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I race with a heart rate monitor all the time. You've experienced exactly what you should expect for a constant heart rate. Heart rate drifts as your body heats up and you dehydrate, so your pace has to slow down to compensate. You're better off trying to hold mostly steady with a few beats drift for the first half, then slowly let it climb by 1-2 beats every couple of miles until around 22, and then kick it in with what you've got left. It takes many iterations to learn the best HR approach for a marathon. Most do not recommend using a monitor in a race, but I've found after running about 15 marathons with the monitor, I can use one to optimize my time. You'll have to be willing to experiment a bit. If you use anything near constant HR, you will always run positive splits. Here's what my splits with average HR per split were in my best marathon this year:
6:41/154, 6:53/163, 6:55/164, 6:52/165, 6:59/167,
6:54/167, 7:16/168, 7:03/168, 7:26/167, 7:08/167,
7:07/167, 7:19/168, 7:10/168, 7:10/170, 7:16/169,
7:17/171, 7:23/170, 7:25/173, 7:26/170, 7:30/173,
7:25/175, 7:30/176, 7:23/176, 7:29/177, 7:51/178,
8:06/180, 3:38(7:31/mile)/178
time 3:12:47, average HR overall: 170
In this race, my target was 3:15 and change, so once I saw I had it in the bank, I didn't bother pushing all out for the last couple of miles.
For further reference, my anaerobic threshold is 177 and my max heart rate is 210 (which is not really a relevant
quantity).
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