As we have been watching The Last Man on Earth, we have loved watching each new arrival spoil Phil Miller’s plans. And we started wondering, how many people might really be left, and who might actually show up in Tucson. So we asked our data science team to take a look, and we find the show has given us some data to work with.
New Arrivals Melissa and Todd bonding.
For review, we know that Phil Miller looked like The Last Man on Earth, and toured North America looking for others-but without luck. We also know he left bread crumbs with his “Still Alive in Tucson” billboards.
But only after two years did a few others start to show up at maybe one person per week. Now Tucson has a constituency of seven, plus one cow.
So we took the famous Drake Equation (below) which is used to calculate the probability of communicating with life outside earth, which includes the probability it was there, intelligent and had the capability to communicate; and re-purposed it for our calculations. In a sense, we are trying to understand a similar probability.
In this case we need to estimate how many survivors are left, the knowledge of where they should meet up, the ability to travel there, the desire to travel, and ultimately the ability to make it to there-in this case Tucson.
When we do this calculation we estimate that Phil and the gang might expect about 60 more arrivals in the coming years, making 67 survivors total. His “Alive in Tucson” signs are a significant contributor to all these arrivals per our calculation. And without those signs, then Phil truly would be alone because the ability to communicate with others is one of the biggest early factors in joining up with others. This actually is a genius stroke (maybe a surprise coming from Phil, or a nugget of his true potential?) because when we think about other survivors, we don’t think it is likely that a survivor would both search the whole country AND leave signs for others along the way.
Alive in Tampa
The calculation is sensitive to how many survivors we start the model with. The US Office of Management and Budget lists about 381 Metropolitan Statistical Areas (MSAs) in the US (even Alaska, but not Hawai’i). And here Phil helped us. Phil probably specifically visited many of these and drove through the rest on his way to other areas in his search for other survivors. This tells us we cannot put too many persons in each MSA otherwise Phil would have likely bumped into someone after visiting the top 150 MSAs—the big cities (Tucson is 53, Tampa is 18). In fact, if we estimate a person in each of the top 150 MSAs, we calculate Phil should have found 7 other survivors—but missing 143 others. Maybe those seven survivors were also drunk in their own Margarita pools. But knowing Phil’s bad luck, it is understandable he missed those seven. (Or maybe we seeded the model with too many survivors.) But, maybe Phil should have tried fireworks, after all that seemed to work out well.
We also put a person each in the second tier MSAs that we mention Phil drives through but we show that he ultimately misses those survivors.
However if we start to add more survivors then it becomes even more likely that Phil would have found someone. For example, if we scale the top MSAs with 10 persons, then Phil should have found 70 other survivors. But since he found none, then this value is likely too high. Also something else funny would happen–if 10 persons were in each MSA, then those survivors would have likely found each other, creating small communities with associated and importantly noticeable activity like agriculture, noise, movement, and maybe most importantly electricity and lighting. This would have increased the odds dramatically of finding these other survivors.
So while this helps us define the upper end of the range, how do we determine the lower end of the range? In this case, we can use the actual arrival rate of survivors to work backward using the Poisson distribution to help us.
What we know is that 6 survivors have shown up. Now we need to estimate the total time which is not precise but close enough here. Start first with Melissa (Week1). Carol (Week2). Carol and Phil are married (Week3). Todd arrives (Week4). Carol and Gail arrive (Week 5/6) and “new” Phil arrives shortly after (Week 6/7). These two values: the number of weeks, and number of arrivals, allows us to calculate the average which is 1 about survivor per week. When I up level this statistic to a 28 day month, the average is 4. And the graph here shows what the distribution of arrivals should look like. 54% of the months should see 3-5 new arrivals. But it is possible to have no arrivals 1.8% of the time and a 5% chance that 7 could show up any month. That is what is fun about the Poisson you could wonder if that is it, then one day a VW bus might pull up with 7 people in it.
Don’t read this chronologically as in how many arrivals in the coming months. Instead this reads what is the probability that 2 persons will come, 3 persons, et al.
But the implication of this simple analysis is clear, at the end of a year, there would be about 52 survivors in Tucson. But this might be too simplistic and too early to trend. After all we should expect some decay, or dropoff, as the pool of potential survivors gets smaller over time, and we should not expect 52 survivors per year forever, and maybe not even in the first year.
So ultimately we reduced the total number of initial survivors by 25% for a total of 289. This then gives 65 survivors who will ultimately make it to Tucson with 43 arriving in year 1, 13 in year 2, and 4 in year 3, then some stragglers in the years that follow. If we start to go lower than the 25% reduction, then it becomes more unlikely that so many survivors would have shown up so far (A 50% reduction for example, gives us 1 survivor per month average, and there is only a 2% chance of getting 4 survivors in a month which we have already seen.)
So that is it, we estimate the US population at 289 survivors, plus or minus.
So in the coming seasons we could expect a small but vibrant community. But it will be up to the Gods (and the writers) how much Tucson will ultimately grow.
Until then we will enjoy watching what happens. But what we do know is that Phil is likely to be continually frustrated no matter who comes.
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