In a time of ‘Big Data’ we tend to ignore individual data points. But sometimes they are the most crucial to further our understanding. One such data point came from the snapshot below – gym 7 – datapoint 16, Sentret
So what is so important and special about this snapshot? I was monitoring this gym for 6 hours 14 minutes when I took the snapshot. The main aim was to establish a better quality data point in the area of 100 CP. There had been one raid in this time and the Aggron motivation was standing at 54.92%.
I had done another snapshot approx. 5 minutes earlier – and it was the very first with the Sentret on 9 CP. But according to my expectation this should have taken another 30 minutes to happen. Actually I had planned to take the exact time when it happened – which I must have missed.
Okay – I need to take a step back here. Why did I expect this to happen 30 minutes later? Well – we can do a simple extrapolation. We know the CP of the Sentret is 10. I assumed (up to this stage) that the minimal decay rate is 1%. This would mean it takes 10 hours for the Sentret to decay from 10 to 9.
From earlier work I knew that the CP shown is actually the rounded CP. With a decay of 1% I would expect:
| Time (hours) | CP (1% decay) | Display |
| 0 | 10 | 10 |
| 5 | 9.5 | 9 |
| 15 | 8.5 | 8 |
| 25 | 7.5 | 7 |
| 35 | 6.5 | 6 |
| 45 | 5.5 | 5 |
| 55 | 4.5 | 4 |
| 65 | 3.5 | 3 |
| 75 | 2.5 | 2 |
| 80 | 2 | 2 |
So why is this single point so important? It single handedly invalidates 90% of all models I tried before. In my second generation data gathering (see part 2 – over fitting) i had gathered two low CP data points – 103 CP at 1.01% decay and 149 CP at 1.08%.
I therefore convinced myself that the minimal decay is 1% and that it takes 80 hours for a extremely weak Pokemon to reach minimum motivation. The importance here is that 10 to the power of zero is 1.
This new data point would indicate that the minimum decay is 10/9 % or 1.11%. While 1.11% looks odd (compared to 1%) we have to look at it in a different way. 1.11% is the same as 80%/72 – or in other words – it takes exactly 3 days (and not 80 hours) for maximum motivation decay.
Now that we have a new hypothesis – 72 hours / 3 days as max time we can look at our data again.
In part 4 we will look how the 72 hours help to find a so far overlooked feature – a discontinuous function. We slowly zoom in on the true algorithm.