Ooh, I just dug up a 6-year-old thread in which I convinced myself that it’s not kosher to use the formula you’re using: “clarifications on how tagtime updates a do-more goal”
Here’s an extreme example illustrating how your formula can bias your statistics:
Imagine there’s an uncanny ping drought. Nary a ping all day and the end of the workday is approaching. If you can get the next ping then you’ll have gotten 100% of today’s pings! So you buckle down and work with laser focus for the last hour and probably that ping is yours. Your formula now says you work 8 hours today.
Of course my version can be just as wrong (you could happened to get pinged 10 times in an hour) but the difference is there’s no bias. With your formula you can adjust how hard you work depending on the ping history.
It’s not nearly as big a loophole as @zedmango’s (work for a few seconds every 5 minutes) but if you tend to focus more the fewer pings have happened – a natural enough thing to do – then your estimate will be inflated.
Using the official TagTime algorithm and counting every ping as exactly 45 minutes of work makes it totally ungameable.