This is completely false, I think you just made those numbers up.
Best case numbers outside of a dungeon are 22.5% escape chance per day. That's best case. In a dungeon it's 7.5%. That's not "extremely low".
If you managed to capture a prisoner right next to a castle and deposit them immediately it would be an average of 13.3 days imprisonment. But if you have to travel some distance which you almost always will it is lower.
Here's the average imprisonment time assuming they spend a number of days outside prison and the rest inside:
| Days outside en route to dungeon | Average days before escape |
|---|
| 0 | 13.3 |
| 1 | 11.3 |
| 2 | 9.7 |
| 3 | 8.5 |
4 | 7.6 |
| 5 | 6.9 |
| 10 | 5.1 |
| 100 | 4.4 |
But there is no minimum time, many of them will escape almost immediately.
| Number of days before reaching castle | Percentage of lords escaped en route |
|---|
| 1 | 22.5% |
| 2 | 39.9% |
| 3 | 53.4% |
| 4 | 63.9% |
| 5 | 72.0% |
| 6 | 78.3% |
| 7 | 83.2% |
| 8 | 87.0% |
| 9 | 89.9% |
| 10 | 92.2% |
So most of the time you're going to lose half of the lords before you even get to a dungeon. If you are attacked while or just before trying to siege an enemy town and the siege takes five days, 70% are going to escape and respawn right near you with an army ready to attack you again.
This is silly, if they are going to respawn with free armies then there should be a minimum time before they can escape, like ten days guaranteed imprisonment after which the chance progressively rises. Or if half of them are going to escape before you can even get to a dungeon then it should take them a while to get their act together.