Cars and rules for 2023

[Daniel3D]

here goes another compromise proposal: Keep the 12..1 linear system from 1st to 12th as it is, and use the following table beyond 12th:

Code Select Expand

Pos.  12    13    14    15    16    17    18    19    20    21    22    23    24    25    26    27    28    29    30
Pts.  1     0.85  0.7   0.6   0.5   0.45  0.4   0.35  0.3   0.25  0.2   0.16  0.12  0.1   0.08  0.06  0.04  0.02  0.01


I like this proposal. I don't think that the point system for the top 12 needs changing. It's been successful for a very long time.
The points beyond 12 are a lot fairer than the current system without being overpowered.

(It doesn't seem we'll get a consensus for adding non-linearity to the upper part of the scoreboard)

It's good to strive for consensus. I think that the non-linearity line is better (contrary to my initial believe) but it's a big change and that is not a thing to force upon players. 

[Overdrijf]

So I would probably prefer the 16 step system (the orange line). Starting at 16 for first place the number 12 gets 3.5 points, the number 20 gets 1 point and the number 36 gets 0.1 points. And that's the part that feels unsatisfying about this one. In a bit of a slow month there might be 14 people on the track, so someone gets 2.5 points for showing up, that feels weird. It also starts using half points very early, doesn't feel extremely elegant. However, you double your score by gaining 4 to 5 places (edit: called it exactly five before this edit). That feels good. Those 2.5 point for showing up and ending 14th? They're not going to completely invalidate your hard fought battles for places 20 to 18, for which you still got 1 and 1.4 points respecitively. Ending 3rd while your rival got the win is also a sensitive blow but not a season ender, as it's the difference between 12 and 16 points, you can still make up for that. (Full order of this system: 16, 14, 12, 10, 9, 8, 7, 6, 5, 4.5, 4, 3.5, 3, 2.5, 2, 1.8, 1.6, 1.4, 1.2, 1, 0.9, 0.8, 0.7, 0.6, 0.5, 0.45...)

(If you start at 12 points rather than at 16 place 12 gets only 2.5 points, place 18 gets 1 point and place 34 gets 0.1 point, which may map onto our average attendance numbers better.)

So that's probably what I would do, the 16 step 521 system (patent not pending). It makes the experience of fighting for second to last place more similar to fighting for first place, it's infinitely scalable, and the point differences you get for positions feel good. Because the score for every position is higher than under the current system we could furthermore consider giving a leading time point per 200 hours rather than 250. (But not if 1st place gets only 12 points, then I'd leave it at the current number.)

Here's my followup "simulation" of this "16 step" system, recalculating this year's results as if they were raced under a different point system but all the results were the same. I didn't touch the LTB points. Those nice in-forum tables are way too clean for me, so I'm going with a big Excel screenshot.



I see two groups of winners and two groups of losers in this system compared to the old one, and they seem to tie into two pairs. One pair of minor winners and losers, one of major winners and losers.

The minor winners are people who score top three places. Alan and Duplode both gain a bunch of points. But they were already on top, having shown up every months and not having gone lower than 4^th place between them. It is instead CTG's score that shows us what can happen. Great results by a great driver combined with months of inactivity pay more than they would have under the current system. They let CTG overtake Zapper, who just happens to be the perfect example of the minor losers. He consistently and persistently places between 4^th and 9^th place every single month, the exact range of places that gains the least in absolute terms (except for the very lowest positions), only getting 1 point extra each. Zapper therefore scores only 9 points extra, 1 for every month not counting his three worst results. Heretic is another example, also only having place 4 to 9 finishes ones you strike off his worst 3 months. He too gains a few less extra points than more inconsistent drivers like yours truly.

Am I happy with this set of winners and losers? Not sure. I don't want to discourage drivers like Zapper, who showed us an amazing solo season. Then again, I personally find it never hurts too much to end behind an amazing and experienced pro driver like CTG. And it does encourage the subtop to shoot for the moon. One or two third places in a season can make a difference. (I also feel like my expectations may be schewed because in essence the current linear system really benefits the subtop, giving them reasonable gaps with the real top but an insurmountable chasm below them that someone who often ends below place 12 can never hope to cross.)

The major losers of this system are good drivers who show up for three races or less, especially if they fail to grab podiums when they do show up. They get overtaken by the major winners: people who get lower results but race more consistently. Stan goes up 5 places when his 3.5 points are turned into almost 24 points, and Daniel goes up a whopping 8 places when his half a point turns into 13.5 points. This is enough to get both of them into the part of the scoreboard with people who actually attended most races, skipping over drivers like Argammon, Marco and Joe, who all drove just one race. (Leo and afullo were not marked, but also find a big juicy score boost.)

Am I happy with this change? While it may seem super broken at first compared to the current system... yes, yes I am happy with this change. It feels like it would be incredibly demotivating to drive hard month in month out and checking the yearly leaderboard just to see you're sinking lower and lower under the weight of people who came in this one time. This feels good. These drivers deserve these positions on determination alone.

One thing that disappoints me a little bit is that there are still cases where the order on the amateur scoreboard is not the same as on the main board. Even with the internal consistency of this points scheme the differences in how many pros end up between amateur results make this comparison inconsistent. (On an only mildly related note, I like how the amateur scoreboard feels a little fuller than the newbie board used to be, and that's good. I think the change was a good thing.)



Conclusion: The thing I really like about how this calculation turned out is how the slower but consistent drivers end up being more part of the pack. This is the part that can also be achieved by only changing the tail end of the scores. And honestly based on these results I think we shouldn't be too stingy when we do that. A good target I think is to give people a fair chance to score at least a full point each race, letting someone with perfect attendance and a serious drive each time end up around 9 points, above most one-time drivers. (The hockey stick looking model starting at 3 points might work.) As for the effect on the higher end of the scale: I'm not actually sure. The rules where your three weakest races don't count already benefits inconsistent drivers. That already to some degree does the job of non-linear scoring. But I also don't really dislike the ranking this system gives. It might take some getting used to...

[dreadnaut]

First of all, thank you all for the many charts and tables! This is awesome ✨

They get overtaken by the major winners: people who get lower results but race more consistently. Stan goes up 5 places when his 3.5 points are turned into almost 24 points, and Daniel goes up a whopping 8 places when his half a point turns into 13.5 points.

In the current point system, drivers in position 13+ are not assigned a score, as I've mentiond before, but a symbolic value used for ordering. F1 gives everyone zero points, and that's it. Look at the decrease ratio of the current system, and how it screws everyone below 12 position. That 90% drop from 1 to 0.10 automatically excludes them from the main competition.

You cannot view this attachment.

Any system that assigns them actual points will see them "major winners" 🎉

I think we all agree on the goal here: to see a larger number of pipsqueaks enjoy the fight for the middle and low scoreboard. To do so, we only have to remove that 90% drop.


The discussion about linear vs exponential scoring is a separate one. The way I understand it:

- Exponential systems are adapted for uncertainty and reward exceptional good results. They add excitement real-world competitions, affected by random events like burst tires or pit-stop mishaps.

- Stunts doesn't have rainy days (yet?) and ZakStunts has evolved to reward consistency. There is little or no uncertainty, since month-long events make it very unlikely that an engaged pipsqueak will miss a race. Top-of-the-scoreboard excitement is in part covered by the LTB points.

- Switching to an exponential system is not going to improve the mid-low scoreboard, where the exponential converges to a linear system. It is also not going to add excitement to the top of the scoreboard, because races lack random events.

[Argammon]

Great work guys!

Ok, here are my 3 cents. Bear in mind that I am writing on my phone, which kind of makes any serious analysis difficult.

- There is too little feedback from the target group, that is those earning low amounts of points on a regular basis. Do they like decimal points at all? Do they care whether they are ranked above a one time pipsqueak like me? What motivates them? I just do not know.

- I would suggest increasing the intercept from 12 to a higher number like 20. Then, more pipsqueaks would get full points. Consider pipsqueak X who typically ends up around place 20. Would it be a big problem if he ends up on the 15th place in a low attendance race and earns 5points? At least it would be an incentive to join races with a low attendance rate.

- Using a decreasing strictly convex.funxtion (what you call exponential) makes effort pay off. It likely takes.more effort (or time) to achieve a 1st place and a 5th place than two 3rd places. A linear scoring system does not reflect that, but the LTB helps. I do not claim this is important and should trump other considerations. I would just like to mention the point. :-)

[Overdrijf]

An additional note about this idea. While starting the exponential points from 10th place isn't my favourite option at the moment (non-integer point assignments larger than 1 feel weird to me), if we were to do that it might make sense to choose an exponential such that its slope at 10th place matches the linear slope from 1st to 10th:

You cannot view this attachment.

By the way, here's what we'd get with the cutoff-at-8th system I have suggested above. Note there are no position changes down to 13th place, and the changes that do happen are quite a bit milder:

Code Select Expand

    Räcer        Races    Pts.    Pts. (12..1)    Position Change
1    Alan Rotoi    12    585    117        0
2    Duplode        12    530    106        0
3    KyLiE        12    400    80        0
4    CTG        6    350    70        0
5    Overdrijf    12    345    69        0
5    Zapper        12    345    69        0
7    dreadnaut    12    290    58        0
8    Akoss Poo    6    250    50        0
9    Heretic        12    224    43        0
10    afullo        12    181    33        0
11    Ryoma        7    151    28.06        0
12    Friker        4    142    28        0
13    Cas        12    127    18.19        0
14    Shoegazing Leo    12    97    9.37        +4
15    Marco        6    96    15.28        0
16    Frieshansen    3    80    16        -2
17    GTAMan15    5    69    10.16        -1
18    Seeker1982    2    56    10.08        -1
19    KaoS        9    55    3.44        +1
20    Stan 286XT    12    53    1.57        +2


Slowly catching up to where the discussion currently is, I like this "hockey stick curve" compromise. (Yes, that's the official mathy term, why do you ask?) The only thing I like a bit less is the non-round numbers. Jumping from 3 to 2.15 and 1.54. So I tried if I could round-numberify this with a variant on the 521 concept. Starting at 3 is a bit awkward, so I cheated a little bit (using one step of 3) to get to a 10 step system (every ten steps is an order of magnitude smaller) that keeps ending up on as round as possible numbers.

The order I end up with is:
12 11 10 9 8 7 6 5 4 3 2.5 2 1.5 1.2 1 0.8 0.6 0.5 0.4 0.3 0.25 0.2 0.15 0.12 0.1 0.08 0.06 0.05 0.04 0.03 0.025 0.02 0.015 0.012 0.01...
(Edit: There were originally a bunch of zeroes missing from the lower end there.)

This is how it graphs out:

The pivot point around 3 points looks a bit janky. I can smoothen that out, but only by using less round numbers (for instance 2.5>2.4 and 2>1.9). Both hockey stick curves look pretty sweeth on a logarithmic scale though.

And that's essentially what happens here. The places 1 through 10 are competing on a linear scale, while the places 7 and below (yes, there's overlap) are competing on a roughly logarithmic scale/exponential curve/I don't know mathy terms.

Running the results from 2022 through this filter a few things become noticable:
1 The amateur league results are entirely unchanged as they never went below 3 points.
2 The top of the board is also almost entirely unaffected. A single 12th place for Usrin that counts because he also had several missed races causes the only points change in the top 11.
3 For the subtop inconsistency is punnished less than under the current system, but not rewarded. What I mean by that is this: if you always end up fourth to ninth having a few races where you're twelfth gives you less points loss than under the current system, but the lack of bonus points for the podium positions like my previous analysis had mean you can't as easily make up for that with a few exceptional results.
4 Because the half points come in starting at 2.5 rather than the 4.5 of my previous simulation the changes in the lower half are less drastic, Daniel with 6 races raced jumps up 4 places rather than 8, not ending ahead of all one time drivers, but Stan with perfect attendance does still jump 5 places up to the "mostly full time drivers" part of the board. (Okay, there is an "inconsistent pro's" section right above all the nice green numbers, but those people just need to race more. I'm talking to you, Overdrijf.)


(The green ones are all the results with a gain of more than 2 full points compared to the current system.)


I think a hockey stick curve is a good middle ground between a linear and an exponential-ish system. The steepness of Duplode's curve might actually be most suited for our competition. Sure, one order of magnitude in 7 steps is steep, but 13th place at 1 point and 20th place at 0.1 points sounds about right, where my system's 15th place at 1 point and 25th place at 0.1 point feels maybe a little wide for a competition where this year each race was attended by 12 to 20 drivers. (Then again: the biologist in me assures me that if a niche is available it will be filled, a large score board attracts drivers.) But overall I think I'm actually in favor of a hockey stick curve now.

[Argammon]

An additional note about this idea. While starting the exponential points from 10th place isn't my favourite option at the moment (non-integer point assignments larger than 1 feel weird to me), if we were to do that it might make sense to choose an exponential such that its slope at 10th place matches the linear slope from 1st to 10th:

point-systems-exp-at-10-3.png

By the way, here's what we'd get with the cutoff-at-8th system I have suggested above. Note there are no position changes down to 13th place, and the changes that do happen are quite a bit milder:

Code Select Expand

    Räcer        Races    Pts.    Pts. (12..1)    Position Change
1    Alan Rotoi    12    585    117        0
2    Duplode        12    530    106        0
3    KyLiE        12    400    80        0
4    CTG        6    350    70        0
5    Overdrijf    12    345    69        0
5    Zapper        12    345    69        0
7    dreadnaut    12    290    58        0
8    Akoss Poo    6    250    50        0
9    Heretic        12    224    43        0
10    afullo        12    181    33        0
11    Ryoma        7    151    28.06        0
12    Friker        4    142    28        0
13    Cas        12    127    18.19        0
14    Shoegazing Leo    12    97    9.37        +4
15    Marco        6    96    15.28        0
16    Frieshansen    3    80    16        -2
17    GTAMan15    5    69    10.16        -1
18    Seeker1982    2    56    10.08        -1
19    KaoS        9    55    3.44        +1
20    Stan 286XT    12    53    1.57        +2


Slowly catching up to where the discussion currently is, I like this "hockey stick curve" compromise. (Yes, that's the official mathy term, why do you ask?) The only thing I like a bit less is the non-round numbers. Jumping from 3 to 2.15 and 1.54. So I tried if I could round-numberify this with a variant on the 521 concept. Starting at 3 is a bit awkward, so I cheated a little bit (using one step of 3) to get to a 10 step system (every ten steps is an order of magnitude smaller) that keeps ending up on as round as possible numbers.

The order I end up with is:
12 11 10 9 8 7 6 5 4 3 2.5 2 1.5 1.2 1 0.8 0.6 0.5 0.4 0.3 0.25 0.2 0.15 0.12 0.1 0.8 0.6 0.5 0.4 0.3 0.25 0.2 0.15 0.12 0.1...

This is how it graphs out:

The pivot point around 3 points looks a bit janky. I can smoothen that out, but only by using less round numbers (for instance 2.5>2.4 and 2>1.9). Both hockey stick curves look pretty sweeth on a logarithmic scale though.

And that's essentially what happens here. The places 1 through 10 are competing on a linear scale, while the places 7 and below (yes, there's overlap) are competing on a roughly logarithmic scale/exponential curve/I don't know mathy terms.

Running the results from 2022 through this filter a few things become noticable:
1 The amateur league results are entirely unchanged as they never went below 3 points.
2 The top of the board is also almost entirely unaffected. A single 12th place for Usrin that counts because he also had several missed races causes the only points change in the top 11.
3 For the subtop inconsistency is punnished less than under the current system, but not rewarded. What I mean by that is this: if you always end up fourth to ninth having a few races where you're twelfth gives you less points loss than under the current system, but the lack of bonus points for the podium positions like my previous analysis had mean you can't as easily make up for that with a few exceptional results.
4 Because the half points come in starting at 2.5 rather than the 4.5 of my previous simulation the changes in the lower half are less drastic, Daniel with 6 races raced jumps up 4 places rather than 8, not ending ahead of all one time drivers, but Stan with perfect attendance does still jumpp 5 places up to the "mostly full time drivers" part of the board. (Okay, there is a 5 man "inconsistent pro's" section right above all the nice green numbers, but those people just need to race more. I'm talking to you, Overdrijf.)


(The green ones are all the results with a gain of more than 2 full points compared to the current system.)


I think a hockey stick curve is a good middle ground between a linear and an exponential-ish system. The steepness of Duplode's curve might actually be most suited for our competition. Sure, one order of magnitude in 7 steps is steep, but 13th place at 1 point and 20th place at 0.1 points sounds about right, where my system's 15th place at 1 point and 25th place at 0.1 point feels maybe a little wide for a competition where this year each race was attended by 12 to 20 drivers. (Then again: the biologist in my assures me that if a niche is available it will be filled, a large score board attracts drivers.) But overall I think I'm actually in favor of a hockey stick curve now.

Nice and thoughtful analysis like always. Quick question: Couldn't your "hockey stick curve" start a bit higher than 12?

[Daniel3D]

We can start at any number but Relatively speaking there is no difference.

I like overdrijf his green curve more than duplode purple one.
But I also agree that with the current attendance duplode purple is the better option.

[Overdrijf]

Nice and thoughtful analysis like always. Quick question: Couldn't your "hockey stick curve" start a bit higher than 12?

Yes. There are essentially four things you can tweak:
1 The number at which the linear part starts. 12 feels good to me so that the lowest positions still end up around or below 1 in most months. It would to me personally feel a bit weird to have the points go from 20 to 6 on a slowish month. But it's no problem for the curve. It could be a solution if we're aiming for a system where we have a good to assign points to a large number of lower place finishers but don't want these non-linear numbers to show up too often.
2 The steepness of the linear part. So you could say start at 24 but take steps of two points. I don't currently see reasons to do this, but they presumably exist.
3 The point where you depart from the linear line and go exponential. At 1 point feels the most natural for a score board, but at that point it's almost like the current system, the curve doesn't add much, hence me choosing to follow Duplode and start at 3 points/place 10.
4 How hard the curved part curves. Although your options here are somewhat limited if you like round numbers.

So it's pretty customizable.

[alanrotoi]

I think we maybe went too far .

[Argammon]

We can start at any number but Relatively speaking there is no difference.

I like overdrijf his green curve more than duplode purple one.
But I also agree that with the current attendance duplode purple is the better option.

Perhaps I was not clear enough. My suggestion is a higher intercept together with a longer linear part. Hence, more pipsqueaks would get integers.

Maybe the 20 I mentioned earlier is exaggerated. I told you I do not have mainstream taste.    But 14 or 15 may be a compromise.

[Overdrijf]

I think we maybe went too far .

I haven't even proposed a fluctuating scale yet, like maybe a "minus 2, plus 1" system. (10 8 9 7 8 6 7 5 6 4 5 3...)

[Daniel3D]

I think we maybe went too far .

I haven't even proposed a fluctuating scale yet, like maybe a "minus 2, plus 1" system. (10 8 9 7 8 6 7 5 6 4 5 3...)

I'll pretend i didn't see this...

We can start at any number but Relatively speaking there is no difference.

I like overdrijf his green curve more than duplode purple one.
But I also agree that with the current attendance duplode purple is the better option.

Perhaps I was not clear enough. My suggestion is a higher intercept together with a longer linear part. Hence, more pipsqueaks would get integers.

Maybe the 20 I mentioned earlier is exaggerated. I told you I do not have mainstream taste.    But 14 or 15 may be a compromise.

O. I see. (No that wasn't clear to me)
As someone who has (so far) always been outside of integers. With the current average participation density I don't think that it is necessary if the "hockeystick curve is implemented" but I'm not at all against it.

[dreadnaut]

@Overdrijf, could you make one more table matching your "hockey stick" one, but with 12 -> 1 step 1, 0.95 -> 0.05 step 0.05?

I'd like to compare a linear + convex to a linear + linear.

[Overdrijf]

@Overdrijf, could you make one more table matching your "hockey stick" one, but with 12 -> 1 step 1, 0.95 -> 0.05 step 0.05?

I'd like to compare a linear + convex to a linear + linear.

Yeah I can do that, not right now but within a day or so.

[Overdrijf]

Here's the table, I ones again marked everyone gaining 2 full points or more. The Amateur Board is not included because there are no changes to it:



It was afraid it was going to feel a bit like "everyone finishing 12th place or lower gets 1 points with a little tie breaking penalty". That fortunately is not quite the case, scores of .75 and below are pretty common.

Compared to the hockey stick there is a slightly greater area at the top untouched, and the people right below that gain significantly less points. Cas no longer gets a bonus over the current system, and Leo is the highest placed pipsqueak gaining more than 2 points. Stan and Daniel sync up to gain 4.66 points and 3 places each. (But Daniel claims the moral victory for ending up between two Corks, that's a sign you did something right.) Neither of them quite close the gap to the pseudo-fulltimers, but they do move up to a slightly more reputable neighborhood.

The scores cross with the hockey stick curve at place 16, where both give 0.8 points. From that point on the linear-linear system gives more points. In the lower section of the board some people therefore gain more points than they do under the "Overdrijf hockey curve" system, the first being ZdnBurns. These are all people with 3 races or less. (Who are probably on average less interested in the end of year standings, but may or may not potentially still be more inclined to come back if they get 0.6 points than if they get 0.03 points.)

As a bonus: it isn't even that bad a curve when plotted logaritnmically...



There is a bit of a lack of elegance (yes, I think elegance is really important, but only in graphs, and maybe ballet dancers), but it is simple to understand. The curve also extends more than far enough, and you could even tie the current 0.1-0.01 step 0.01 (or step 0.005) to the end of it if needed.