Position Time Bonus

[Duplode]

In this post, I will sketch a possible implementation of a position time bonus system for ZakStunts, in the context of the discussions about LTB (leading time bonus) reform started in the 2024 pre-season that we're revisiting now (cf. the Cars and rules for 2025 thread). Position time bonus is a way to expand LTB to further positions on the scoreboard. The idea originates with the podium time bonus system (which helpfully also abbreviates to PTB  ) used in the later seasons of USC; a similar suggestion was also made by Alan Rotoi in 2021. The system presented below is far from the only reasonable alternative bonus system, or even the only way to do PTB (the USC system, for instance, was different in quite a few ways). While I do feel it could be implemented successfully, it is also meant as exploration of the design space, highlighting some aspects we would want to consider in this or any other possible LTB reform.

General premises

In addition to the main goal of providing further opportunities for earning bonuses and thus involving more pipsqueaks in the bonus fights, which would be the main point of adopting PTB, there are some positive aspects of the current LTB system that are worth trying to preserve in any reform. I would highlight three of them:

• Waste of "partial credit" -- hours that do not add up to a whole bonus point -- should be kept to a minimum. (The current system achieves that with accumulated leading hours carrying over across races until the pipsqueak earns a point.)
• It should be possible to track your progress and know what you need to do to earn your next bonus. (With the current system, you just have check how far your total hours are from 240 or 480. In the pre-2020 system, which gave points to the two pipsqueaks with the most hours in each race, while it was possible to get LTB +1 with as little as 24 hours, you'd always be at risk of being overtaken late in the race.)
• The amount of bonus points given shouldn't be as large as to unbalance the season scoreboard. (The current system is a marked improvement in that aspect over the pre-2020 one, as the total amount of bonus points fell by about a third, mainly thanks to hours after gaining an LTB point not carrying over.)

The extent to which the PTB system below addresses these goals is up to discussion, and to the evaluation of you all.

The system

Without further ado, let's look at how this version of PTB is supposed to work. It gives bonuses for time spent in the top 6 positions, with the bonus gains being weighed by position. Top 6 is a familiar threshold at ZakStunts, being used for things like XP Points and car coefficient updates.

To make gains incremental and granular in a way that extends to the whole top 6, bonuses are granted in increments of 0.05 points. In that aspect, the mechanics are similar to the current system: you accumulate hours and, at certain amounts, earn your next (fraction of a) point.

For each position, the weights are applied through the number of hours needed to earn the next 0.05, as follows:

• 1st place: 0.05 every 14 hours (1 × 14)
• 2nd place: 0.05 every 28 hours (2 × 14)
• 3rd place: 0.05 every 42 hours (3 × 14)
• 4th place: 0.05 every 70 hours (5 × 14)
• 5th place: 0.05 every 112 hours (8 × 14)
• 6th place: 0.05 every 182 hours (13 × 14)

(Why multiples of 14? I'll get back to that later.)

A pipsqueak can earn at most 2 PTB points in a single race. While that doesn't make a big difference to the amount of points available (without the limit, the maximum would be 2.1 points for a lead of 14 × 42 = 588 hours), it makes the system tidier in a couple ways: by making the maximum PTB per race a whole number, and by making such a maximum still attainable even if hard to reach (at 560 leading hours out of 600) rather than nearly impossible (as it would be at 588 out of 600).

There is no carryover of hours between races, as the granularity of the 0.05 point increments should be enough to make that superfluous.

Within a race, however, hours are transferred between positions when the scoreboard changes. For instance, if a pipsqueak spends 72 hours in fifth place (out of 112 needed to get 0.05 at that position) and then moves up to second, those hours are converted to 72 × 2 / 8 = 18 hours, and so they will only need 10 hours in second place (instead of 28) to get the next 0.05. Internally, that could be implemented by tracking the fraction of "credit" earned towards the next 0.05, or by incrementing a counter every hour according to the proportions shown above. (How to display that information to pipsqueaks is a different matter, which I'll get to in a moment.)

Initial comments, potential pros and cons

Quoting myself from the 2025 rules thread:

We could perhaps begin by looking at possible motivations for changing LTB. Looking back at past discussions, I would highlight two issues that I've seen mentioned with some frequency:

• Most pipsqueaks never or only rarely partake in LTB fights.
• Intense LTB fights can be exhausting and time-consuming.

To my eyes, the primary goal of adopting PTB is dealing with the first of those issues: involving more pipsqueaks in bonus battles, while providing further incentive, and benefits for, posting replays regularly. It does not directly address the second issue; however, it becoming possible to earn bonus points while in lower positions might ease some of the tension that an LTB fight can bring.

The choices of granting bonuses at multiples of 14 hours and of using Fibonacci (1-2-3-5-8-13) multipliers for the positions might appear surprising. Playing a bit with the values suggests that is one of the very few combinations that gives, at the same time, reasonable point gaps between the top 6 positions, nice fractions for the maximum bonuses per position, and evenly spread intervals on the 600-hour race window (which is specially important to avoid wasting too many hours at the lower positions). The table below shows some of those properties:



Note, in particular, that in a system of granular bonuses without carryover it's a good thing to have "hours for maximum" close to 600, as that minimises waste. (Having it equal to 600, however, wouldn't be quite as good, as it would make the maximum essentially unreachable.)

While the system conceivably might be made even more granular by using 0.01 or some other smaller fraction instead of 0.05 for the minimum bonus amount, my view is that doing so would only make season scoreboards harder to follow for little benefit.

With bonuses being granted in 0.05 increments, this is a very nearly a continuous system. One of the consequences of that is LTB tactics, be them aimed at reaching your next 240 hours or stopping someone else from doing so, will be greatly simplified. In my book, that counts as a negative, as the nature of such tactics under the current rules makes the fights more interesting than they have ever been. However, for those whose main concern is making bonus fights less exhausting, simpler tactics could also help with easing the pressure on the contenders.

Across all pipsqueaks, this PTB system would give a maximum of 4.65 points per race (while the sum of the "maximum bonus" column in the table above is 4.55, the 2-points-per-pipsqueak limit usually won't need to be applied if multiple people spend time on first place). While that might look like a large increase over the current rules (a bit under 2 points per race in average), or even the pre-2020 system (in the absence of ties, a maximum of 3 per race), the points should be spread across more pipsqueaks, and in a much more even manner, so chances are the season scoreboard wouldn't become unbalanced. Ideally, we'd evaluate the potential effects of adopting PTB with some simulations. While I haven't done so beforehand to avoid delaying this post too much, I plan to try that over the coming weeks.

Last but not least, there's the important matter of how to report the bonus battles in a clear way to drivers and spectators. Replicating the detailed hours table we use for LTB six times, one for each position, feels like overkill. It would probably be more useful to have a concise summary displaying the situation of everyone who has been in the top 6 in the current race. Something like this:



"Pos." is the current position on the scoreboard. "Points" is the PTB earned so far. "Progress" is how far on the way to the next 0.05 the pipsqueak is, reflecting in a more user-friendly way the internal counter I mentioned when discussing how hours would transfer upon position changes. Finally, "Hours to next" is how many hours remain to the next 0.05 assuming the positions don't change (for pipsqueaks currently outside of the top 6 that doesn't make sense, so it is left empty). A table like this might well cover most information useful in practice to pipsqueaks, so the detailed hours charts could be relegated to a secondary page, or removed entirely. (I'd be happy with keeping a leading hours chart, though, even if it's just for nostalgia reasons  )

[Argammon]

This is a very detailed and thoughtful proposal and definitely a considerable improvement over the current system. I like the system per se but find the 0.05 steps somewhat arbitrary and to quote what @Chulk wrote on Telegram: "[...] I am not entirely convinced of the way to show progress, but I can't think of [...] a better proposal."

The modified proposal

• Everyone gets 1 point after 280 hours (or 0.5 points after 140 hours)
• The second place accumulates minutes at half the speed of the first place, and so on, with the sixth place accumulating minutes at 1/13 of the speed of the first place. So, the second place needs 2 real minutes to gain 1 stunts minute.

The benefit

Progress can always be displayed in a simple way:

- Argammon: 60 stunts hours 20 minutes
- Duplode: 200 stunts hours 0 minutes
- Spoonboy: 70 stunts hours 13 minutes

Considering the pipsqueak Duplode, and remembering that all pipsqueaks need 280 stunts hours to gain 1 point, Duplode knows that he needs 80 hours in first place, 160 hours in second place, etc., or a combination, to obtain one bonus point.

Under this proposal, since everything is measured in stunts minutes, there's no need for conversion when pipsqueaks change positions. For example, if a pipsqueak spends 130 real minutes in 6th place, they accumulate 10 stunts minutes. When they switch to 1st place, they still have those 10 stunts minutes and will continue to accumulate additional stunts minutes at a faster rate.

[Akoss Poo a.k.a. Zorromeister]

CTG used at Unskilled Stunts 'Podium time bonus', if I remember well.

Btw, that will only interest people who favorize collecting as much points as possible to finish as high as possible in Season's Standings. For those who focus on winning as many races as possible, it will not lure out replays or times.

[dreadnaut]

Great work @Duplode, a perfect way to start the discussion. Some version of PTB could a nice extension of the current system, and I agree with many of your points. A few dissenting thoughts:

- The exhausting part of the current LTB system is the 'battle': timing choices, counter-replays (and counter-counters), alternating leadership. It is also the exciting part, where decisions matter. Decisions are important because they make the difference between an interesting mechanic, and a bonus system that "happens" to you.

- Intervals smaller than 24 hours might be unfair to folks in different timezones, more than the current system. We probably need some math to check.

- I don't think a new system should be easier for people at the top of the scoreboard. Both reward and difficulty should increase as one climbs towards the podium. Strong players, big bets.

- I agree on transferring hours if you step down: you have no control on someone submitting a stronger replay. I would throw away hours if you submit a strong replay and step up: it's your choice to go for more points, against collecting your current bonus. Will you play conservatively, or be bold?

I haven't sketched numbers yet, but I'm thinking a "chunky PTB" system might be more interesting than the "continuous PTB" you suggest.

Maybe bigger time periods, and bigger bonuses? Or a reverse system? For example (not an actual proposal!): first place gets 1 point every 240 hours, second place 0.6 points every 240 hours, third place 0.4 points every 240 hours, etc.

[Duplode]

Thank you, those are some good comments from y'all to get things started!

@Argammon So, if I got it right, the idea is replacing the "Hours to next" column in my mockup, which shows how much remains to the next 0.05 adjusted by position, with one that displays hours (and minutes) to the next whole point, always using the 1st place multiplier for consistency. That sounds perfectly fine; when it comes to displaying whatever is clearer to everyone is good enough. It's worth emphasising that the unit we use for display need not be the same one used internally in the code.

(I picked 0.05 as the step size, by the way, mostly because that is the smallest fraction we currently have on the season scoreboard.)


@Akoss Poo a.k.a. Zorromeister Indeed, this system is directly inspired by podium time bonus at USC 

The point about motivation is an interesting one, and it would be good to hear from a wide range of pipsqueaks about how they see it. From observing things as they stand now, my feeling is that there is some ambivalence about LTB among those who compete regularly for it, and that below the top people tend to post replays regularly even with little in the way of tangible rewards. Still, I think something like LTB remains necessary as a safeguard against extreme hiding at the top, and so if we're going to have it, we might as well make make the battles more accessible for those who enjoy them -- while, as a side benefit, allowing those with more relaxed strategies of posting replays along the month but without joining dogfights for the lead to not go empty handed.


@dreadnaut LTB fight tactics are at a sweet spot under the current rules, and they are something I'd miss in a simpler system. A bit further below, I'll talk more about how that might apply to PTB.

I'm not sure I see how intervals under 24 hours could create timezone unfairness, in particular with a system of granular bonuses with little waste of partial credit. Do you have an example of how that might play out?

I'm afraid throwing away hours when someone steps up would be very problematic, for two reasons. Firstly, I don't think we want to punish people for trying to improve. Secondly, it seems likely this would disproportionately affect pipsqueaks moving upwards from the midfield, which goes counter to the spirit of extending LTB into PTB.


On a chunkier system, that's a valid point in the design space as well. I can see the appeal of having larger milestones to strive for than a 0.05 step. While steps of 1 point would be too large for the lower positions, 0.5 would likely work fine everywhere (assuming there is carryover -- more on that in a moment). Perhaps the best thing to do would be mixing step sizes, having two steps of 0.5 point and a final one of 1 point in each race (so LTB +1 and LTB +2 becomes PTB +0.5, PTB +1 and PTB +2).

With larger steps and a chunkier system, it becomes absolutely necessary to have some form of carryover, as otherwise it would be pointless -- in both senses! -- to set up bonuses for the lower positions. Pulling in the other direction, given that the expansion to PTB would make the system more complex in quite a few ways, it is tempting to simplify it elsewhere by eliminating carryover so that there is one less thing for people to keep track of. That can be argued either way, though.

If we were to adopt larger steps, then, the question would become how to set up the carryover. Full carryover (that is, excess hours always transfer to the next race) is not very different from a continuous system when it comes to tactics, as you can nearly always leave it to the next race to sort things out. The only advantage in terms of making the system more interesting would be the bigger milestones.

The alternative, then, would be some form of partial carryover, not unlike what we have in the current LTB system. For instance, we might make it so that excess hours only carry over if the pipsqueak hasn't attained 1 whole point in the race. That could bring two significant advantages, at least from my point of view:

• Firstly, much of the tactical richness of the current LTB system would be restored. Partial carryover is, IMO, the secret sauce of the current system, given how it introduces a qualitative difference between LTB +1, for which you can rely on carryover, and LTB +2, for which you must buckle down and sort it out before the deadline.
• Secondly, it would reduce the total amount of points being distributed, specially at the very top, which means less risk of unbalancing the season scoreboard.

When doing partial carryover in this way, some care might be needed to avoid weird edge cases. For instance, if there were fixed steps of 1 point, someone who earns 0.8 "credit" in a race (say, by leading for a some time early in the race and then spending most of the remaining hours in 3rd and 4th places) might get to 1 point very quickly in the next race, and then spend the rest of it outside of any PTB fight unless they make a serious push for the lead. However, I think mixing step sizes, as suggested above, would make that much less of a problem in practice.

[Argammon]

@Duplode:

Yes, the systems are mathematically identical if, using my terminology, you need 14 stunts hour for 0.05 points. The difference is indeed how it is displayed:

Let's consider the following screnario:

"Within a race, however, hours are transferred between positions when the scoreboard changes. For instance, if a pipsqueak spends 72 hours in fifth place (out of 112 needed to get 0.05 at that position) and then moves up to second, those hours are converted to 72 × 2 / 8 = 18 hours, and so they will only need 10 hours in second place (instead of 28) to get the next 0.05. Internally, that could be implemented by tracking the fraction of "credit" earned towards the next 0.05, or by incrementing a counter every hour according to the proportions shown above. (How to display that information to pipsqueaks is a different matter, which I'll get to in a moment.)"

Using my terminology the pipsqueak spent 72 real hours to earn 9 stunts hours. Hence, they need 5 more stunts hours to obtain 0.05 points or equivalently 10 real hours in second place. As far as I see it, it would be sufficient to display the number of stunts hours obtained behind each pipsqueak's name.

I will chime in on the discussion about a "chunkier" system in a separate post.

[Argammon]

[...] The alternative, then, would be some form of partial carryover, not unlike what we have in the current LTB system. For instance, we might make it so that excess hours only carry over if the pipsqueak hasn't attained 1 whole point in the race. That could bring two significant advantages, at least from my point of view:

• Firstly, much of the tactical richness of the current LTB system would be restored. Partial carryover is, IMO, the secret sauce of the current system, given how it introduces a qualitative difference between LTB +1, for which you can rely on carryover, and LTB +2, for which you must buckle down and sort it out before the deadline.
• Secondly, it would reduce the total amount of points being distributed, specially at the very top, which means less risk of unbalancing the season scoreboard.

When doing partial carryover in this way, some care might be needed to avoid weird edge cases. For instance, if there were fixed steps of 1 point, someone who earns 0.8 "credit" in a race (say, by leading for a some time early in the race and then spending most of the remaining hours in 3rd and 4th places) might get to 1 point very quickly in the next race, and then spend the rest of it outside of any PTB fight unless they make a serious push for the lead. However, I think mixing step sizes, as suggested above, would make that much less of a problem in practice.

I like this suggestion. To keep it simple, I would prefer to keep this part identical to the present system, meaning pipsqueaks earn full leading-time points and stunts hours beyond 280 do not carry over to the next race. To make it a bit more realistic to gain 2 points, one may say that 240 stunts hours are enough per point. This way, the new system remains "spicy" like the present system but also makes it easier for midfield pipsqueaks to gain some leading-time points.

I am not too concerned about the edge case you are describing (a pipsqueak earned 0.8 * 240 = 192 stunts hours). In such a scenario, one of the midfield pipsqueaks would have an opportunity to gain some valuable hours since one of the usual suspects is out of contention for a month.

[Argammon]

CTG used at Unskilled Stunts 'Podium time bonus', if I remember well.

Btw, that will only interest people who favorize collecting as much points as possible to finish as high as possible in Season's Standings. For those who focus on winning as many races as possible, it will not lure out replays or times.

I think this is a valid point, but it applies to the current leading-time system as well, perhaps even more so. Taking myself as an example, I am not going to participate in the leading-time fight next season should the system remain unchanged. Having a job and a family makes it difficult (and exhausting) to compete for the top spot for an entire month, particularly if the opponent is a motivated top pipsqueak like @Duplode or @alanrotoi. On the contrary, I am much more willing to submit a replay if I find it likely that it is good enough to stay in the top 6 for a while.

But as you pointed out, all of this is only relevant if you care about the season's standing at all.

[Overdrijf]

Wow, this is all developing fast.

I'll be back to try and have a detailed opinion about the different variants, I just wanted to express my support for the general concept. I feel like if more people have a realistic chance to fight for what is now LTB it will do its job of motivating people to race all around the month better. And the stepped implementation, where a higher position is better, means that it should still motivate the top drivers as well.

[Duplode]

After some more consideration (see the final part of my previous reply), I feel a chunkier, less granular system, as encouraged by @Argammon and @dreadnaut , would be an improvement over my initial proposal. That being so, here is an amended version of it:

Chunky PTB

Position time bonus is earned for time spent in the top 6 positions, with the gains being weighed by position.

Bonuses are granted in three steps (contrast with the two steps of the current LTB system, or the forty of the granular system in the opening post):

• A first step of 0.5 point, or PTB +0.5;
• Another step of 0.5 point, or PTB +1 in total; and
• A final step of 1 point, or PTB +2 in total.

For each position, the weights are applied through the number of hours needed to reach the next step. Earning PTB +0.5 requires:

• 1st place: PTB +0.5 at 120 hours (1 × 120)
• 2nd place: PTB +0.5 at 240 hours (2 × 120)
• 3rd place: PTB +0.5 at 360 hours (3 × 120)
• 4th place: PTB +0.5 at 600 hours (5 × 120)
• 5th place: PTB +0.5 at 960 hours (8 × 120)
• 6th place: PTB +0.5 at 1560 hours (13 × 120)

(Note that we're back to multiples of 12, in contrast to the multiples of 14 in the initial proposal.)

To simplify the description, I will use "stunts hours" to mean the equivalent for PTB purposes of an hour in the lead. 1 stunts hour, then amounts to 1 (real) hour in 1st place, or 2 hours in 2nd, and so forth. We can, then, say that PTB +0.5 is given at 120 stunts hours. Following the same proportion, PTB +1 is given at 240 stunts hours, and PTB +2 at 480 stunts hours

There is partial carryover of excess hours: unused stunts hours are transferred to the next race as long as PTB +1 hasn't been reached. (Note the current LTB system handles carryover in pretty much the same way, with the final +2 step having to be reached without the help of carryover.)

Within a race, stunts hours are conserved when the scoreboard changes. For instance, a pipsqueak that spends 160 hours in fifth place will have earned 160 / 8 = 20 stunts hours, needing a further 100 Stunts hours to get PTB +0.5 (in fifth place, that amounts to 800 real hours). Should they move up to second, the situation in terms of stunts hours remain the same, and so they will only need 100 × 2 = 200 real hours in second place (instead of 240) to get PTB +0.5.

Notes

This revised PTB system is quite straightforwardly an extension of the current LTB system, and so much of the intuition about its workings should remain relevant, including when it comes to tactics. In addition to PTB +1 and PTB +2 steps with partial carryover, the proportion of 240 (stunts) hours for each whole point is also retained: since the reintroduction of carryover makes fine tuning of bonus window sizes less critical, we can afford going back to more familiar numbers. 

Besides the extension down the scoreboard, the other significant change relative to the current system is the introduction of the PTB +0.5 step. I see that as necessary to keep the system appealing for the entire top 6. In particular:

• PTB +1 requires 720 (real) hours at 3rd place, which is more than the 600-hour window of a race. Depending on carryover to earn any points after spending a whole race in 3rd place would feel like a betrayal of the podium time bonus heritage of the system 
• Similarly, PTB +1 calls for 3120 hours at 6th place. That amounts to more than five races, and is far too long for a first step in a system meant to make bonus battles more accessible.

Adding the PTB +0.5 step has at least one more major advantage: it would make battles for the lead early in a race more likely to be meaningful on their own, rather than as preparation for something else that might happen after the public days end (or many races later, or never). Furthermore, smaller amounts of carryover (with PTB +0.5, 119 stunts hours is the maximum that can be transferred between races) should make that mechanic easier to grasp and keep track of.

Wrapping it up for now, some detail on how stunts hours are to be added to each pipsqueak's total. The approach I suggest is to, after each real hour, add the fraction of a stunts hour corresponding to the position (one stunts hour for 1st place, half a stunts hour for 2nd, and so on). That is in contrast with only adding whole stunts hours (one stunts hour after one real hour for 1st, two real hours for 2nd, etc.), which would lead to needless waste of hours. Internally (that is, without showing it directly on the site to pipsqueaks), the counter might even be kept as an integer, with the increment for each stunts hour being 1560, the least common multiple of the position weights. 1560 is divisible by 60, so an internal counter like that can be easily converted to stunts hours and minutes for display on the site.

[alanrotoi]

Ok this is getting better! From a scientific point of view, to strenghten an idea we must ask it questions. If it answers right it gets stronger, a stronger truth. So don't get me wrong if I try to find glitches or holes.

- How can we test the system to avoid that this system favors the top pipsqueaks  (those who usually gets the 80% or 90% of the extra points)?

I mean, I don't want to creat an even more unreacheable elite.

I like the idea of the system and its soul. We have to find a way to test it before implementing.

[Argammon]

I like the system suggested by @Duplode above.

@alanrotoi: Duplode's system is better for the sub-top pipsqueaks than the current one without a doubt. One way of going even more in that direction would be to reduce the weights from (1,2,3,5,8,13) to (1,2,3,4,5,6).

Advantage of the change: The sub-top pipsqueaks need less hours to get points.
Disadvantage of the change: When the weights are close, the top pipsqueaks have less of an incentive to try to take the lead because sitting in 3rd position may be good enough.

Which of the two (advantage vs disadvantage) should we put more weight on?

[Duplode]

- How can we test the system to avoid that this system favors the top pipsqueaks  (those who usually gets the 80% or 90% of the extra points)?

Simulating how past races would have played out under the system, something I plan to do in the near future, should be one of the useful things for spotting pitfalls of that kind. Up to now, I don't think we have paid a lot of attention to the dynamics of position changes below the top. Simulations could help identifying some of the possible scenarios, in particular when it comes to how the extra points would be distributed.

Disadvantage of the change: When the weights are close, the top pipsqueaks have less of an incentive to try to take the lead because sitting in 3rd position may be good enough.

This also applies to the lower positions (say, going for a podium place versus staying in 5th). PTB does make it a bit more affordable to be conservative about pushing for the higher positions. Since making it too affordable would be self-defeating when it comes to making races more exciting, it's probably better to err on the side of larger gaps -- which are anyway easier to justify for bonuses than for the main scoreboard. 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.

[dreadnaut]

Simulating how past races would have played out under the system, something I plan to do in the near future, should be one of the useful things for spotting pitfalls of that kind.

I can put some time aside this week-end to implement a rough version 🛠

[Duplode]

I can put some time aside this week-end to implement a rough version 🛠

That would be very nice, thank you!