The Law of Diminishing Returns

Some Fire Economics School…

With modern day construction, there is something we know very well as structural firefighters nationwide: the fire environment has gotten hotter and hotter over the years. This is mostly because building materials, and the stuff we fill our homes with are made out of synthetic materials tend to burn at higher temperatures than anything our grandparent’s or even parent’s generation has ever fought. Watch this YouTube video and you’ll get my point.

For those of you who aren’t in the fire service, now you see what we are up against. We have made great efforts in our own technology, by bettering our protective gear, but we are largely vulnerable to the threat of flash over. Flash over is the point at which everything in the room spontaneously ignites. I don’t care how great of gear you have, if you are in the room at the time of flash over, you’re done for. So how do we cope?

In order to prevent flash over from occurring, we teach our newest members to “pencil” a super heated environment. “Penciling” is essentially opening up the nozzle of your hose stream in short busts towards the ceiling (heat rises) for to cool the atmosphere above you. You don’t want to pencil for too long as that water turns to steam and steam displaces air at a staggering ratio. If the room is dominated by super heated fire gasses, you run the risk of displacing so much air at once, it could drive the hot gasses down on to you and cause severe burns. You also don’t want to pencil an environment that is not warm enough to cause steam conversion, as you are essentially just dousing a part of a house that had no business getting soaked in the first place. That’s just bush-league and we pride ourselves in being professionals.

We teach our newest firefighters to pencil the atmosphere incrementally as they advance further into a building towards the origin of the fire only when they begin feeling the heat. We don’t want to soak an area of the house that doesn’t need it, but we want to stay safe against the threat of flash over. As a firefighter, I learned it was best to start penciling when the heat drove me to my knees. The initial blasts of water evokes some frightening sounds. Imagine the hiss of spraying water on a hot pan or a BBQ and multiply that times a hundred! As the atmosphere cooled above me, small water droplets would start raining down on my mask which gave me the green light to advance a few more feet towards the fire. Repeat as necessary and you could find the fire easy peasy. A few times I got a little overboard and the water returning onto my mask was more of a waterfall than a few droplets. Our crew would pay for that later on in the incident as we’d then have to remove all that extra water.

Cap Is Rambling Again…How About The Economics?

What’s the lesson here? Well in terms of firefighter survival and professional tactics, “penciling” is an incredible lesson in the Law of Diminishing Returns. The law of diminishing returns holds everything constant except for one input into an economic equation. The law states that more of that input given everything else constant, gives you an initial benefit, but that benefit decreases with each extra incremental input to the point where it actually leads to be a detriment. The change in benefit between each input is called the marginal return. In the example I just gave we’ll keep the fire environment relativity static. We’ll analyze what return, or benefit, we get from each 3 second pencil into an atmosphere that is seconds away from flash over.

You find yourselves interior on the fire attack team with a rapid change in conditions. You’re driven to your belly by the heat. Your partner cusses and yells that “It’s hot as f#c$!” Luckily you brought a hose line in. You know the danger of opening up too quickly on the heat, so you give your first burst of water cautiously. The air above you crackles and boils. You pause a second. It’s still hot as hell, so you give the air another cooling burst. The noise is less intense and you’re able to pull your head slightly up off the floor. Ahh! Breathing room. It’s still warm though, so you open up for another burst. The results are a little better and you are able to get back up onto your knees. You haven’t advanced yet because you want to give it one more burst. You open up and water rains down onto the floor. The air temperature remains unchanged. At this point you’ve reached the peak the water’s effectiveness. The marginal return, or additional benefit, from that last burst of water was essentially nil.

So, after getting a lot out of the first burst (aka not burning to death), the second and third bursts still helped you but at a decreasing amount. After the fourth burst, you are soaking the ground with water and being an unprofessional dip$hit. That in the nutshell is the law of diminishing returns. I’m sure we can think of plenty more examples of this law in the fire service. We wouldn’t commit a second alarm response to a single vehicle car fire, because the benefit of the second, followed by the third, fourth, fifth, etc. engine would be a waste of resources. That 5th high rise hose pack making it’s way to the burnt popcorn on the 14th floor’s return would be a big fat zero.

The Take Away…

The law of diminishing returns is something that I look to quite often on the fire ground, my personal life, and in my studies in economics. We all know the saying that you can have too much of a good thing, but it’s incredibly hard to pinpoint that exact level when enough is enough. On an incident, it’s fairly straightforward to see where more companies should get committed or released, but in the financial world or personal enjoyment, it’s tough. Pick any input into your equation: a beer out of the cooler let’s say. With each successive beer you open, ask yourself how much more happy that beer will make you compared to the beer before it (i.e. what is your marginal return). Yes it will still make you happy, but by a decreasing amount. I know I’m treading into some dangerous territory here with some of you degenerates. I don’t care who you are and what your argument is, if you keep treating each beer as having an equal benefit, you can prove my point the next day. Trace an arc between that first delicious beverage and that throbbing headache you’re nursing. At some point in the middle, you’ll find the peak where the marginal benefit of another cold one was zero. Maybe that was the beer you should have perhaps ended the night on. We’ll touch more on this concept in later posts, but that’s the law of diminishing returns in a nutshell.