The idea of focusing on this specific position pairing (QB+Kicker) was partly based on columns I had read years back (one example is here).  For some time, I've been wanting to investigate this methodically, and I hope you'll find it interesting-- if you can make it through the deep-diving content below.

The Hypothesis: Why pair QB + K?  The prevailing reasoning behind pairing is to de-risk your lineup ("higher floor" strategy): "If your QB doesn't manage to get a passing TD, you still get the points from the kicker's FG."  And-- assuming your QB is good enough-- the kicker not getting a FG during a drive means you possibly got points from a QB passing TD, instead.  But let's look at the numbers....

The Analytical Process

I will start the discussion by leading through an analytical thought process, with purposeful misassumptions on the way to try and keep it more interesting.

Question 1: Let's start by asking What is the correlation between weekly kicker results and QB results?  We ask this because, If the kicker has a risk-mitigating effect, then we might expect a negative correlation-- more QB points would result in fewer K points.  A lower QB score results in higher K points.  (Can you see the problem?)

Answer 1: No: the correlation is 0.17, therefore not negative.  The reason?  The best teams will have both QB and kicker scoring higher -- the worst teams will have both QB and K score lower on average.  So when we look at the overall correlation, we mostly see this built-in trend (of good teams vs. bad teams).  [See the first, left-most bar labeled "Results"].

So question 1 was not the best one to ask. If we got a negative correlation, we might be done. But a positive correlation means we can't conclude yet. First, we need to remove this good-team/bad-team trend.

Each bar corresponds to the discussion in the text: Answer 1, Answer 2... So the first bar is "correlation between kicker results and QB results":

Solution: To solve the fact we didn't get negative as hoped, let's discard the idea of measuring absolute point results. Instead, let's observe instead how the correlation changes, compared to expected point correlations.  Therefore Question 2: How much do projection models predict the QB + K to correlate?  In other words, "before the week starts, what trend do model projections expect", between these two positions?

Answer 2: Kicker and QB are expected (from projection models) to correlate much higher than 0.16.  Before the results come in, statistical models expect their fantasy points to have a correlation coefficient of 0.55!  [The second yellow bar, the tall one labeled "Projections".]   This is because both positions are expected to do well whenever their teams are expected to score a lot.

This seems interesting...:  Before they game, QB + K are expected to correlate strongly..., but then it turns out they correlate weakly.  Hypothesis: Isn't that an indication that real game-events give a counteracting effect?  If the results correlate less than the expectations correlate, doesn't that mean there's de-risking going on?

To investigate this hypothesis. we ask Question 3: Do the errors to projections have a negative correlation?     In other words, if a QB scores more than expected, does that mean the kicker scores less than expected?  Now-- by measuring in relative points, instead of absolute points-- it feels like we're defining the real question we wanted to investigate from the beginning.  To calculate the trend between errors, we need to calculate "Actual fantasy score minus expected fantasy score" for both positions (i.e. calculating error from expectation)-- and then look at the correlation.

Answer 3:  It turns out no.  Kicker-error and QB-error correlate with 0.11, which is not negative.  It is, however, the smallest correlation so far.  [See the 3rd yellow bar above, labeled "Errors".]  

Why didn't that work?  In short, based on the above, the explanation has to be that QB scores and K scores tend to move in the same direction-- i.e. booms or busts affect the whole team, due to NFL randomness-- and this effect causes more dramatic movement than any "offsetting" effects.  If the QB has a worse game than expected, then the Kicker also has a worse game.  The upshot is that when a team does unexpectedly bad, then the whole team does bad-- QB and Kicker included.  

Great-- we've already made a lot of progress in framing the right question.  But let's take it another level-- to make sure we get at the right answer.  We especially need to consider: We don't actually care at all about analyzing the worst QBs.  Nobody is really thinking about improving their fantasy roster by pairing a kicker with a crappy quarterback.  The original intent was to look at QBs who are expected to perform, and then wondering if their kicker de-risks the net score. 

Approach 4:  For every week, pick out the top-10 QBs (based on the QB model).  Also pick out the Kicker who is on the same team as each of those top QBs.  Then ask the same questions we just tried (questions 1 and 3): what is the correlation between results, and what is the correlation between errors-from-expectations?

Answer 4a and 4b:    (4a) The fantasy point results of top QBs correlate 0.05 with kickers-- smaller than any correlation we got before!  [See the 4th bar in the above bar chart]  That's partly a sign that we're eliminating the good QB/bad QB divide, which is progress.  (But btw, it's also a sign of a smaller sample size.)    (4b) The top-QBs and top-Ks have projection errors with correlation at 0.035.  This is the smallest number yet.  [See the 5th, right-most bar in the above bar chart]  

Bravo-- we've got it smaller and smaller!  Maybe signs of kicker de-risking?  Unfortunately, the answer is still "no".  We need that number negative: "close to 0" is not good enough.  A correlation of 0 would mean "no effect", but we still have a positive number, which means QB-K pairing actually still makes your roster more volatile (the two positions are likely to both overachieve or both underachieve).

We're almost at the end, but let's look at hard numbers to make sure we're forming the right conclusions.  Here are some remaining analysis. Ultimately, the above analysis only gives an indication. To really check what's going on, we need to actually calculate fantasy points and deviations.

Further simulations, to reveal Points and Variance

Question 5: How does kicker pairing affect the total point expectation?  Look at the below chart, showing the average fantasy points of QB+K combinations.  A complexity I need to explain is that-- for the purpose of smoothing things out-- I have averaged in pairs, so I averaged QB1 and QB2 together, and QB3+QB4, etc.  (Because otherwise we get strange effects like QB6 scores higher than QB3, or things like that.  ....I made that example up, by the way.)

Answer 5, explanation: Notice that, going from QB 1&2avg down to QB9&10 avg., there's a clear decrease in expected points due to the QB.   (That's what we should expect, if indeed the QB scores faithfully follow the projection models.)  So now, what we really want to do is compare the 6th, final bar of each cluster to the other bars (the other bars represent using top rated kickers without trying to pair)-- because that final blue bar is the one that represents QB-own-Kicker pairing.  

Result 5:  It is clear that the blue 6th bar tends to be lower than the other bars-- meaning that kicker pairing tends to slightly decrease total fantasy point results.  

Approach 6:  It might seem like a bad result that pairing QB+K results in (slightly) fewer fantasy points.  But remember: it was never the objective to score more points, with QB-kicker pairing.  In fact, the philosophy from the outset was that we accept a lower point ceiling (in order to increase the floor).  So really we're not so interested in the above result (except if the difference was large).  What we really want to know is question 6 "Do we decrease QB+K volatility by pairing?  And we answer this by measuring the standard deviation of the errors.  This yields a number indicating the volatility, so we can compare kicker-pairing with the strategy of using other top kickers.

Result 6: Now look at the second chart, just above ("Standard deviations...").  For the majority of top-10 QBs (clusters on the right side), you can see that QB+K pairing generally causes more volatility.  However, one interesting nuance here: QB1&2 actually do seem to benefit from reduced volatility when paired with their kicker.  So maybe... if you have the top 1 or 2 QBs, using any of the other top 10 kickers may actually cause slightly more randomness.

But for all other QBs who are not the weekly top-2, consider the final picture showing a smoothed histogram of errors: The histogram makes it clear that there is not a noticeable benefit in volatility from kicker pairing, and in fact--if anything-- pairing tends to slightly widen the distribution.

Blue curve is error from unpaired QB+K combinations; Orange curve is paired. Upshot: very little difference, and pairing might actually make it worse.

Blue curve is error from unpaired QB+K combinations; Orange curve is paired. Upshot: very little difference, and pairing might actually make it worse.

• Upshot: Generally don't waste effort trying to strategize QB-kicker pairing, and instead go for the most point projections.  In a rare case you have a QB1 or QB2 for the week, you can consider kicker pairing if you want to reduce volatility, but otherwise there is no benefit.  QB and Kicker tend to move in the same direction depending on if it's a fluky bad game or an exceptionally good game.

• EDIT: No, don't overinterpret this as meaning "avoid all QB+K pairing". A top-rated QB + top-rated K, on the same team, is not at risk of a lower expected score. The above analysis is about pairing even if the kicker is not a top-ranked option.

Thanks for reading!