As a fantasy sports owner, you’ve probably run into this familiar situation — you draft a player and in one game he plays amazingly. And in the next, it’s a total dud. Maybe in game three, it’s somewhere in between. While we all hope for consistently good play from our players, we are often met with variability in their level of play.
Interestingly, when we evaluate a player’s history of play, we generally look to the mean or average of whatever metric is most meaningful to us (e.g., fantasy points if you’re in a fantasy league). As we learned in the last blog post on anomaly detection, the mean is interpreted as the expected value of a randomly selected observation from the monitored process. For example, Atlanta Braves starting pitcher Chris Sale has a mean K/9 value of 11.82 so far this season. This means that any time he has a start, we’d expect the number of strikeouts he records per 9 innings pitched to be 11.82.
Realistically, we don’t expect Chris Sale to hit this exact number every time he starts a game. There will be a degree of variability from start to start, attributable to a variety of factors. The quantification of variability is most commonly done through a metric called standard deviation.
You may have heard of this metric before, but how do we use it to quantify variation and more importantly, how do we interpret it?
The calculation can look a little scary, but its interpretation is actually fairly straightforward.
Standard deviation is also an average (and in a practical sense, is strictly positive); it is the expected distance a randomly selected observation is from its mean in either the positive or negative direction. In the Chris Sale example, the standard deviation for his K/9 is 2.87. This means that for any given start, we’d expect his K/9 to be +/- 2.87 from the mean of 11.82. This range of values (11.82 +/- 2.87) represents an expected range rather than an expected value. Clearly, if the specific standard deviation value were larger, say 9.37 in the case of Toronto Blue Jays starting pitcher Easton Lucas, this would imply greater variability in his K/9 values from start to start. And if it were smaller, say 1.55 in the case of San Diego Padres starting pitcher Stephen Kolek, then this would imply less variability in his K/9 values from start to start.
Because we typically just focus on the mean and tend to ignore the standard deviation, we’re only privy to half of the story. Some players might have high mean performance values but live in a frustrating boom/bust cycle because their standard deviation is also large in value. By incorporating standard deviation into our calculus, we can better understand the risk involved in rostering certain players.
Because of the importance of understanding and quantifying variation, starting next week, we will have a free weekly report to show the top and bottom performers in terms of mean and standard deviation. This extra insight will help you Manage with Confidence.
RJ SPORTS ANALYTICS 