Based on their estimates, the rate of blood clots while not on any birth control is 4.2 per 10,000 women in a given year. (Heit and Gunter confirm that about 3 to 5 women per 10,000 will get a blood clot each year.) So that's a 0.04% chance of getting a blood clot. Very small chance, but it happens.
For women taking a levonorgestrel-containing birth control pill (an older one), they estimated that 6 extra cases per 10,000 women would occur each year. For women taking a drospirenone-containing pill, they estimated that 13 extra cases per 10,000 women would occur each year; and for women taking a desogestrel-containing pill, they estimated 14 extra cases per 10,000 women. So we're basically looking at a difference between 0.04% chance and 0.18% chance.
"Even though the risk is slightly increased, it's still very low," says Heit. So what causes this difference? It's thought that the estrogen in birth control is what mostly accounts for this overall increased risk, and the newer types of progestin might also directly affect the clotting mechanism or they might impact estrogen in a way that affects your clotting, says Gunter.