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Is there any evidence that “growth”-style indexes and growth ETFs outperform their respective base indexes?
You are correct that over a short term there is no guarantee that one index will out perform another index. Every index goes through periods of feat and famine. That uis why the advice is to diversify your investments. Every index does have some small amount of management. For the parent index (the S&P 500 in this case) there is a process to divide all 500 stocks into growth and value, pure growth and pure value. This rebalancing of the 500 stocks occurs once a year. Rebalancing The S&P Style indices are rebalanced once a year in December. The   December rebalancing helps set the broad universe and benchmark for   active managers on an annual cycle consistent with active manager   performance evaluation cycles. The rebalancing date is the third   Friday of December, which coincides with the December quarterly share   changes for the S&P Composite 1500.  Style Scores,   market-capitalization weights, growth and value midpoint averages, and   the Pure Weight Factors (PWFs), where applicable across the various   Style indices, are reset only once a year at the December rebalancing. Other changes to the U.S. Style indices are made on an as-needed   basis, following the guidelines of the parent index. Changes in   response to corporate actions and market developments can be made at   any time. Constituent changes are typically announced for the parent   index two-to-five days before they are scheduled to be implemented. Please refer to the S&P U.S. Indices Methodology document for   information on standard index maintenance for the S&P 500, the S&P   MidCap 400,the S&P SmallCap 600 and all related indices. As to which is better: 500, growth,value or growth and value? That depends on what you the investor is trying to do.