# Philosophical setup instructions for TagTime

#21

Ultimately it’s just total time spent doing a particular task. You’re correct that if you work only, say, 5 hours on each project, there will be some projects that never receive even a single ping (about 0.1% in this case[1]), but it doesn’t actually matter whether you do those 5 hours all in one day or spread the work out over an entire year—the probabilities of being pinged (or not) are purely dependent on the amount of time spent on the project.

[1] `exp(-5/0.75) = 0.001272`

#22

Oh, very cool! That makes sense since each minute is equally likely to be picked.

So a 15 minute task would get pinged 1 - exp(-0.25/0.75) = 28.3% of the time, and a 45 minute task would get pinged 1 - 1/e = 63.2%. Those are much higher probabilities than I would have guessed!

hours prob
0.1 0.124826681
0.2 0.234071662
0.3 0.329679954
0.4 0.41335378
0.5 0.486582881
0.6 0.550671036
0.7 0.606759279
0.8 0.655846213
0.9 0.698805788
1 0.736402862
1.1 0.769306818
1.2 0.798103482
1.3 0.823305554
1.4 0.845361735
1.5 0.864664717
1.6 0.881558171
1.7 0.896342871
1.8 0.909282047
1.9 0.920606068
2 0.930516549
2.1 0.939189937
2.2 0.946780656
2.3 0.95342385
2.4 0.959237796
2.5 0.964326007
2.6 0.968779073
2.7 0.972676278
2.8 0.976087007
2.9 0.979071987
3 0.981684361
3.1 0.983970642
3.2 0.985971533
3.3 0.98772266
3.4 0.9892552
3.5 0.990596437
3.6 0.991770253
3.7 0.992797545
3.8 0.993696604
3.9 0.994483436
4 0.99517205

Now I’m curious if there’s a formula for the expected error for what TagTime says.

#23

I think your table is what @harding made a graph of above, and expected error is what I was getting at here: