The most ubiquitous conclusion has been that the diversification of positions within the basket, and the resultant variety of individual trade outcomes, will lead to the apparent experience that some trades will be executed really well, and others not so well, and that the overall effect will be that the average execution level will be pretty good. This theory reduces the concern facing those who are trying to figure out whether the best price obtainable was achieved when they are working a single order, rather than a basket.
Why do I refer to the "apparent experience" of best execution? There is a glaring problem with the measurement of "best execution" as it applies to buy and sell orders in securities, which is shared with all kinds of scientific measurements, which need an effective "control" group for accurate measurement.
The basic measurement tool of best execution is called the volume-weighted average price, or something derived from it, which kind of means what it says. If you are a big part of the volume, the price you get is going to materially affect the benchmark by which your skill in execution will be judged. In this way, when your order is big enough to affect the market, "best execution" is kind of up to you -- and whomever you can convince to be the other side of your trade.
As with any transaction, and with all other things being equal, you might be expected to get a better price if you can be patient, and remain relatively anonymous with respect to source and size, but in any case there is no real way to determine that. The price you get is the price available for your size at the time, and if you are a large part of the volume, the VWAP -- your standard of measurement -- will simply reflect that truth.