If you crashed at mile 11, you likely outran your training.
How long was your training plan? What was your longest run? Weekly average?
Most of us enter our first half marathon woefully under trained and the training we did was at a higher than needed pace or effort.
I closely followed the Higdon "Novice I" plan. My training took me all the way up to 12 miles towards the end. I didn't have any difficulty with that distance-wise. My crash during the race wasn't due to distance - it was the pace. No training regimen I'm aware of calls for you to run 10+ miles at race pace.
I'm pretty sure I went out the gate too fast and couldn't sustain it for 13 miles. I'm not sure if starting slower would have netted me a better time or not. I'm curious if re-fueling would help me or if it might do more harm than good.
I also only drank water/Gatorade at maybe 3 of the mile markers because I didn't want to slow down. So I end up sloshing most of it all over myself and the drinking throws off my breathing.
Higdon makes great "get you to the finish" plans but you definitely have to learn to pace yourself on race day. I certainly wouldn't blame the mile 11 wall on in-race nutrition. As you build your base mileage over the years, you'll progress to some other training plans that have more tempo runs over greater distance. You are correct regarding race pace at greater than ten miles. However, I'm a firm believer in 14-mile slow runs in prep for the half marathon somewhere around week 9 or 10 of a 14-week build. I also like to drop a 10K and 10-mile race in the training plan.
For fuel, you simply don't need anything for a two-hour pace or less if you've been training aerobically (and you should). Our body stores roughly 2000 calories of glycogen and 10,000+ calories of fat. As long as you are training at low efforts the majority of the time (70-80% of volume), you should be allowing your body to burn fat vice glycogen. On race day, your body is burning 800cal per hour at race pace. Even with no fat burning, you have ample glycogen in your body to sustain a two-hour run.
So, a sip of water every few miles should suffice. I personally like to take a Gu at the turning point just to keep the hunger pangs at bay until I get to the finish line. Yes, I'm hungry when I finish. I promptly throw down some fruit carbs and water. Then a full protein laden meal within the hour.
Steve Gangemi is one of my favorite doctors that writes about aerobic training:
http://sock-doc.com/aerobic-vs-anaerobic-exercise/. Great five part series with links in each blog post to some great information on aerobic training. As you'll read there, it takes time to build a good aerobic base.
