# The Fantasy Football Philosopher: Considering Consistency

In this ‘philosophical’ series, we will explore broad – and often rhetorical – fantasy football queries. The question that centers this article is relatively simple: *Does player consistency matter?*

Let’s formalize our question a bit. Of course, *consistency *is generally thought of as a positive asset in a fantasy context. You’d rather have the RB2 that posts respectable numbers every week than one who puts up a goose egg once a month.

However, what if we really *isolate *consistency, making it the *only difference *between two players? Let’s consider the following two players (assume this is for a 16-week fantasy season):

**Player A:** scores 10 points every week

**Player B:** scores zero points every odd week and 20 points every even week.

Which player do you prefer? Both will score 160 points over the season; indeed, both will *average *exactly 10 PPG. Ignore playoffs for now – you probably would want to front-load points in the regular season to *make *the playoffs – and just focus on trying to get the best record possible. Although this is a thought exercise, it has very real implications: you might be choosing between a player with an A profile (Robert Woods) and a player at the same position with a B profile (Tyler Lockett).

All told, this is a subtly tricky question. Clearly option B will give you a great chance to win in even weeks and a poor chance to win in odd weeks; would you rather just have an ‘average’ chance to win every week with option A? The answer does depend a bit on context, and we will flush it out in the sections below. All data comes from nflfastR.

##### Fantasy Landscape

To start comparing options A and B, we need to understand the *distribution *of fantasy scoring. To do this, we can generate thousands of ‘lineups’ from the 2020 season (the most recent season will give us the best picture of the modern fantasy landscape). The algorithm is simple:

- Randomly select a week. For concreteness, say this is Week 7.
- Randomly select the Week 7 performance of one of the top-12 performing RBs from Weeks 1-6. This is, in essence, a ‘random RB1’ for the roster, and replicates reasonably well what actual fantasy managers do: generally, managers start players who have performed well in the season so far.
- Select a random QB, RB2, WR1, WR2, WR3, and TE1 in the same fashion (i.e., for the RB2, randomly select the Week 7 performance of an RB ranked 13 – 24 from Weeks 1-6).
- Sum these positional scores; this is the fantasy roster score.
- Do steps 1-4 a total of 10,000 times.

Once all is said and done, we can plot the *distribution *of all of these hypothetical lineups:

This is mostly mound-shaped or, in statistical parlance, a *Normal *distribution. It’s just a *bit *skewed to the right (fatter on the right side), for the simple fact that the *individual positions are skewed to the right*. For example, here’s the distribution of all of the RB1 scores; you can see there is a ‘right tail’, or a long slope pointing out to the right, that represents ‘boom’ performances from stud RBs (the ‘bust’ tail is capped near zero, since it’s hard to score very far below that!).

We know that this ‘right skew’ in skill positions is why it’s so valuable to have a top positional player (CMC, Travis Kelce, etc.). However, when we *add *these positional scores to get the distribution of roster scores, the result approaches a Normal distribution. This is called the Central Limit Theorem, or CLT for short, which eventually says ‘when you add things up it becomes Normal’. Anyways, that’s a discussion for another time…

##### Win Probabilities

Now that we know the distribution of the fantasy landscape, let’s think about how options A and B affect win probability. The curve in the chart below is the same from above (distribution of roster scores). The vertical dotted line marks 100 points, or the expected value for a high-scoring team (notice it’s on the right side of the distribution, above the average score). The two arrows basically outline option B: either 110 points (player scores 20 points) or 90 points (player scores zero). You can think of the vertical dotted line as option A: the rest of the team scores 90 and this player always scores 10 points.

Let’s think about this chart for a second. The red shaded region is the area under the curve that you *lose *when the player from option B scores zero; the green shaded region is the area under the curve that you *gain *when he scores 20. What do you notice?

**The red area is larger than the green area. **This is simply because, at 100 fantasy points, the line is sloping

*down*( in technical terms, a negative derivative). This means that

**the probability of winning falls more when the player scores zero than it rises when the player scores 20.***

You can think about this intuitively. When you’re scoring a lot of points, you’re already out ahead of the pack (the rest of the league). While adding 10 points to your total won’t do much – you’re already in the lead against most teams – *losing *10 points will hurt, since it will bring you closer to the average team. In this case, inconsistency is *bad; *with an inconsistent option, you will lose more games on down weeks than you will win on the up weeks.

Sharp readers might note that this is entirely depend on *where on the curve you sit. *The above is for a high-scoring team; what about a low-scoring team that expects to score 65 points? See below:

All of the intuition from the last chart applies to this chart, just flipped: here, **inconsistency is good**. If your team is already bad, scoring zero won’t make much of a difference; you probably were going to lose anyways. However, the *boom *weeks (scoring 20 points)* *could make a big difference because it brings you closer to the average team.

One last case; how about for a perfectly average team?

The green and red shaded areas are basically the same size here, so it might seem that consistency doesn’t really matter. However, recall that the fantasy distribution is skewed *slightly to the right*, so a perfectly average team will have a *slightly *larger green shaded region (fatter tail on the right) and thus will *slightly *prefer consistency.

Anyways, let’s put this all together on one chart. The x-axis is points scored for your roster, and the y-axis gives the win probability based on this score. The middle line – in between the green and red – shows this relationship for the average team. As you might expect, the higher points you score, the higher win probability you have: this approaches 100% as you get near 130 points (with these roster settings) and 0% as you fall to 40 points.

The green shaded region shows the *win probability gained *from boom weeks for player B (+40 points in this example so we can really see the effect), and the red shaded region, symmetrically, shows the *win probability lost *from bust weeks for player B (0 points). Note the same pattern we saw above: for low points scored, the green region is *far larger* than the red region; when you start scoring more points, the red region, or win probability lost, trumps the green region.

##### Win Totals

Now that we’ve discussed the effect of inconsistency on win probability, let’s extend to win *totals*. We’ll consider a team that scores +x points above their baseline on odd weeks and -x points below their baseline on even weeks (shown here on the x-axis). The ‘baseline’ is just defined as a 50th percentile score for an average team, a 25th percentile score for a bad team and a 75th percentile score for a good team. The y-axis is the number of expected wins in 16 games. So, for example, a ‘good’ team with zero inconsistency projects to win 12 games.

These charts confirm what we saw above: inconsistency is bad for good teams and good for bad teams, and this effect increases as inconsistency gets stronger. For the most extreme point here (+/- 20 points) good teams win almost two less games while bad teams win almost two more.

Notice that average teams see their win total go *slightly *down (-0.3 wins). This is because of that *right-skew *in the overall fantasy landscape that we mentioned earlier.

Finally, we can visualize an ‘inconsistency’ of +/- 20 points against the strength of a team (x-axis). The y-axis is just the amount of expected wins added (or subtracted).

Again, we see a negative relationship: the better the team, the worse the effect of inconsistency. This peaks at about +2 wins for a 15th percentile team and bottoms at -2 wins for an 85th percentile team (things get a bit wonky if we go all the way to the zero and hundredth percentiles). Note the important intersection, or ‘break-even’ point, at about 47%. We saw above that inconsistency is *slightly bad *for average teams because of the right-skew in fantasy; therefore, the lines above don’t cross at 50% (an average team). Instead, consistency only starts being good when you are slightly *below *average (47th percentile or worse).

Finally, it’s important to note that these expected wins are *on average. *Boom/bust lineups lead to boom/bust records, which generally means winning a lot or losing a lot; we’re only focusing on the *average* here.

##### Conclusion

Fantasy football is all about context. Your decision to target boom/bust inconsistency depends on a variety of factors: the rest of your lineup, who you are playing, how much you are behind/ahead, your record, the playoff picture, etc. However, when selecting players over a long horizon with other variables reasonably equal (say, on draft day), we’ve shown that **consistency is good for average and above average teams. **Inconsistency – defined here as scoring the same amount of points, but in boom/bust cycles – is **only good for** **slightly below average teams or worse. **

Don’t hear what I’m not saying: the inconsistent profile discussed here certainly has its time and place. Even though it decreases *expected* win totals (for average and above average teams), it *does *add more ‘season upside’: you’re more likely to reel off a ton of wins (and of course, a ton of losses) than with a more consistent team, even if the *average *number of wins is lower in the long run. This might be exactly what you are going for in a given situation. The point in this article is that, in a neutral situation, consistency is good for *maximizing expected wins *– a pretty important metric – for average teams or better.

The verdict is out. Boring is good!

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*The area under the density curve, or the integral, between two points is the probability that the random variable exists between those two points.