No, it varies with product and is heavily conditional on your entry. Your experience is to be expected, adverse selection is often just sufficiently large enough to deter you from improving your execution prices by turning a liquidity-taking strategy into a BBO-pegging strategy, i.e. arbitrage-free between peg order and marketable crosses.
Not to sure how much data you need, but I found Coinscious quoted the most affordable prices for historical data. You can get them as flat files or they offer API access. Their free level might work for you to start.
CME ED Futures
If we take 3m CME ED Libor IR futures, the value is \$2,500 * IMM - that is, the movements in the contract price are amplified by \$2,500. If the contract moves from 95.00 to 95.01, that means a movement in the value of a position of 1 contract by +0.01*\$2,500=\$25. That relationship does not change, but the tick size does change when each ...