Have you ever heard that the average speeder only gets to their destination ten seconds earlier? I have, or at least something to that affect. I think this ignores the obvious in trying to influence people. Life is not about the averages, it is about the rarities. Almost everyone lives for the rarities.
The average is the day that traffic moves normally, whatever normally is for your commute. The rarity is that you get stuck behind that slowpoke who drives exactly the same speed as the person next to them. The average is that you come to a red light and can turn right on red. The rarity is that you find yourself behind someone too pensive or distracted to make the turn. On the average day you get that same parking space, but sometimes you've been beaten to it.
The cumulative effect of this is that you remember those rarities, while the averages all blend together and don't matter. So, what do you do? Go a little faster to try to get there earlier. Pass those last few cars before you take the exit. Maybe, if you've got time to spare, you leave earlier, but that's a hassle. So, despite what the averages tell you, you rush to get there a little faster.
The result is that on average you get nowhere. The rarity is that you make in before the pensive, slow poke whose after your parking space. Is it worth it? You decide.