Will Any Batter Ever Hit .400 Again?

Only 35 batters have ever hit .400, and 10 of those occurred in 1887, and "In 1887, when a player received a bases on balls (walk) he was also awarded a hit in his official statistics. The rules of the day and Major League Baseball recognize the statistics as they were recorded." 12 others all achieved this mark in the late 1800's, so only 13 did it in the 20th century. Ted Williams was the last to do so (in 1941), so the .400 club hasn't gained a new member in the past 74 years. However, streaks do end: there were 37 years between Triple Crown winners in horse racing, and 45 years between Triple Crown winners in baseball. But is it likely any hitter will ever hit .400 again?

The short answer is no. Not if the current trend of league-wide worsening hitting continues:

Data from Baseball-Reference

The steroid era accounts for the major increase throughout the 1990's, but since 2006 the league-wide batting average has been in a virtual free-fall. 

But what about the leaders, the hitters at the top, since we're concerned with anyone capable of breaking .400? For the most part, the trend of decreased average in recent years holds there too:

Data from Baseball-Reference

Using these leaders since 2006, I've attempted to quantify the respective probability each batter could've hit .400, given their batting average at the end of the year:

Year	Player	BA	Z-Score	P-Value
2014	Jose Altuve	0.341	-3.20	0.07%
2013	Miguel Cabrera	0.348	-2.57	0.51%
2012	Buster Posey	0.336	-3.12	0.09%
2011	Miguel Cabrera	0.344	-2.82	0.24%
2010	Josh Hamilton	0.359	-1.94	2.60%
2009	Joe Mauer	0.365	-1.66	4.84%
2008	Chipper Jones	0.364	-1.57	5.87%
2007	Magglio Ordonez	0.363	-1.88	3.04%
2006	Joe Mauer	0.347	-2.54	0.56%

In this case, the p-value represents the probability each player could've hit .400, given that they actually hit what's shown above. Therefore the fewer at bats, the more uncertain we are they couldn't actually have hit .400. Thus Chipper Jones's 5.87% is the highest, since he had the fewest at bats of these 9 players. 

Just as the league-wide batting average has declined, so have these z-scores and their respective p-values. Over the course of a full season with 500+ ABs, it's virtually impossible (now) to get a hit in 2 of every 5 trips to the plate. That being said, through 257 ABs...

Year	Player	BA	Z-Score	P-Value
2015	Paul Goldschmidt	0.354	-1.54	6.19%