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what is the effect of problem size of the complexity of divide and conquer algorithms and why ?

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Considering the partition algorithm in quick-sort , depending on any input sequence it will be called  n times only so then what is the usage of dividing the problem into equal halfs , through recurrence relation formation I am able to figure out that time complexity is less if we have problem to be divided at each level in equal halfs but I am not getting logic behind this .
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