网友的括号打得不对。应该这样表示：

This applicant is (by far) the better than that one.

by far 是个表示程度的介词短语，跟 much，a lot 作用相同，修饰比较级。better 之前这个 the 加不加，其实与 by far 无关。原句加 the 有误。

This applicant is (by far) the better than that one. （错）

This applicant is  (by far) better than that one. （正）

那么，什么时候才加 the 呢？—— 1. 比较级后有名词，加  the；2. 比较级后 + of 时，加 the。例如：

Prevention is by far the better option.
预防是目前最好的解决办法。
"We were by far the better team," added Ferguson.
“我们现在表现得更好。”弗格森说。
This one is by far the better of the two.
这个在两个之中要好得多。

加 the 的原因是，名词需要冠词，且是需要特指的冠词。第3句其实是 the better one 的省略。