Patience. Most runners lack it. And most runners would be well served to adopt a mindset where patience rules their decisions about training, how they analyze their training, and coping with injuries.
On a related note: You should have a long-term training plan. If you've never run a marathon, then you need to give yourself more than 12 weeks to train for it. Similarly, if you're trying to PR in the marathon or other distance, bettering your finish time will likely be done in small gains rather than one race where you run a 10-minute PR. Patience.
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When you get injured, you need to do your best to fight impatience. You're injured. Accept the fact that the original training plan you had is no longer valid. Could you go crazy on the elliptical and do hours of General Strength and Mobility (GSM)? Sure. But the body heals faster when the macro stress is lower, so you're probably better off maintaining levels of GSM and doing a bit of pool work or walking (assuming your injury is one that would safely allow for those modalities) to give your body more energy to heal.
You're a runner, so you're dying to get back to running, yet you need to give your body time to heal. When you spend hours cross-training, you may or may not be aiding the healing process. I get that you're dying to run, but you need to be intelligent about the road back to running.
What you can't do is this. Let's say you have a goal race—a half marathon—in 12 weeks. During week 10 you get a foot injury. You're out for 10 days with no running, then you need another 10 days to get back to normal running (for example, some light running every other day). So now, after missing three weeks of running, you're seven weeks out from the race. If you've raced that distance before, then you should be able to finish the race. Will you PR? No. But can you finish? Yes.
Should you try to get back on the original schedule, the pre-injury schedule? No way. You just got injured and the volumes that the original plan had you running in week seven are much too high for you—a you that has missed three weeks of normal training.
This is where acceptance comes in. You have to accept the idea that while you won't be able to PR at the race, you can have a good time and run the race. Note: this is where a coach can help because he or she can give guidance as to all of the intermediary steps between the injury and the race.
When you get injured, be patient. Accept that when you experience an injury, the training plan that you originally had is no longer going to work. You'll have to come up with a new plan. If you're impatient with this process, then you'll either get injured again or you'll be extremely disappointed in your race performance.
Instead be patient, knowing that consistency is the key to long-term improvement.race.