By Subvertadown

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Expectations , Understanding StatisticsOne way to visualize a position’s impact on your roster score is to look at the distributions of scores. (The below curves have been smoothed within 1 point.)

It is also interesting to see the distributions of projected scores, for comparison— i.e. what range of scores are rankers or modelers guessing?

Kicker and QB are both shown here, for contrast. Kicker scores almost always fall in the 0-15 range, and they are almost always predicted in the 5-11 point range. **QBs cause a lot more variance**.

"But wait", you might say, "it's not just the range of outcomes that matters, but **how much the outcomes differ from expectations**! You should evaluate the randomness after first subtracting the expected scores."

And you’re right! That is actually the way you should be thinking about playing fantasy. It is the right way to treat risk. So don’t consider QBs as providing a safe cushion of reliable points. Instead ask how much their score can vary from the projection.

When I was first seeking fantasy stats information, I was mostly looking for distribution curves like the ones below. They show the distribution of errors, relative to projected scores. Here they are unlabeled for now (see further down for labeled graphs), just to show that some positions vary ±10 whereas other positions vary ±20:

The distribution shape of these *deviations *is actually very similar to the distribution shape of the total *points*. The** shapes of the distributions change very little**.

You can see this in the following graph, using QB as the example. The black curve represents point scores, but re-centered at 0.

Meanwhile, the grey curve represents the error *relative to* the projected points (also accounting for fluctuations in weekly average). The shape improves and there is a **slight overall narrowing**… but only from 8.0 down to 7.5 (root-mean-square deviation). The tails continue to extend just as wide.

You may have expected to find more certainty when using projections. You might have thought a highly-ranked QB probably scores high, so the error would be less. But the disappointment comes with every fantasy position, as the errors-from-projection are as almost as wide as the point distributions themselves. **No source of projections is capable of reducing the large amount of randomness in individual fantasy positions.**

Also be wary of thinking some quarterbacks are just "more reliable". I have also analyzed the 5 quintiles of these QB projections, and **QBs expected to score highly have the same amount of projection error as QBs expected to score low**.

Meanwhile **kicker projection errors are the least bad**. Despite poor predictability, the point randomness of kickers is small. Here is the bar chart of the projection errors (standard deviations), for all positions. (They are ordered from lowest to highest correlation coefficient, to match my related post about interpreting the correlation coefficient).

And here are 3 charts of position error distributions after subtracting projected points; I have grouped them by narrow/average/wide. (QB is included in each, to provide a reference point.)

K, TE, and RB2 introduce less error. QB, D/ST, and RB1 introduce the most. WR1/WR2 fall in between.

I hope at least this section has provided some intuition for you, which you can use to align your expectations from projected scores. Errors are wide, variations of 10 points are common, and rankings (projections) don’t do as much as you might think to lesson that error.

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