Significance of walks vs. strikeouts in FIP calculation According to Wikipedia, the baseball FIP statistic is calculated using:
$$
\frac{13HR + 3BB - 2SO}{IP} + C
$$
Why should walks be more significant than strikeouts? If the equation were to include hits, which it specifically doesn't, I would understand the higher constant relative to strikeouts because a hit can result in a greater number of total bases and because hits allow for runners to advance even when they are not forced to.
A walk, as far as this equation is concerned, is simply the only fielding independent failure to get an out, whereas a strikeout is the fielding independent way to get an out. Thus, they should be of equal consequence in this equation.
My understanding is that it should look like this:
$$
\frac{13HR + K(BB - SO)}{IP} + C
$$
where $K$ is some constant.
Why is the equation calculated the way it is?
 A: The following is based on the derivation provided by Tom Tango at http://www.insidethebook.com/ee/index.php/site/comments/tangos_lab_deconstructing_fip/
Short answer: FIP is based on runs per game. A walk contributes more to giving up a run than a strikeout contributes to not giving up a run. There is no reason to expect that a strikeout would diminish runs in a game the same as a walk would contribute to runs produced.
First some motivation. The FIP equation is based on Christina Kahrl's concept of the three true outcomes of home runs, walks, and strikeouts (source). They are called such because fielding and luck play much less of a role in the realization of, say, a walk, then, say, a ground ball up the middle. The ground ball could easily lead to an out or a hit depending on some combination of luck, defensive positioning, defensive ability, the way the ball was hit, and the type of pitch. It's not that the batter can't influence the outcome of a ground ball, more that variables outside of the ability of the pitcher and the hitter play a much greater role in the outcome than a walk. Hence a measure based on the three true outcomes may better represent a hitter or pitcher's "true" ability. This is as opposed to statistics like ERA or OBP, where the defense plays a much larger role.
The FIP equation is given by https://library.fangraphs.com/pitching/fip/ as:
$$
\frac{13HR + 3(BB+HPB) - 2K}{IP} + C
$$
FanGraphs defines the statistic as follows: "Fielding Independent Pitching (FIP) measures what a player’s ERA would look like over a given period of time if the pitcher were to have experienced league average results on balls in play and league average timing." Note that I treat HBP as walks going forward.
How could we derive a stat like the one described in the FanGraphs definition?
A starting point could be expected runs produced for a plate appearance, given an event realization, above the average runs generated per plate appearance. The precise mechanism for computing expected runs from outcomes is beyond the scope of this answer (see https://library.fangraphs.com/principles/linear-weights/) for details. They are based on the expected runs above average for each event in each situation, weighted by the likelihood of each situation. These are something like 0.3 for BB, 1.4 for HR, and -0.25 for strikeouts (per plate appearance). In addition, we have -0.03 for balls hit in play (BIP). By definition, taking an expectation over this yields 0:
$$
E(\text{runs above avg} / PA) = E(0.3BB + 1.4HR - 0.25K - 0.03BIP + error)  = 0
$$
We want expected runs, not expected runs above average for each event. So we add the average value of runs per PA (~0.1) to each outcome to get the average runs given the realization:
$$
E(\text{runs} / PA) = E(0.4BB + 1.5HR - 0.15K + 0.1BIP)
$$
We are only interested in the three true outcomes. Since every BIP is not one of the three true outcomes, we can re-arrange as follows:
$$
E(\text{runs} / PA) = E(0.3BB + 1.4HR - 0.25K) + 0.1
$$
To use this, you would need to plug in the expected BB/HR/K per plate appearance for a pitcher. To make the resulting statistic a bit more intuitive, convert to expected runs per game by multiplying the by the average number of plate appearances in a game (~40):
$$
E(\text{runs} / \text{game}) = E(0.3BB + 1.4HR - 0.25K) + 4.0
$$
Now the values on the RHS are in units of BB/HR/K per game. These are usually measured on a per inning basis, so plug in the per inning stats and multiply by 9:
$$
E(\text{runs} / \text{game}) = 2.7BB/IP + 12.6HR/IP - 2.25K/IP + 4.0
$$
Which is pretty close to FIP. Differences arise due to an adjustment for earned runs, different estimations of the numbers plugged in, different values of expected runs per outcome, rounding, and so on. But the above explanation should provide intuition for 1) what is measured and 2) where the weights come from. The constant is usually adjusted to make the statistic look more like ERA.
Of course, the statistic is not perfect- check out xfip at https://library.fangraphs.com/pitching/xfip/ for a stat that corrects for some of the luck involved in hitting home runs.
