They won the pennant but their underlying stats were not that good. The reason they came in first is that they performed remarkably well in "clutch" situations.
First, let's look at their underlying stats. Yesterday I presented a formula that estimates a team's winning percentage. I found each team's HRs, BBs, and non-HR hits per game for both their pitchers and hitters and then converted this to a differential. Then I came up with the following formula for winning percentage using regression analysis:
Pct = .5 + .071*NONHR + .047*BB + .157*HR
(some technical notes on this at the end). This formula predicted that the 1959 White Sox would have a winning percentage of .512, while it was actually .610. So they exceeded their predicted pct. by .099 (not .098 due to rounding). This was the third highest positive differential since 1920. The highest belonged to the 1931 Cardinals. But Retrosheet does not have situational splits for them. Next is the 2007 Diamondbacks. But they did not make it to the World Series.
The table below shows the standings for the 1959 AL using the predicted pct. The White Sox are 4th.
The White Sox were actually out homered by their opponents (with the biggest negative differential). But they were third in both walk differential and nonHR differential. Now let's look at how they did in "clutch" situations vs. other situations. The table below shows how the Sox hitters did in various situations.
Now what the Sox pitchers did.
Now the differentials followed by some discussion.
The total line, of course, refers to all plate appearances. The Sox had modest differentials here. They batted .250 while the Sox pitchers held their opponents to a .242 AVG. With no runners on base, the differentials are even lower. But now look at their differentials with men on. For AVG, it is .013, much higher than the .005 with none on. For OBP, the differential jumps from .009 to .023. SLG goes from .001 to .010.
With runners in scoring position (RISP), they had a .040 differential in AVG!. It was actually negative in nonRISP situations. Sox pitchers held opposing batters to a .221 AVG with RISP. Their OBP differential jumped from .007 to .040 while SLG jumped from -.014 to .063. Incredible. Their hitters' SLG went up .032 with RISP while the pitchers lowered it by .044.
Moving to close and late situations, the Sox outhit their opponents by .024 while it it was only .005 in nonCL situations. The OBP differential rose from .010 to .043 while for SLG it went from -.012 to .076. Another stunning swing. The Sox hitters actually had an SLG of .400 in close and late situations, by far their highest for any case.
So it is pretty easy to see what happened that year. I have not looked at other teams, but the case of the 1959 White Sox must be very unusual.
Technical notes: The regression was linear. The r-squared was .806 and the standard error was .035, which amounts to 5.67 wins per 162 games. I also put each team's data in groups of 5 years and then did the same regression. The r-squared was .917 and the standard error in terms of wins fell quite a bit (I think it was about 2.2 wins but I left that data at the office). So some of the randomness is mitigated by aggregating over 5 years. The coefficient values were about the same in each regression.