Wikipedia:Reference desk/Archives/Mathematics/2016 June 30

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June 30

Series of numbers, continuing/extrapolating

I have a series of numbers. It's actually the 'exp requirement' in a game, but that's probably not important.

It's not a linear or a straight-forward progression, so I'm not sure how to work out how the series is likely to continue?

1399, 1571, 1758, 1961, 2183, 2423, 2685, 2969, 3277, 3612, 3976 — Preceding unsigned comment added by 86.20.193.222 (talk) 03:57, 30 June 2016 (UTC)

Well, 100 + 121.64 x - 1.9613 x² + 0.27839 x³ for x ∊ {10, ..., 20} is within ±0.63 of the quoted values. -- BenRG (talk) 05:46, 30 June 2016 (UTC)

The game appears to be Gravitee Wars Online, in which case a more complete set of data is at [1]. --RDBury (talk) 07:20, 30 June 2016 (UTC)

The extended list from that page is 1399, 1571, 1758, 1961, 2183, 2423, 2685, 2969, 3277, 3612, 3976, 4370, 4798, 5262, 5765, 6310, 6900, 7539.

$\lfloor 1400+1640(x/10)+727(x/10)^{2}+144(x/10)^{3}+65(x/10)^{4}\rfloor$, for x in 0..17, comes reeeally close to giving all of the values. It fails only at x=0, and $\lceil 1399+\cdots \rceil$ fails only at x=10. If the deltas were confined to [0,1) or (0,1] it would work, but they span [0,1]. Maybe they do use this formula and the odd value is due to a rounding error somewhere. You can reduce the delta span down to about 2/3 by adding more digits, but that's less interesting. -- BenRG (talk) 09:04, 30 June 2016 (UTC)

According to the the web page, the sequence starts 0, 50, 104, 162, 224, 291, 365, 444, 531, 626, 729, 831, 963, 1096, 1241, but the formula doesn't work for these values. (From graphing the data it appears that the 831 listed is a typo and should actually be 841.) I don't think a single quartic covers the range; perhaps the function is defined piecewise, which would explain why a quartic fits it so well on the top half. Or perhaps there's an exponential term that needs to be added. --RDBury (talk) 14:48, 30 June 2016 (UTC)

Crud. The fourth-order differences still look like random noise, which makes me think it should still be a quartic, but the best fit to all of these points only comes within ±5 of them. Worse, the difference looks like unmodeled signal, not noise. A quintic fits to better than ±0.5, and the difference looks like noise, but I'm starting to sense a trend in my answers here...

I never bothered searching OEIS, but then I realized, why wouldn't it have XP level sequences? And indeed it does have at least two. Sadly, this isn't one of them, but the Runescape formula is interesting, since it rounds the level differences to integers, not the thresholds. -- BenRG (talk) 08:40, 1 July 2016 (UTC)

The first differences of the GWO sequence are basically linear on a log plot. But it still doesn't fit to better than ±0.5. -- BenRG (talk) 08:45, 1 July 2016 (UTC)

Yeah, it's that game.

I am suprised that the formula could be so complex; I suspect there is actually some simple formula, but it might just be "*x% until y amount, then *z%"...and so forth. I thought it might be easier than it seems to reverse-engineer the answer.

The formula above that almost-works-out would fail for higher numbers in the range - and it's common in that game to get to 'level 100' and beyond, and the above lists are just looking at the first 20 or so levels...so I'm still unsure if I can predict/estimate what the required exp value is for levels. Maybe we'll just have to note it down as we level up - although that does take weeks/months.

And sadly, the developer of the game is no longer active. — Preceding unsigned comment added by 86.20.193.222 (talk) 03:20, 1 July 2016 (UTC)