Cars and rules for 2023

[Daniel3D]

I am for linear-linear as well.

No opinion on NoRH.

[Cas]

Uhm... I'll have to re-read it better. It's so hot here that it's hard for me to concentrate on things that require careful analysis. But I think linear-linear sounds better, if I understood it well.

I wouldn't add NoRH, but I'm OK if it's added. I featured it in R4K because I knew that some people found it important. I'm an agnostic, so to me, NoRH doesn't really exist, as it can't be proven, ha, ha. But I don't think it hurts.

[Duplode]

Alright, please allow me one more roll of the dice. I still think we can improve on linear-linear by adding a modest amount of non-linearity to positions beyond 12th. I'll show my favourite way of doing that, then present a couple season simulations using it, and finally compare it with some of the alternatives.

Let's start from the @dreadnaut 's premises from several posts ago: our currently points system is broadly okay; and the main problem with it is the drop from full points at 12th to tiebreaker points at 13th is too abrupt and comes up too early on the scoreboard. One simple strategy to fix that while keeping everything else mostly unchanged is to shift the tiebreaker points further down the scoreboard, and fill the intermediate positions:



As to how to fill those positions, I suggest an (approximate) exponential between 12th and 24th, tweaked to get rounder values. Using @Overdrijf 's helpful framing, that is a 12-step system, as it takes 12 positions to go from 1 to 0.1. I believe this choice gives us a good balance between extending the range of meaningful points far enough down the scoreboard and keeping the relative gaps between one position and the next large enough for them to feel meaningful.

Here is the points table, split into the three regions:

Code Select Expand

FULL POINTS      TRANSITION      TIEBREAKERS
Pos.  Pts.       Pos.  Pts.      Pos.  Pts.
1     12         13    0.85      25    0.09
2     11         14    0.7       26    0.08
3     10         15    0.6       27    0.07
4     9          16    0.5       28    0.06
5     8          17    0.4       29    0.05
6     7          18    0.3       30    0.04
7     6          19    0.25      31    0.03
8     5          20    0.2       32    0.02
9     4          21    0.17      33    0.01
10    3          22    0.14
11    2          23    0.12
12    1          24    0.1

And, for the sake of a prettier visualisation, a log scale plot of it:



Note this is quite different from the hockey stick system Overdrijf has been looking into, as there is no attempt here to match the exponential and linear slope at their meeting point, as doing so at 12th place would have made the exponential too steep. (By the way, while I did suggest something similar to this system elsewhere in the thread, this time I considered the details much more carefully.)

Besides the balance between absolute points and relative gaps mentioned above, there are many nice little details about this system, which hopefully should help making sense of it:

• Several assignments in the transition range look easy to remember: 14th gets 0.7, 16th gets 0.5, 18th gets 0.3, 20th gets 0.2, 24th gets 0.1.
• No gaps smaller than 0.05 above 20th place.
• Starting anywhere from 12th to 16th and moving eight steps down (so that one stays within the transition range) makes the points exactly five times smaller.
• There is a symmetry of sorts in terms of orders of magnitude: we have 9 linear steps (3th to 12th) to go from 10 points to 1, then a 12-step exponential transition to 0.1 at 24th, and finally another 9 linear steps to the end at 33rd.
• 33 happens to be the number of pipsqueaks in the actual Indy 500 grid, so we even have an in-universe justification for why the tables ends at 33rd! 

That should be enough theory for now. Let's look at the 2022 season simulation, using the same format of the Overdrijf tests just above: 

You cannot view this attachment.

As might be expected, we get results similar to the linear-linear ones, but somewhat less pronounced due to the non-linearity. Only Stan and Daniel get 2 or more extra points, though Leo gets very close to that (note that the three of them have raced at least half a season). In terms of positions, the main differences are that Stan doesn't overtake Ryoma (but still overtakes Erik and BJ), and that HunterBoy344 and ZdnBurns don't overtake Kaweashkar (but still overtake Shorty). The point gaps involved aren't too large, so an extra one or two favourable results could well have been enough to overcome them. One thing that doesn't change is that Daniel still ends up between Zak and BJ.

I have checked the results from 2018 to 2021 as well, and the results are consistent: the propelling effect for results beyond 12th is somewhat smaller, but remains very noticeable and, to my eyes, enough for the system to pay its weight. If you want to look for additional examples, here are summary spreadsheets with the changes in positions and real scores for the last five years: brief-system-comparisons.ods

P.S.: There are at least two interesting other ways of filling the gap between full points and tiebreakers. The simplest possibility is a triple linear system, in which we switch to 0.1 steps at 12th, and then to 0.01 steps at 21th. Alternatively, we might switch to 0.1 steps at 12th, then to 0.05 steps at, say, 18th, and finally to 0.01 steps at 24th, thus ending up with a quadruple linear system. The main disadvantage of triple linear is that we reach 0.01 and the tiebreakers a little too early, while the main disadvantage of quadruple linear is that it is perhaps a little too inelegant. Both of those systems behave pretty well otherwise, being pretty similar in results to the 12-step exponential transition.

P.P.S.: I'll also attach the latest version of my simulator spreadsheets, in case you feel like trying it: You cannot view this attachment.

[dreadnaut]

Thank you Dup! Looking at your table, as it sometimes happens when one has made up their mind, I see a confirmation of my point: non-linearity rewards the exception — two examples can be Ryoma above Stan, or Kaweashkar above HunterBoy and ZdnBurns. That goes agains what I would like to try, which is reward consistency in the lower parts of the scoreboard.

I'll be a bit dictatorly this time, and choose linear-linear for 2023. And 2024 we can go exponential for the first 4 spot, linear 5-12, reduced linear 13+ 💥

[Daniel3D]

Good choice dreadnaut.
I don't think there is really a wrong choice in the ideas, the all feel like improvement, just different flavors.

How about the cars for 2023.
I would opt against one of Ryoma this time because a lot of them feel rushed and unfinished.

Unless someone can name a hidden gem among them..

There are a lot of new cars to choose from.

[Overdrijf]

This all moot and already decided, but I like arguing about graphs, so i'm going to do it.

The simplest possibility is a triple linear system, in which we switch to 0.1 steps at 12th, and then to 0.01 steps at 21th.

I actually kind of like this option. It's essentially the same type of system as the 521 thing, but with less granularity. Instead of making the steps 3ROOT10 times smaller every time the total value has gotten 3ROOT10 times smaller the steps get 10 times smaller every time the total value has gotten 10 times smaller. The curve is more consistent and it gives less of a bump in score to the really low positions relative to the low midfield than switching to steps of 0.05, so places 12 and just below are more worth fighting for. It's infinitely scalable too, after 0.01 you get 0.001 etc. Even if it would be more theoretically consistent if the positions above 10 points would get 20 and 30 points rather than 11 and 12.

One option that I wouldn't dare propose with a straight face but that's fun to think about is the intermediate, a system based on the regular second power root of ten, using steps of 1 and 0.3. (10 9 8 7 6 5 4 3 2.7 2.4 2.1 1.8 1.5 1.2 1 0.9 0.8...) I suspect it would graph pretty cleanly. And 14 steps for an order of magnitude is pretty reasonable too. The reason I wouldn't pitch it with a straight face is that the steps of 3 just make such a mess of non-round numbers.

And 2024 we can go exponential for the first 4 spot, linear 5-12, reduced linear 13+ 💥

Nah, we should probably refrain from changing every aspect every year. I'll be back to argue points systems for the 2028 season. Next year we'll do the number of cars or the team rules or the race lengths or a bonus for automatic gears or something. Not to mention side score boards for NoRH, GAR, on road RH, same car all season and more.

[dreadnaut]

And 2024 we can go exponential for the first 4 spot, linear 5-12, reduced linear 13+ 💥

Nah, we should probably refrain from changing every aspect every year.

Oh, I was actually serious! We are changing the bottom of the score system this year, but we could change the top next time: introduce non-linearity to heat up the battle for the championship, while keeping the mid-low scoreboard compatible.

I'm open to changing multiple things, as long it is still possible to observe the effect of each change separately.

[Duplode]

Looking at your table, as it sometimes happens when one has made up their mind, I see a confirmation of my point: non-linearity rewards the exception — two examples can be Ryoma above Stan, or Kaweashkar above HunterBoy and ZdnBurns. That goes agains what I would like to try, which is reward consistency in the lower parts of the scoreboard.

That's fair. I would just note that, more than the non-linearity itself, the big discontinuity at 12th place is to blame here. There's no good way to avoid that discontinuity while keeping the 1st-12th linear range as it currently exists, though adopting a very gentle linear slope for the further positions will provide some compensation for those who take part in lots of races over the season. I sense a hockey curve system, with the cutoff being around 8th or 10th, should be able to minimise this distortion. That's a matter for next year, though  I'm happy enough with having helped to put the point system back on the agenda -- and anyway I still have a few new cars to test!

[alanrotoi]

And for the cars rules, what about a "ban a car rule"? The track designer could ban a car for his race.
For example:

• A track designer can ban a car for his track
• Any car can't be banned more than (two or three times maybe?)

Also to complement this rule the championship could extend the car limit in one extra car.

[afullo]

Before deciding anything though, I'd like to hear from @Cas, @afullo, @Shoegazing Leo, @stan286xt, @Daniel3D, ...

Sorry but I have been particularly busy in the latest few days, so I had not the time to analyze properly the various options...

[KyLiE]

do we want a "NoRH" side-scoreboard back for 2023?

That's not something I'd be keen on.  Personally, I'd prefer to focus on the main competition.  Besides, we have Race For Kicks for that.

[Argammon]

Hello everyone,

first of all, I would like to wish you a merry Christmas. 

I was thinking it would be nice to post a short teaser on the upcoming season on the main page of Zakstunts. The teaser could contain details like when the new season is going to start, the car bonuses for the first track etc. I am hoping this would attract the interest of new pipsqueaks, who may be browsing the page between Christmas and new year's eve.

[Cas]

On Alan's idea... it's definitely something to think about, but very carefully. Being able to ban a car is a great power. I'd say, for example, that if a track designer chooses to ban one car, then he/she can't change any bonus values. This I suggest because frequently, bonus tweaking serves precisely the purpose of virtually banning or securing the participation of a certain car, so if you do it one way, you can't do it another.

Another thing to consider is why somebody would want to ban a certain car. The most common reason is to prevent PG races. I usually "ban" slow cars on my tracks or make fast cars more competitive because I like designing fast tracks and I feel that my creation ends up being very boring if a slow car ends up being the "car of the race", but I think my case is not common. Now, for PG, everybody will want to ban the Indy most of the time, but for slow cars, there are many. I'd say at most, a car should be banned twice in a season and a banned car should accumulate bonus just like unused cars do.

[alanrotoi]

On Alan's idea... it's definitely something to think about, but very carefully. Being able to ban a car is a great power. I'd say, for example, that if a track designer chooses to ban one car, then he/she can't change any bonus values. This I suggest because frequently, bonus tweaking serves precisely the purpose of virtually banning or securing the participation of a certain car, so if you do it one way, you can't do it another.

Another thing to consider is why somebody would want to ban a certain car. The most common reason is to prevent PG races. I usually "ban" slow cars on my tracks or make fast cars more competitive because I like designing fast tracks and I feel that my creation ends up being very boring if a slow car ends up being the "car of the race", but I think my case is not common. Now, for PG, everybody will want to ban the Indy most of the time, but for slow cars, there are many. I'd say at most, a car should be banned twice in a season and a banned car should accumulate bonus just like unused cars do.

I like the fixes. We should brain this idea but for a possible implementation in 2024.

[Cas]

True. With all these details and with the many more that surely can still come up, it's better to have it well polished for implementation, if that is done.