
Originally Posted by
hozn
Ok, these are good ideas. I do like Bob's idea is 10,20,30 bonus points for miles 13.
If someone wants to propose a diminishing mileage formula that seems reasonable, I'm generally in favor of the idea. I was trying to see if I could find other similar scoring systems that had been used elsewhere, but hadn't turned up anything in brief research.
As "food for thought"  here's a quick example of a "tiered" system of diminishing returns for the number of miles ridden in a given day, separate from the bonus points idea. This is setup so that after every 10 mile increment, the value of the next incremental mile is reduced by, for example, 10%. In other words, 1 point per mile up to 10, 0.9 points per mile for anything between 10 and 20, 0.81 points per mile for anything between 20 and 30, etc. The Excel formula to calculate that is: 10*((10.9^ROUNDDOWN(MILES/10,0))/(10.9))+MOD(MILES,10)*(0.9^ROUNDDOWN(MILES/10,0)) That decreases a little bit faster than the previous example, with the 101st mile being worth 0.35 points. You can make it diminish faster or slower easily enough by changing the 0.9 figure either lower or higher. The table below shows what happens every 10 miles for 0.95, 0.9, 0.8, and 0.7.
One could mix and match so that you have a similar tiered idea, but with accelerating discounts (i.e., maybe you start with a 0.9 factor but make it 0.8 after 40 miles and 0.7 after 80 miles or whatever). Again  it all depends on what you want the results to look like.

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Originally Posted by
LhasaCM
As "food for thought"  here's a quick example of a "tiered" system of diminishing returns for the number of miles ridden in a given day, separate from the bonus points idea. This is setup so that after every 10 mile increment, the value of the next incremental mile is reduced by, for example, 10%. In other words, 1 point per mile up to 10, 0.9 points per mile for anything between 10 and 20, 0.81 points per mile for anything between 20 and 30, etc. The Excel formula to calculate that is: 10*((10.9^ROUNDDOWN(MILES/10,0))/(10.9))+MOD(MILES,10)*(0.9^ROUNDDOWN(MILES/10,0)) That decreases a little bit faster than the previous example, with the 101st mile being worth 0.35 points. You can make it diminish faster or slower easily enough by changing the 0.9 figure either lower or higher. The table below shows what happens every 10 miles for 0.95, 0.9, 0.8, and 0.7.
One could mix and match so that you have a similar tiered idea, but with accelerating discounts (i.e., maybe you start with a 0.9 factor but make it 0.8 after 40 miles and 0.7 after 80 miles or whatever). Again  it all depends on what you want the results to look like.
For the “average” participant, I do like the idea of this tiered system to keep points closer between long distance riders, and around the block riders.
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Originally Posted by
LhasaCM
As "food for thought"  here's a quick example of a "tiered" system of diminishing returns for the number of miles ridden in a given day, separate from the bonus points idea. This is setup so that after every 10 mile increment, the value of the next incremental mile is reduced by, for example, 10%. In other words, 1 point per mile up to 10, 0.9 points per mile for anything between 10 and 20, 0.81 points per mile for anything between 20 and 30, etc. The Excel formula to calculate that is: 10*((10.9^ROUNDDOWN(MILES/10,0))/(10.9))+MOD(MILES,10)*(0.9^ROUNDDOWN(MILES/10,0)) That decreases a little bit faster than the previous example, with the 101st mile being worth 0.35 points. You can make it diminish faster or slower easily enough by changing the 0.9 figure either lower or higher. The table below shows what happens every 10 miles for 0.95, 0.9, 0.8, and 0.7.
One could mix and match so that you have a similar tiered idea, but with accelerating discounts (i.e., maybe you start with a 0.9 factor but make it 0.8 after 40 miles and 0.7 after 80 miles or whatever). Again  it all depends on what you want the results to look like.
Diminishing returns appears to directly penalize for riding more. Riding a century in subfreezing weather (add in wet conditions) is pretty miserable, with each mile becoming worse, and often necessary for those living farther away for commutes and attending events. Adding bonus points is a direct reward and encourages daily riding and can accomplish similar "leveraging" results without giving the appearance of being punitive. Accelerating returns seems more positive and encouraging than diminishing returns.
Below is an example, of accelerating returns/points. At first it appears no difference in point spread, but if that century rider skips a day of riding and a daily rider does 10 miles, they would gain 65 points on the sporadic century rider (and more importantly team points). Again, with the theory that daily riding for most will also translate into more participation, such as convoys, social events, Strava titles, pointless prize competing, forum posts, etc...
If someone rides at least 10 miles a day, there is no loss of points, i.e. no penalty for riding more, but was dramatically encouraged to ride daily by the scoring system. It would be very difficult to voluntarily forfeit up to 55 bonus points just because it was subfreezing temps and/or wet conditions. It's not really a change to the current scoring system (1 mile is still 11 points), but an extension of it, with the same goal of encouraging daily riding.
Last edited by Bob James; 12022017 at 08:23 AM.

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Originally Posted by
Bob James
Diminishing returns appears to directly penalize for riding more. Riding a century in subfreezing weather (add in wet conditions) is pretty miserable and often necessary for those living farther away for commutes and attending events. Adding bonus points is a direct reward and encourages daily riding and can accomplish similar "leveraging" results without giving the appearance of being punitive. Accelerating returns seems more positive and encouraging than diminishing returns.
Below is an example, of accelerating returns/points. At first it appears no difference in point spread, but if that century rider skips a day of riding and a daily rider does 10 miles, they would gain 65 points on the sporadic century rider (and more importantly team points). Again, with the theory that daily riding for most will also translate into more participation, such as convoys, social events, Strava titles, pointless prize competing, forum posts, etc...
If someone rides at least 10 miles a day, there is no loss of points, i.e. no penalty for riding more, but was dramatically encouraged to ride daily by the scoring system. It would be very difficult to voluntarily forfeit up to 55 bonus points just because it was subfreezing temps and/or wet conditions.
I think "losing points" and "being penalized" are not the right way to think about it. More miles will always equate to more points, just the rate of point accumulation will change as you ride.

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Originally Posted by
LhasaCM
As "food for thought"  here's a quick example of a "tiered" system of diminishing returns for the number of miles ridden in a given day, separate from the bonus points idea. This is setup so that after every 10 mile increment, the value of the next incremental mile is reduced by, for example, 10%. In other words, 1 point per mile up to 10, 0.9 points per mile for anything between 10 and 20, 0.81 points per mile for anything between 20 and 30, etc. The Excel formula to calculate that is: 10*((10.9^ROUNDDOWN(MILES/10,0))/(10.9))+MOD(MILES,10)*(0.9^ROUNDDOWN(MILES/10,0)) That decreases a little bit faster than the previous example, with the 101st mile being worth 0.35 points. You can make it diminish faster or slower easily enough by changing the 0.9 figure either lower or higher. The table below shows what happens every 10 miles for 0.95, 0.9, 0.8, and 0.7.
One could mix and match so that you have a similar tiered idea, but with accelerating discounts (i.e., maybe you start with a 0.9 factor but make it 0.8 after 40 miles and 0.7 after 80 miles or whatever). Again  it all depends on what you want the results to look like.
These formulas look like they are being written by taxwriting legislators. Just make points=miles**a, where a is .9 or something. Similarly, the 3 mile bonus scheme can be calculated as ARGMAX(10*miles,30). This limits the nondifferentiability of the resulting point function. With this, I retire back into complete apathy regarding this issue.

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Originally Posted by
aaronwelsh
I think "losing points" and "being penalized" are not the right way to think about it. More miles will always equate to more points, just the rate of point accumulation will change as you ride.
hmm...you could have a point As a long distance rider, I see a goal to devalue miles as negative, versus a goal that encourages daily riding as positive. At the same time, I am more impressed by those who ride 510 miles (or more) a day, making multiple commute, errand and social rides, over myself riding a recreational half or full century (yes, even I would consider going to Krispy Kreme or visiting the local cows as recreational).
I'm not advocating for any change in the current scoring system, but only commenting because "some" change is being considered.

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Originally Posted by
Bob James
Diminishing returns appears to directly penalize for riding more. Riding a century in subfreezing weather (add in wet conditions) is pretty miserable and often necessary for those living farther away for commutes and attending events. Adding bonus points is a direct reward and encourages daily riding and can accomplish similar "leveraging" results without giving the appearance of being punitive. Accelerating returns seems more positive and encouraging than diminishing returns.
Below is an example, of accelerating returns/points. At first it appears no difference in point spread, but if that century rider skips a day of riding and a daily rider does 10 miles, they would gain 65 points on the sporadic century rider. Again, with the theory that daily riding for most will also translate into more participation, such as convoys, social events, Strava titles, forum posts, etc...
I am fully on board with the idea that, mathematical equivalence or not, whatever we do should be most commonly perceived as encouraging something, not discouraging something else. (Hence why we couldn't just take freeze points as it was constructed  there was no benefit to riding more than 9 miles.)
I agree that both constructs numerically have similar impacts  they offer a greater reward for greater frequency of riding so that the 100th mile isn't worth as much as the 5th, but can be perceived very differently. One benefit of the earlier idea (not having tiers but having the diminishing returns for each incremental mile) is that it doesn't set any sort of magic mile marker or judgement as "this number is what's most valuable." I think one of the other ideas behind a sliding scale of sorts to reduce point spreads in an attempt to keep the competition from being a foregone conclusion before the end  though theoretically diminishing returns also makes big swings harder to make (i.e., harder to make up a deficit) so it could all be a nothingburger.
How would you feel about a "1 point per mile plus a continuously diminishing bonus" construct? In other words, as mileage approaches "infinity" the bonus goes away rather than dropping out at 3 or 10 or whatever specific number is chosen, but it stays at the one point per mile throughout? For example, you have a 10 point bonus for miles 1, 2, and 3 as proposed elsewhere, but then the bonus is reduced by 10% for each incremental mile. That'd look like:
What would be great would be to take some more specific data and see what the three different approaches do to some other numbers over the course of a competition. I'll work something up when I get a chance today for a few hypothetical riders (and what I actually did last year since I have the data).

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Originally Posted by
aaronwelsh
I think "losing points" and "being penalized" are not the right way to think about it. More miles will always equate to more points, just the rate of point accumulation will change as you ride.
Bob rode like 6,000 miles during Freezing Saddles last year while working full time. I'm pretty sure that there's no way that a progressive point tax system won't feel like a penalty.

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Originally Posted by
aaronwelsh
I think "losing points" and "being penalized" are not the right way to think about it. More miles will always equate to more points, just the rate of point accumulation will change as you ride.
True numerically  but since there many ways to get the same general effect, perception is important.
Originally Posted by
DismalScientist
These formulas look like they are being written by taxwriting legislators. Just make points=miles**a, where a is .9 or something. Similarly, the 3 mile bonus scheme can be calculated as ARGMAX(10*miles,30). This limits the nondifferentiability of the resulting point function. With this, I retire back into complete apathy regarding this issue.
Yep  those formulas are just like income tax brackets (rate a applies up to here, rate b applies to the next range, etc.) I think I realized this morning that I'm way too interested in the thought experiment just because I haven't worked that part of my brain enough in quite a few years, which also means it'll take me a while to work to the "here's the simple version of the complicated thing I threw out there".
And also  I'm not necessarily advocating for anything. I'm not going to win where something more than 3 miles counts regardless, so I'm just tossing things against the wall to see if anything sticks since there seemed to be some interest in a change.
Last edited by LhasaCM; 12022017 at 08:47 AM.
Reason: added my motivation

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Originally Posted by
LhasaCM
True numerically  but since there many ways to get the same general effect, perception is important.
Yep  those formulas are just like income tax brackets (rate a applies up to here, rate b applies to the next range, etc.) I think I realized this morning that I'm way too interested in the thought experiment just because I haven't worked that part of my brain enough in quite a few years, which also means it'll take me a while to work to the "here's the simple version of the complicated thing I threw out there".
And also  I'm not necessarily advocating for anything. I'm not going to win where something more than 3 miles counts regardless, so I'm just tossing things against the wall to see if anything sticks since there seemed to be some interest in a change.
Since we're cyclists, perhaps it makes sense to think of it as a "breakaway headwind." It makes it easier for smallmiles participants to stay with the peloton. It makes it somewhat more difficult for the largemiles cyclists to go off the front.
It's certainly a fair question whether that's what we want. FS has always rewarded consistency with points. These schemes would increase the incentive for lowmilage participants to up their miles (since they won't simply get a firstmile bonus), with the downside of reducing the incentive for the highmilage cyclists to ride further. Since there are far more lowmilage participants, and since FS is a community activity, I think this may be an improvement.
I suspect that the highmilage riders are more interested in who rides the furthest, rather than who earn the most points. To that end, we should probably let individuals compete on pure mileage, while teams will compete on points. (Maybe that's already what we do?)

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