‘my slippage cost would have doubled’ - can I check my intuition? Suppose the market is 99-101 (ie, mid of 100) and you want to buy. You queue at 99. Assume there’s 50% probability of the market moving up and 50% probability of moving down (not unreasonable at this frequency). If the market ticks down, you get filled at 99. If it ticks up, you pay up and get filled at 102. That gives an expected fill at 100.50 (99 or 102), or slippage of 0.50 vs mid. If you take liquidity, you get filled at 101, or a slippage of 1.00. This is 2x vs your algo.
PS, I love skiing, so pretty relevant discussion!
Your intution is correct. So in summary:
Cost of always paying up: 0.5 tick
Cost of passive trading: 50%*-0.5 + 50%*1 = 0.25 ticks
Net improvement: 0.25 ticks: about half the original cost
This is purely theory, but my actual trade statistics come in at almost exactly this level of improvement. Interestingly on a big move the slippage can be much bigger than 1.0, but the market in reality doesn't just move up or down, sometimes it stays the same (at least for the duration of my order). When it stays the same, I will end up getting filled at my passive level. So the chances of a passive trade are a little higher than 50%, which compensates for the fact that paying up costs me a little more than 1.0 on average. So the real figures are something like (not exactly, I don't have the real numbers):
Cost of always paying up: 0.5 tick
Cost of passive trading: 45%*-0.5 + 10%*-.5 + 45%*1.2 ~ 0.26 ticks
GAT