The standard deviation and interquartile range are two measures of the spread of a distribution. It is potentially misleading to rely on standard deviation to assess player consistency in fantasy football for a couple of reasons.

Standard deviation is the square root of variance, which is the sum of squares of the deviation from the mean. In small sample sizes, such as a NFL season, a single outlier game can distort the mean. There is a related problem that the reader may assume that 68% of the values are within one standard deviation of the mean, which does not hold if the values are not normally distributed.

Consider the following player, who has a random score between 10-15 in 15 games and then a 40-point explosion in week 17. This player is extremely consistent, and the "inconsistent" game is not problematic from a fantasy perspective, as there is no downside from a player having an occasional big game.

In [28]:

```
gamelog1 <- c(sample(10:15, 15, replace = TRUE), 40)
gamelog1
```

In [29]:

```
library(psych)
describe(gamelog1)
```

Using standard deviation as a measure of consistency presents a misleading picture in this case because the mean is artifically inflated by one outlier. It also suggests that 11 of the player's games (16 x .68) fall between 6.5 (13.7-7.2) and 20.9 (13.7 + 7.2) fantasy points, which overstates the amount of week-to-week variance because the minimum value is 10 and only 1 game falls outside of the range of 10-15.

Interquartile range (IQR) shows that 50% of the values are between 10.75 and 13.25 which is more accurate, and probably says more about consistency than deviation from the mean that is skewed by an outlier.

In [30]:

```
summary(gamelog1)
```

Consider another player who is more inconsistent on a weekly basis, but does not have a big game. Standard deviation depicts this player as much more consistent than our previous player, despite this not really being the case. IQR is higher for player 2 than for player 1, despite a much lower standard deviation.

In [35]:

```
gamelog2 <- sample(7:17, 16, replace = TRUE)
gamelog2
```

In [36]:

```
describe(gamelog2)
```

In [37]:

```
summary(gamelog2)
```

In [ ]:

```
```