What Price Improvement Actually Means
Price improvement, as used by Citadel and other market makers, means executing a trade at a price slightly better than the National Best Bid or Offer (NBBO) at the moment of execution. For example, if the NBBO is a buy at $10.01, Citadel might execute your buy order at $10.009 — a 'price improvement' of $0.001 per share.
The Problem with the Comparison
The NBBO is not the best available price in the market — it is the best quoted price. In a competitive exchange environment, actual execution prices frequently improve on the NBBO through order matching and price discovery. By comparing its execution to the NBBO rather than to actual competitive exchange execution, Citadel is comparing itself to a floor rather than a ceiling.
What the Research Says
Multiple academic studies and SEC analyses have found that retail investors would receive materially better execution prices if their orders were exposed to competitive exchange trading rather than internalized by Citadel. The 'price improvement' Citadel provides is real but systematically inferior to what competitive markets would provide. The difference between what Citadel gives and what competition would produce is Citadel's profit — funded by retail investors.