A great article on the basics of koi reproduction in your pond.
...It takes approximately a year for eggs to fully develop within the female koi. Eggs formed in the spring of the first year will be dropped in the spring of the following year. The eggs produced by the female are not fertile. The male of the species releases sperm onto the eggs after the female has dropped them. After the spawning has taken place, new eggs will begin to form. These eggs will be released during the next year's spawning.
How Do Koi Fish Reproduce in Freshwater Ponds? (sciencing.com)