To be honest, I find that variances in warm up have very little effect on the outcome of my races. I always aim to be at the race at least an hour early. But, sometimes it doesn't work out or sometimes, my body demands extra trips to the porta-potties and my warm up time is compromised. I cannot think of any instances where lack of warm up time has led to me having a bad race.
On the other hand, I do recall two instances where I had practically no warm up and yet ran pretty well.
At one very small 5K, my wife and daughter came with me to the race and we arrived with 10 minutes or less until the start. I left them at the car and hurried to the start to get my number, go the bathroom, and line up. I won the race fairly easily with a time that was as fast or faster than what I'd predicted to my wife before the race.
At another 5K, I was having lower GI issues before the race and felt lucky that I was able to get to the starting line at all (and lucky that there were ample facilities so that I didn't have to stand in line long for my repeated trips to the bathroom). This was a slightly larger race than the one mentioned before. I had won the race two years previous, but did not run the previous year. The previous year's winner was in the race and was probably the local favorite since he was a local high school runner just back from his first year of college. We started with a pack of 4-6 runners and with a mile to go, we still had a pack of 3-4 runners. I set the pace for much of the race because I came into the race wanting to run a fast pace. With a mile to go, there were still three runners in the pack. I didn't break away until about 600m out when I surged just after we turned off of the road onto the high school property. In the end, I won though my time was probably a bit slower than I had hoped for.
So, although a good warm up is probably best, I think that the stress that comes from not being able to warm up as one would like also helps prepare one to run. For me, a lack of anxiety has been a better predictor of poor race performance than warm up. I know that too much anxiety or mishandled anxiety can be a bad thing, but if I don't feel any pre-race stress or if I am thinking about things other than the race, then I'm not prepared to race.