Position Time Bonus

[Chulk]

With the (1,2,3,5,8,13) weights, the relative change in gains between e.g. 1st and 3rd is similar to that between 3rd and 5th, which seems appropriate to my eyes.

You can never go wrong with Fibonacci!

[Duplode]

An update: I started working on a PTB simulator yesterday. The core of it is broadly in place; I now mainly need to tidy up the presentation of the values. As a teaser, here's a screenshot of the raw output for ZCT269:

[Duplode]

All right, I now have some simulation results to share!

First, I'll begin by discussing a side effect (and perhaps a glitch, in @alanrotoi 's sense) of the system that the simulations made obvious: if 240 (stunts) hours is kept as the PTB +1 threshold, PTB +2 is significantly easier to reach than under the current LTB system. It's not difficult to see why that happens. Suppose that two pipsqueaks alternate between first and second through the entire race. In such a scenario, either of the pipsqueaks would need 360 hours in the lead to reach PTB +2, since 360 + (600 - 360)/2 = 480. 360 hours is just two and a half days more than 300 hours (half of the 600-hour window), and five days less than 480 hours (the current threshold for LTB +2).

Easier PTB +2 is not really a good thing IMO, as the extra points go almost entirely to regular lead challengers, largely cancelling any equalising or narrowing effects the new system could have over the bonus fight. Fortunately, it is not difficult to tweak the system to minimise that: just increase the PTB hour thresholds a bit. The list below shows how many times LTB +2 was reached in the 2024 season, and how many times PTB +2 would be reached in 2024 given different thresholds:

Rule		+2 occurrences
LTB, 2024 results		4
PTB, +1 at 240 h		6
PTB, +1 at 264 h		5
PTB, +1 at 288 h		2

PTB +1 at 264 (stunts) hours, or 11 days (which means PTB +0.5 at 132 hours, or 5½ days, and PTB +2 at 528 hours, or 22 days) is arguably the sweet spot for keeping +2 roughly as difficult as it is now; in contrast, the 288 hour threshold is too draconian (as @Argammon had foreseen when considering the initial proposal, which had a 280 hour threshold). Note that the higher thresholds have relatively little effect over the lower positions, given there's full carryover below the PTB +1 threshold.

With that aspect covered, then, here are the PTB point distribution for the three thresholds mentioned above, next to the actual LTB points for 2024:



My overall impression is that it's pretty encouraging that there would be 13 people earning PTB over the season, with 6 or 7 of them above two points, and that the distribution for the 264 threshold in particular feels right where we'd like it to be.

One detail in the results above might look curious: why would Erik get more points with the 264 threshold than with the 240 one? That happens because of carryover. With the 240 threshold, Erik would get PTB +0.5 in ZCT275 by a small margin, and then get PTB +1 in ZCT276. With the 264 threshold, though, he would just miss PTB +0.5 in ZCT275, therefore bringing almost 125 stunts hours into ZCT276, which would be enough to get him PTB +2 there.

It is worth mentioning a few details of counting of hours that I have used for the simulations that differ from how LTB works right now:

• The time spent in each position is counted in real minutes, which are converted to stunts minutes only at the end of the race, when it's time to calculate points and carryover.
• The "50 minutes hour" which is used at ZakStunts for the first hour of a lead interval wasn't adopted, as it is no longer necessary with minute-based counters, and would be very confusing to set up given the interaction with the factors.
• There is no carryover across seasons in the simulations. With the possible exception of the transition between systems in the first season with PTB, such a rule feels superfluous under PTB, as the awkwardness of having results from one season affecting the next one would IMO no longer pay its weight, given that bonus points would become more accessible with PTB. (Note, by the way, that Overdrijf would still get his bonus point even without cross-season carryover: PTB +1 on ZCT271 with the 240 threshold, and PTB +0.5 on both ZCT271 and ZCT272 with the 264 and 288 thresholds.)

The 2024 simulation results, including detailed hour totals, are attached below for y'all to inspect.

[Chulk]

What about simply reducing carry-over ratio? That way carry-over would have a lesser impact

[Duplode]

What about simply reducing carry-over ratio? That way carry-over would have a lesser impact

Carryover is not much of a problem IMO, and has little influence over the PTB +2 situation, as there is no carryover beyond the PTB +1 threshold. The anomaly with Erik's points, in particular, looks harmless to me. If we really wanted to get rid of it for the sake of consistency, one possibility would be removing carryover between PTB +0.5 and PTB +1. (How it works now: suppose the PTB +1 threshold is 264. If you get 200 stunts hours, you'll get PTB +0.5 for the first 132 hours and carry 68 stunts hours to the next race.) Removing that, however, would mainly affect the lower positions, so I'm not sure it's worth doing. In any case, later I can try redoing the simulations with that change to better grasp the effect.

[dreadnaut]

Thanks for the preview Duplode! Is it a time consuming process? Would you be able to test the PTB-264 effect on 2023 and 2022 as well, to get extra data points?

[Duplode]

Would you be able to test the PTB-264 effect on 2023 and 2022 as well, to get extra data points?

Sure! It's not very time consuming at all; I should be able to post these in the evening. (A preview of the preview: as far as I recall from when I was trying out the simulator, the trends were broadly similar.)

[Duplode]

Here are the simulation results for 2023 and 2022, including PTB-240, PTB-264 and PTB-288:

2023

Rule		+2 occurrences
LTB, 2023 results		3
PTB, +1 at 240 h		8
PTB, +1 at 264 h		4
PTB, +1 at 288 h		0

2022

Rule		+2 occurrences
LTB, 2022 results		4
PTB, +1 at 240 h		4
PTB, +1 at 264 h		3
PTB, +1 at 288 h		2

The trends are similar overall, with PTB-264 still looking the best balanced option to me. It's worth noting the effect of adjusting the threshold becomes more significant in seasons with more concentrated leading time like 2023.

Attached below are the detailed results from season 2018 to season 2023. For 2018 and 2019, I have also included approximations of what LTB under the current rules would be like (they are approximations because of differences in details like rounding).

[dreadnaut]

I've updated the rules for 2025 with a first draft, have I missed anything?

Position Time Bonus (PTB)

The system tracks how long you stay in one of the top-6 position on the scoreboard.

• Pipsqueaks in first position gain 0.5 bonus points for every 132 hours they hold the position during the race.
  
• Pipsqueaks in the following five positions gain 0.5 bonus points for amounts of hours multiple of 132: ×2, ×3, ×5, ×8, and ×13.
  
• When moving position, pipsqueaks carry hours over, scaled up or down using the coefficients above. E.g., if you have 100 hours in 4 position, and move up to second place, you will bring 100 / 5 * 2 = 40 hours.
  
• Pipsqueaks can gain at most 2 bonus points per race.
• Position-time calculation starts on the first day of each race. If the track is available earlier, position time is not calculated.
• Position-time calculation ends with the start of the quiet days.

[Duplode]

I've updated the rules for 2025 with a first draft, have I missed anything?

I think the only thing missing is carryover. Something like this:

• Pipsqueaks who get less than 1 bonus point in a race carry unused hours to the next one. E.g. if you get 100 leading hours in a race, you'll start the next one with 100 leading hours; if you get 200 leading hours instead, you'll bring 68 to the next race, as the other 132 earned you PTB +0.5.

BTW, it's a good occasion to settle what we're going to do about cross-season carryover. More specifically:

• Confirm whether we're eliminating it for future seasons (IMO we should get rid of it); and
• Decide what to do, on an exceptional basis, with the carryover leading hours from 2024 (I think it could make sense to convert them to the new system, in order to honour any expectations from the previous rules).