample size. Of course, pulling in data from past seasons can counter this and significantly increase the sample size. At this point it's also worth noting that Week 17 was included in the stats and there's plenty of well-documented arguments as to why this week should be left out of any fantasy analysis as well. In other words, there isn't a shortage of variables to tweak to gather more information.

Returning to matters at hand, a quick glance at Amani Toomer's stats makes it easy to find the culprit for him as well. He had 204 yards and three touchdowns in a week-16 contest against the Colts. Another way to look at it is that he had 15% of his yardage and 37% of his touchdowns for a 16-game season in one game. That means there isn't as much to spread around for the other 15 games. Sure, you'd have the inside track to victory if you had Toomer in your lineup for his big game, but the other 15 weeks would find your team at a slight disadvantage to opponents fielding what would appear to be a comparable wide receiver. Unlike Burress, Toomer is an established veteran and he didn't go through any quarterback or offensive changes last year. Since he enters this year in a practically identical situation, the standard deviation is probably a reliable indicator.

Using Standard Deviation on Draft Day
As for using this information to structure a fantasy team, look to the St. Louis receivers to see how the standard deviation can be useful on draft day. Based on last year's averages, Marty Booker and Torry Holt look to be identical receivers. Both players averaged 9.64 fantasy points per game, but that doesn't tell the whole story. While Booker's standard deviation is a slightly higher than average 6.83, Holt comes in as low man on the totem pole at 4.39. That means Holt is an extremely consistent performer and fantasy owners can start him each week with a good deal of confidence. Banking on Marty Booker's standard deviation to improve with Kordell Stewart at quarterback is a long shot, so it's fairly easy to see which player should garner more consideration on draft day.

The Holt/Booker comparison might not be the best example since Holt is rated higher on most boards anyway, but consider a situation in which Isaac Bruce and Jimmy Smith are both available to see a more legitimate benefit of this analysis. It would be easy to look at last year's totals and decide that Isaac Bruce was a slightly better player, coming in with a 9.46 average as compared to Smith's 9.17. But looking at the standard deviations, Bruce has a 7.58, which is considerably higher than Smith's 5.15. An oversimplification of this number tells us that Bruce is going to give fantasy owners a couple of big games and a lot of dogs, whereas Jimmy Smith is a lot more likely to actually provide those 9+ fantasy points each week.

A look at Isaac Bruce's stats will reveal the validity of this claim. Against the Chargers, Bruce scored through the roof with 163 yards and three touchdowns for 34.3 fantasy points. He finished with 149.5 fantasy points for the year, meaning that an incredible 23% of them came in one game. To put it another way, Bruce had 912 yards and four touchdowns remaining from his season totals to spread over the other 15 games. That's not enough to put him in a lineup in most leagues and the poor outings preceding the outburst made fantasy owners apt to have him on their bench for that one anyway. (Incidentally, the trend isn't a new one for Bruce who, in 2001, also had three of his six touchdowns in one game.)

The Other Side of the Coin
While a low standard deviation should generally steer fantasy owners toward players boasting this mark, those with high standard deviations aren't without their merits. For example, consider a weak fantasy team facing a strong fantasy team. The owner of the weak team might want to purposely start some guys with high standard deviations hoping that the players hit one of their spikes that week. It's not playing the odds and the most likely outcome has the weak team losing badly, but in some cases it might be the only chance the team has for victory. Similarly, in leagues that give rewards for the high weekly score, owners might want to shoot for the moon and go with players with a high standard deviation.

To revisit Terrell Owens, having a weekly prize for high score would be a great argument in favor of choosing him and his 9.44 standard deviation over Marvin Harrison on draft day since his lows are infrequent and generally less consequential than middle-of-the-pack receivers anyway. Standard deviation can even help you make decisions based on your personality. Lets face it, it's fun to beat the tar out of your opposition and as long as you don't mind taking it as well as you can dish it out, Owens increases your chances of having a through-the-roof score. If you're a more even-keel type and need more consistent production to keep yourself happy, Marvin Harrison is the guy for you.

Just remember not to overdo it with this approach, because a high standard deviation is indicative of a player that only has big games once every handful of starts. Supposing you insert three players in your lineup that only have big games once every four starts, there's only a 1 in 64 chance that all three will hit their big game on the same week, whereas there's nearly a 50% chance that all three will bomb. In other words, that strategy will work out great for you once every four years, yet it will fail you miserably every other week.

As a final point, don't forget that some of these high performances can be predicted based on the strength of the opposing defense so always give that some credence. Standard deviation can of course be tracked for any position, but wide receivers were chosen for this article specifically because they do seem to be more inconsistent than other players and less predictable based on weekly match-ups. As a result, this analysis is particularly useful when looking at that position.

Further Information and Calculating Standard Deviation
For those interested, a more complete but still very readable explanation of this useful statistical tool can be found at this, or numerous other sites on the web.

Even if you don't find yourself overly interested in the theory of standard deviation or doing a lot of math with a calculator, Microsoft's Excel comes with a handy tool to calculate it for you. Simply fill in a spreadsheet with rows containing each player's fantasy points per game and use the formula STDEV(A1:P1) to calculate the standard deviation, where A1 and P1 are the starting and ending cell locations on the row for the individual game scores. Excel will take care of the rest.