In the last part I suggested the existence of a lower bound. I used my assumed algorithm using 250 and 72 as constants to find out the best Pokemon to determine this lower bound.
To do this I calculated expected T(max) for different values
| CP | Hours calc |
| 302 | 71.44 |
| 301 | 71.54 |
| 300 | 71.65 |
| 299 | 71.75 |
| 298 | 71.86 |
| 297 | 71.96 |
| 296 | 72.07 |
I don’t know why I do these calculations and then ignore them. But while looking for the best Pokemon to show the lower limit I asked trainer HachitoBeak (my son) if he had a Pokemon with exactly 300 CP. He didn’t have a Pokemon with exactly 300 CP (he had one with 299) but he offered to power one up to exactly 300 CP. With hindsight this might have turned out to have been a great oversight. You will learn in part 6 why.
My ‘house gym’ is my neighbour (a castle) and 167 m away from where I type this right now (praised be Ingress which allows these exact measurements). I used a 98% lvl 40 Dragonite as reference. It is convenient – but often lasts not very long as it is also an Ex-Raid gym. But let’s go to the Farfetch’d data first.
| Time | Dragonite | Farfetch’d |
| Max | 3783 | 300 |
| Berries | 2 | 2 |
| 14:25 | 3783 | 300 |
| 14:34 | 3726 | 299.5 |
| 15:10 | 3498 | 297.5 |
| 15:28 | 3385 | 296.5 |
| 15:46 | 3270 | 295.5 |
| 16:04 | 3158 | 294.5 |
| 16:22 | 3045 | 293.5 |
| 16:40 | 2930 | 292.5 |
| 16:58 | 2817 | 291.5 |
| 17:16 | 2703 | 290.5 |
I tried to simultaneously feed berries to both Pokemon. Unfortunately this didn’t work as my son had interface issues. I later found out that his berry must have registered approx. 15 seconds after I fed the second berry to the dragonite. Datapoint 1 therefore was ignored in the analysis.
You might notice that all Farfetch’d data is in half CP. There is a reason for this insanity. I calculated that it takes exactly 18 minutes between a change in the display for the Farfetch’d – with the first one expected when the CP declined to 299.5 after 9 minutes. For maximum accuracy (see part 1) I tried to set a timer to 16 minutes and took a snapshot on my phone as soon as the Farfetch’d motivation decayed by another point. I missed the value for 298.5 by approx. 1 minute – so it isn’t in the table.
Doing a linear regression across the data I get
Hourly decay = 1.1100%
Standard Deviation = 0.0008%
This is probably as close as you can get to 1.111% and it clearly seemed to show my lower boundary. I slapped myself on the back when I saw the data on my screen.
With hindsight I probably should’t have congratulated me this much for this data point at this stage. After all – I should have taken a 297 CP Pokemon instead if I had remembered my own calculations. And the hypothesis at this stage would have predicted 1.1165% decay for the Farfetch’d. But in science mistakes happen – and sometimes you just get lucky.
I will investigate in part 6 why this might have been a very lucky mistake – and I will reveal the final algorithm.