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Expected VBD: Explaining How and Why We Draft

Ever wonder why we suggest waiting on defenses and kickers even when VBD says it's time to draft them?

Back in 1996, Joe Bryant introduced the fantasy world to the principles of Value Based Drafting. Footballguys readers understand how VBD works: a player's value is not determined by the number of points he scores, but by how much he outscores the other players at his position. And while that logic makes sense, Footballguys has always told you that you can't draft solely based on VBD scores.  If you draft strictly according to VBD using a worst-starter baseline, the 11th best defense in a 12-team league should be drafted before the 25th running back (in start-two running backs leagues). Even if you use a lower baseline, VBD will generally suggest selecting defenses and kickers much earlier than is appropriate.

Instead of drafting according to strict VBD, you should be drafting to something I'll call Expected VBD, which is best defined by an example. Suppose Russell Wilson has three equally possible outcomes this year: he has a one-in-three chance of scoring 425 fantasy points, 325 fantasy points, and 225 fantasy points. Further, let's assume that the baseline number of fantasy points at the quarterback position is 300 fantasy points.

We would project Wilson to score 325 points, which would be the weighted average of his possible outcomes. This means VBD would tell you that he is worth 25 points, because 325 is 25 points above the baseline. Expected VBD works like this: If Wilson scores 425 points, he'll produce 125 points of VBD. If he scores only 325 points, he'll be worth +25, and if he scores only 225 points, he's going to have -125 points of VBD. In real life, players with negative VBD scores can be released or put on your bench. So if Wilson scores 225 points (probably due to injury), you'll start another quarterback, roughly a quarterback who can give you baseline production.

So when Wilson scores 225 fantasy points, his VBD is 0, not -75. That means his Expected VBD would be (125+25+0)/3, or 50. Wilson's VBD according to our projections may be only 25, but his Expected VBD is twice as large because Expected VBD does not provide an extra penalty for sub-baseline performances. Not surprisingly, different positions have different amounts of Expected VBD associated with them.

I've collected data on the average draft position of quarterbacks, running backs, wide receivers, and tight ends going back to 2000, and I have ADP data on placekickers and defenses/special teams going back to 2006. In this article, I'm assuming a 12-team league that starts 1 QB, 2 RB, 3 WR, 1 TE, 1 PK, and 1 D/ST. I've used standard Footballguys scoring except when otherwise noted. In addition, all negative VBD scores are given VBD scores of zero (this is because sub-baseline players can be benched or cut).  Let's start with quarterbacks.

Quarterbacks

On average, the highest drafted quarterback will produce a little over 80 points of VBD.  Meanwhile, QB12 -- who has a VBD score of 0 in our projections -- has produced, on average, 30 points of VBD. I calculated the average number of points scored by QB1 through 24 (in terms of Average Draft Position), and plotted them in blue in the chart below. The black line shows the smoothed logarithmic curve which best fits the data. I've included the logarithmic equation and the R^2 for those statistically-inclined readers who care about that stuff.

A graph showing Expected VBD for QBs (Please connect to the internet to view images inside articles.)

The curve shouldn't be too surprising, but it highlights an important point: the Expected VBD for "backup" quarterbacks in fantasy leagues is not zero. The fifteenth drafted quarterback is still expected to produce about 15 points of VBD, because some years, QB15 turns into a top-ten quarterback. It was only two years ago that Cam Newton had an ADP of QB24 and finished the year as QB5. Ignoring a player's sub-baseline results (i.e., using Expected VBD instead of projected VBD) means throwing out his worst performances. When we count a player's best performances but throw out his worst, his average performance that counts improves. The worse his bad performances are (and the better his good performances are), the more it improves by. This means the difference between a player's projected VBD and his Expected VBD will be larger when his range of possible performances is wider. As we'll soon see, the "Expected VBD" for QB12 is much higher than the "Expected VBD" for PK12 because for quarterbacks (and running backs, wide receivers, and tight ends), the range of possible performances is so much wider (and thus, they get the benefit from cutting out all the really bad performances).

Running Backs

The next chart shows the actual, average points of VBD produced by the first 40 running backs according to ADP.  For runnign backs, wide receivers, and tight ends, I have assigned 0.5 points per reception to produce these VBD values. The running backs graph is similar to the quarterbacks graph, except the top running backs produce nearly twice as many points of VBD:

A graph showing Expected VBD for RBs (Please connect to the internet to view images inside articles.)


In the equation in each graph, the most important piece of information is the coefficient before the "ln(x)" variable. That's not as scary as it sounds: fantasy production decreases logarithmically (and not linearly) as you go down your draft board. The larger the coefficient, the steeper the drop. With the QB graph, the coefficient was -25.6; here it is -32.5. This is simply quantifying what your eyes can tell you: that the slope of the running back curve is quite steep, which reinforces what you've experienced in every single standard fantasy footall draft you've ever played in: running backs go early and often because the position dries up extremely quickly.

The other important takeaway here is that that RB25 doesn't have a value of zero. In fact, the 25th running back selected in fantasy drafts should be expected to produce about 20 points of VBD.

Wide Receivers

The next graph shows the average VBD produced by each of the highest 50 drafted wide receivers.

A graph showing Expected VBD for WRs (Please connect to the internet to view images inside articles.)

The wide receiver curve is a little less steep than the running back one -- the coefficient is -24.8 -- but the key takeaway again is that the "last starter" wide receiver should be expected to produce close to 20 points of VBD.  The fact that the dropoff rate is steadier is a main reason why running backs are more valuable than wide receivers in fantasy football (at least in traditional leagues that start 2 RBs and 3 WRs).

In 2009, Miles Austin was the 63rd wide receiver drafted but finished as WR3. Two years ago, Jordy Nelson had an average draft position of WR46 but finished third in this scoring system. And last year, Michael Crabtree and Randall Cobb were drafted as WR4s but finished as WR2s. When looking at Expected VBD instead of simply projected VBD, the wide receivers outside of your top 40 become much more valuable. And that's why you'll take them before your fantasy defense or kicker, even if their projected VBD is lower.

Tight Ends

The tight end graph is very similar to the quarterback graph, except the values are just a little lower throughout (as is the coefficient).  This makes sense, because, on average, TE 4 is generally drafted after QB 4, TE 10 is generally drafted after QB 10, etc.

A graph showing Expected VBD for TEs (Please connect to the internet to view images inside articles.)

Placekickers

We all intuitively know that placekickers are not very predictable from year to year. But now we have some data to prove that point. From 2006 to 2012, the highest drafted kicker averaged fewer than five points of VBD. Once we smooth the curve, things look slightly better, but you can see why people wait on kickers. Among the top twelve kickers, it's close to impossible to figure out which one will do best. And the coefficient is miniscule on the logarithmic variable: this means the dropoff in Expected VBD is tiny when it comes to the kicker position. If you're nearly as likely to hit on PK12 as you are on PK1, there's no incentive to selecting a kicker early regardless of his projected VBD.

A graph showing Expected VBD for PKs (Please connect to the internet to view images inside articles.)

The kicker graph looks very different than the other graphs. But what about that other position we advise you to wait on?

Defenses/Special Teams

For D/STs, there is no standard scoring system. Here, I used the scoring system in the Fantasy Football Players Championship: 1 point for each sack, 2 points for every takeaway, 6 points for all defensive/special teams touchdowns, and 5 points for each safety. Defenses/Special Teams also receive 12 points for each shutout, 8 points if the opponent scores between 2 and 6 points, and 5 points if the other team scores between 7 and 10 points. Take a look at how the highest-drafted defenses have fared since 2006:

A graph showing Expected VBD for D/STs (Please connect to the internet to view images inside articles.)

As with kickers, there is very little correlation between average draft position and points of VBD. Consider this: In 2012, none of the five highest drafted defenses finished with positive VBD at the end of the season. The fact that the coefficient for the running backs (-32.5) is significantly larger than the coefficient for defenses (-2.5) tells you that there's a much bigger dropoff between RB5 and RB10 than there is between DT5 and DT10. (But since it's logarithmic instead of linear, there's not necessarily a bigger dropoff between RB55 and RB60 than between DT5 and DT10.) Once we look at Expected VBD, it becomes clear that unlike at the other positions, the top projected kickers and defenses aren't much better than the bottom ones.

Putting it All Together

I've presented a lot of graphs in this article, but I've saved the best for last.  This one plots the Expected VBD curves for each position (the label on the right side of the graph displays the corresponding color for each position). By placing all the positions on one graph, you can see how drastic the differences really are. On the horizontal axis is the ADP information; on the vertical axis is the number of Expected VBD points.

A graph showing Expected VBD by ADP for all positions (Please connect to the internet to view images inside articles.)

Why isn't the #1 projected D/ST selected earlier in fantasy drafts? Because that position is expected to produced only about 15 points of VBD, which is roughly equal to QB15, RB31, WR42, or TE12. And the situation is even worse at kicker. Since so many offensive players are expected to produce 15+ points of Expected VBD, a rational drafter would wait a long time to select a kicker or a defense. It doesn't matter if your top-projected fantasy defense has a projected VBD of 40 points. We know that, on average, the top defense comes in well below expectations, and the dropoff curve is nearly flat. This graph helps explain why you should wait on drafting kickers and defenses.

The table below reproduces the graph above but in numerical form: it displays the number of points of Expected VBD at each draft slot for each position:

ADPQBRBWRTEPKDT
1 84.2 126.5 107.5 58.5 8.1 14.6
2 66.4 103.9 90.3 45.7 7.4 12.9
3 56 90.8 80.2 38.3 7 11.9
4 48.6 81.4 73.1 33 6.7 11.2
5 42.8 74.1 67.5 28.9 6.5 10.6
6 38.1 68.2 63 25.5 6.3 10.2
7 34.2 63.2 59.2 22.7 6.1 9.8
8 30.7 58.8 55.9 20.2 6 9.5
9 27.7 55 52.9 18 5.9 9.2
10 25 51.6 50.3 16.1 5.8 8.9
11 22.5 48.5 48 14.3 5.7 8.7
12 20.3 45.7 45.8 12.7 5.6 8.5
13 18.2 43.1 43.8 11.3    
14 16.3 40.6 42 9.9    
15 14.6 38.4 40.3 8.6    
16 12.9 36.3 38.7 7.4    
17 11.3 34.3 37.2 6.3    
18 9.9 32.5 35.7 5.3    
19 8.5 30.7 34.4 4.3    
20 7.2 29 33.1 3.3    
21   27.5 31.9      
22   25.9 30.8      
23   24.5 29.7      
24   23.1 28.6      
25   21.8 27.6      
26   20.5 26.6      
27   19.3 25.7      
28   18.1 24.8      
29   17 23.9      
30   15.8 23.1      
31   14.8 22.3      
32   13.7 21.5      
33   12.7 20.7      
34   11.8 20      
35   10.8 19.3      
36   9.9 18.6      
37   9 17.9      
38   8.2 17.2      
39   7.3 16.6      
40   6.5 15.9      
41     15.3      
42     14.7      
43     14.1      
44     13.6      
45     13      
46     12.5      
47     11.9      
48     11.4      
49     10.9      
50     10.4      

Final Thoughts

I will close with two additional points that are worth keeping in mind, and both further deflate the value of kickers and defenses. It is very likely that your waiver wire will contain PKs and D/STs that will produce more points of Expected VBD than the QBs/RBs/WRs/TEs on your wire. To the extent that this is true, you would probably want to subtract the Expected VBD value of each waiver wire position from the values above to get an "Expected VBD above replacement" value at each position. This would make kickers and defenses even less valuable than the other positions.

We now know why you would take a running back with a lower projected VBD over a fantasy defense: he could still have a much higher number of Expected VBD points. But there's also a reason why you might draft a running back or wide receiver who is projected to score even fewer Expected VBD points than a particular D/ST. Using Expected VBD points is great and gets us nearly all the way to identifying how we draft. But what drafters really want to maximize isn't their number of Expected VBD points. Think about your fantasy league: your goal is to win your fantasy championship. As a theoretical matter, something like "Fantasy Championship Win Probability Added" would be an even better draft guide than Expected VBD. I would define Fantasy Championship Win Probability Added as, for each player, the marginal increase in your chances of winning your fantasy league you receive from drafting a particular player. If the 34th running back has a wide variance, this might mean there's a greater chance that he holds no value but also a greater chance that he turns into a top-twelve running back. In that case, even if his Expected VBD points is low, the small chance that he turns into a star could be more likely to help you win a title than gaining a few more points out of your fantasy defense.


More from Chase Stuart:

Running Back Production by Quarter (2014) - July 24
Running Back Workload Part II - July 18
Running Back Workload - July 11
Running Back Fantasy Production in Wins and Losses - July 7
Quarterback By Committee 2014 - June 19
Rearview QB - June 5
A Starting Point for 2014 Running Back Projections - May 27
How to Project Receiving Yards In 2014 - May 14
Cross-Team Running Back Handcuffs - August 28
Search our Stats: A Guide to the Data Dominator, Historical Data Dominator, and Game Log Dominator - August 14