Let's try to answer some of those questions the best we can.
If fouling a ball off was an easily measured skill -- if percentage of balls fouled was a good measure of that skill at least -- then you'd expect the skill to show through most years. Strikeout rate, for example, is fairly decent at measuring your ability to make contact. Strikeout rate stays fairly stable -- you could use shorthand to say that almost 75 percent of your strikeout rate next year is described by your strikeout rate this year.
Foul percentage doesn't work that way. Your foul percentage this year describes about 40 percent of the variance in your foul percentage next year. That makes foul percentage more unstable than isolated slugging percentage, number of home runs per plate appearance, or ground ball rate. Brian Roberts was 11th in baseball foul percentage this year, he was barely above average in 2013. So it goes.
If you up the minimum number of pitches seen from 300 to 1000, you finally push the predictive ability past 50 percent. So, once you look at players over that threshold, you can see that Pablo Sandoval was No. 1 in foul percentage this year -- he fouled off 26 percent of the pitches he saw -- and also in 2013, when he fouled off 25 percent of the balls he saw. (Second in 2012.) Still not as "sticky" as ground ball rate when seen as a whole, and just barely better than on-base percentage.
Perhaps that has something to do with your average two-strike approach. When Fuld asked me what the data on foul balls looked like, he wondered if better hitters had a better two-strike approach.
It does look like the league does have a two-strike approach. The average hitter fouled off 18 percent of all pitches he saw in 2014. He fouled off 16 percent of the pitches he saw in zero- or one-strike counts. He fouled off 24 percent of the pitches he saw in two-strike counts, as he hunkered down and tried to make more contact.
But if you correct for swings, the average batter is only slightly better at making contact in two-strike counts -- his fouls per swing only go up from 41 percent to 43 percent. Considering that the pitchers are throwing whiffier breaking and off-speed stuff more in two-strike counts, it's probably still a significant difference.
Not every hitter takes the same two-strike approach every year. Your two-strike foul rate is half as well-correlated year-to-year as your regular foul ball rate -- at both sample levels. So players hunker down to differing levels in different years.
Take a look at 2014's leaderboard for the most extreme two-strike approaches. These are the (1,000-pitch minimum) leaders in foul rate in two-strike counts minus foul rate in one- and zero-strike counts ("IncreaseFoul%").
It's an interesting group of batters, and it includes Fuld himself. These guys really upped the fouls with two strikes -- but only Victor Martinez was also in the top 20 in 2013. Perhaps pitchers can adjust to most batters that show a large foul ball split like this. Could a pitcher just throw two-strike pitches further away from the zone against someone that shows a propensity for fouling off pitches?
There is a relationship between power and whiffs -- not a strong one, but there is a positive correlation between swinging strikes and isolated power -- but there is no relationship between this two-strike approach metric and power. There was only one weak relationship between his two-strike change in foul ball rate and an overall stat -- "IncreaseFoul%" did describe about 22 percent of the variance in strikeout rate.
Fuld wondered if you could identify players that were shooting themselves in the foot with their two-strike approach. "Could you maybe use that data to tell a guy, 'Well, your two-strike approach, we appreciate the idea but ...'" Fuld said before an August game with the Athletics.
If you're not cutting down on your strikeouts with a two-strike approach, and you're mostly known for power anyway, perhaps you should just grip it and rip it (or take) with two strikes. Jonny Gomes, we're looking at you.
Unless you're Pablo Sandoval, it seems like aiming for contact that results in a foul ball is a tough skill to replicate anyway.