Hit interestingness scores (phase 2)

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savesigita
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Re: Hit interestingness scores (phase 1)

Postby savesigita » Sat Mar 16, 2013 2:09 pm

avij wrote:This is exactly what I've been trying to avoid. We'd end up again in a situation where the upgrades/downgrades would be arbitrary.


Which will be a good thing if it won't involve the sacrifice of very interesting hit and subsequently the lack of interest and the trust of the users in the website...

avij wrote:There may also be other reasons for increasing or decreasing the score slightly based on the user's own knowledge of the hit.
I think this covers the information that is recorded in the comments. One of the components for the score calculation can be user's own rating of the hit (either positive or negative). It will be just one metric among the many others, with an appropriately assigned weight (to be determined at the later stages). We'll also need to limit the usage of this capability, ie. it shouldn't be possible for a user to declare that ALL his/her hits should deserve the interestingness boost. The details of this can be discussed in the later stages.


but, of course, with a user's own rating hit, the problem can be solved, and of course there should be a limit: the casualities i mentioned about can't happen very often in daily life but, still, when they happen, they need to be underlined! and since there is a limit they can have a good proper weight!
it is the way to keep EBT "human" and creative, avoiding that it becomes only an amount of cold numbers of days and distances.

there is also a solution like each user can make his own ranking for his/her own hit http://ebt.uservoice.com/forums/127893-general/suggestions/3593826-my-best-hits but this second solution is not strictly connected to the topic so i won't go further.

dserrano5 wrote: Don't forget that comments are already being ignored now and we've been EBTing for 10 years without that causing problems.


10 years... we are making changes, aren't we?!

dserrano5 wrote:If users are given the chance of asking their hits to be given more score, then they will overwhelm the support team with pointless requests. IMO users should only have an option to downgrade the score.


sad that you have a very low consideration of EBT users, a group of pointless request-makers! I think, instead, that with the parameter of "user's own rating hit", limited, people will rate only the few very interesting hits!

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Re: Hit interestingness scores (phase 1)

Postby avij » Sat Mar 16, 2013 2:39 pm

A kind reminder that we're still in phase 1, where we're supposed to list all the factors that make hits interesting or not. The scoring and weights come at a later stage.

I guess we're pretty much finished with this phase. I'll try to write a summary of this phase and some guidelines for the next phase shortly.
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Re: Hit interestingness scores (phase 1)

Postby klapotec » Sat Mar 16, 2013 2:48 pm

savesigita wrote:sad that you have a very low consideration of EBT users, a group of pointless request-makers! I think, instead, that with the parameter of "user's own rating hit", limited, people will rate only the few very interesting hits!

hmm I have a very high opinion of EBT users (but then I know quite a few personally), but for this Murphy's law comes into play: any system that can be abused will be abused; the more ways a system can be abused, the more abuse there will be :?

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Hit interestingness scores (phase 2)

Postby avij » Sat Mar 16, 2013 5:39 pm

OK, I see some of you are impatient to move forward. So, let's move forward to the next phase.

I have now written a summary of the findings of the first phase. It incorporates most of the ideas that have been presented in this topic so far (related to the 1st phase). You may want to have a brief look at that list now. There is a chance that we may drop some of those metrics later on, if those are deemed impractical or ineffective for some reason, but until then, let's keep them on our list.

The next step is to figure out how to convert those listed metrics into numbers.

Some hints and guidelines for this phase:
  • Please note that we're still discussing individual metrics at this stage -- the formula for combining all of them is scheduled for the next phase
  • For simplicity's sake, we should use the same scale for all the individual metrics. I propose a scale of 0-100.
  • You don't need to consider how important this particular metric is. We'll assign the weight (=importance) later on.
  • If the hit fulfills the best criteria for some particular metric, it should be assigned a score of 100 for that particular metric
  • Please try to use the full scale from 0 to 100 (or 1 to 100 if it's easier for you that way)
  • Negative metrics ("this is a meeting hit") can also be scaled from 0 (or 1) to 100 (we'll take care of the sign in the next phase)
  • "Simple mathematics" is preferred, but if you can justify using "higher mathematics", feel free. Some metrics can be scored linearly, but for some metrics it might be useful to use logarithmic scale, for example.
  • Methods that rely only on the information of that single hit are preferred. Yes, we can do full statistical analysis of how frequent such hits are, but if we can come up with a close enough approximation through other means, it'd be a bit easier to implement.
  • The brainstorming topic has lots of material related to this phase, feel free to use the ideas presented there
  • When thinking about the scores, please also pay attention to how the proposal would work with triples and up. Generally, we can assign scores for each leg of the hit separately and combine them in the next phase.
  • If you can improve someone else's proposal, go ahead and provide your counterproposal. There are probably quite a few methods for calculating the numbers. Only saying that "this is bad" is not productive, try to come up with your own proposal instead.
  • For the hit frequencies, I'd suggest that we use the hit grouping method. I think it solves more problems than it creates. The capping methods described in the brainstorming topic would also work, but the grouping would also solve a few somewhat unrelated user interface issues. In summary this'll mean that if someone finds a bundle of notes from some other user, that counts as a "single occurrence" for the frequency calculations. The individual notes will still be hits with all the same score.
  • Relatedly, I'd also like to put more weight on the long-term hit frequencies than short-term frequencies. If a tracker moves to some other tracker's territory, there's a chance that they'll initially get some higher rated hits. The hit grouping makes this less of a concern for anyone. However, if the users continue having daily hits, the interestingness of those next hits will slowly decrease.
Here's an example (this can be improved if you can come up with something better):

Hit with an unusual denomination
Scoring: 0 for the most common hit denomination (fivers), 100 for the least common hit denomination (200e), others linearly between those two.

Here's a summary of all hits and their denominations on EBT, including moderated hits:

Code: Select all

mysql> select denomination, count(distinct serial) from hits group by 1;
+--------------+------------------------+
| denomination | count(distinct serial) |
+--------------+------------------------+
| 5            |                 559156 |
| 10           |                 159650 |
| 20           |                 141445 |
| 50           |                  38525 |
| 100          |                   4219 |
| 200          |                    846 |
| 500          |                   1040 |
+--------------+------------------------+
(total: 904881)


Applying some basic linear scoring, we'd end up with these scores:

Code: Select all

mysql> select denomination, count(distinct serial), 100-(( count(distinct serial) - 846) / (559156-846))*100 from hits group by 1;
+--------------+------------------------+----------------------------------------------------------+
| denomination | count(distinct serial) | 100-(( count(distinct serial) - 846) / (559156-846))*100 |
+--------------+------------------------+----------------------------------------------------------+
| 5            |                 559156 |                                                   0.0000 |
| 10           |                 159650 |                                                  71.5563 |
| 20           |                 141445 |                                                  74.8170 |
| 50           |                  38525 |                                                  93.2512 |
| 100          |                   4219 |                                                  99.3959 |
| 200          |                    846 |                                                 100.0000 |
| 500          |                   1040 |                                                  99.9653 |
+--------------+------------------------+----------------------------------------------------------+

An alternative would be to use the logarithmic scale:

Code: Select all

mysql> select denomination, count(distinct serial), 100-( log(count(distinct serial) - 846) / log(559156-846))*100 from hits where denomination not in ('5','200') group by 1;
+--------------+------------------------+----------------------------------------------------------------+
| denomination | count(distinct serial) | 100-( log(count(distinct serial) - 846) / log(559156-846))*100 |
+--------------+------------------------+----------------------------------------------------------------+
| 10           |                 159650 |                                              9.501058064713135 |
| 20           |                 141445 |                                             10.421196432291310 |
| 50           |                  38525 |                                             20.372392921419873 |
| 100          |                   4219 |                                             38.609834187384350 |
| 500          |                   1040 |                                             60.190511050902900 |
+--------------+------------------------+----------------------------------------------------------------+

In this scenario 5e notes would (also) get zero and 200e notes 100 points.

We'd also need to consider how common the denominations are in each country. For example, the least common denomination for hits in Austria is 500e instead of 200e, and the hit ratio of other denominations could be different as well.

If you can come up with better proposals, go ahead. We'd need to come up with similar methods for all the metrics and I could use your math skills for that. I can provide extra statistical information as needed. The field is yours. Discuss :)

As usual, if you have something that you'd like to say that isn't related to this current phase of assigning scores for individual metrics, please use the brainstorming topic. Thanks.

(note: I'll likely be a bit absent for the next few days due to other commitments, don't expect immediate and/or long replies for your proposals from me in the next few days)
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Re: Hit interestingness scores (phase 2)

Postby avij » Sat Mar 16, 2013 6:45 pm

Extra increase to score based on user's own judgment
(the "decreasing of the score" case will probably need to be handled separately)

Scoring: x/y*100 or x, whichever is smaller, where
x = the extra importance points (on a range from 0 to 100) given to this hit by the user
y = all the importance points that the user has assigned to his/her hits

In practical terms this would mean the user has a number of "importance points" that he/she can divide freely between all his/her hits. Assigning all of them to one hit is okay, and assigning them evenly across 100 hits would also be okay. The choice would be up to the user. The scores of all such hits will need to be recalculated whenever the user changes the point assignments.
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Re: Hit interestingness scores (phase 2)

Postby lmviterbo » Sun Mar 17, 2013 3:25 am

avij wrote:Applying some basic linear scoring, we'd end up with these scores:

Code: Select all

mysql> select denomination, count(distinct serial), 100-(( count(distinct serial) - 846) / (559156-846))*100 from hits group by 1;
+--------------+------------------------+----------------------------------------------------------+
| denomination | count(distinct serial) | 100-(( count(distinct serial) - 846) / (559156-846))*100 |
+--------------+------------------------+----------------------------------------------------------+
| 5            |                 559156 |                                                   0.0000 |
| 10           |                 159650 |                                                  71.5563 |
| 20           |                 141445 |                                                  74.8170 |
| 50           |                  38525 |                                                  93.2512 |
| 100          |                   4219 |                                                  99.3959 |
| 200          |                    846 |                                                 100.0000 |
| 500          |                   1040 |                                                  99.9653 |
+--------------+------------------------+----------------------------------------------------------+

An alternative would be to use the logarithmic scale:

Code: Select all

mysql> select denomination, count(distinct serial), 100-( log(count(distinct serial) - 846) / log(559156-846))*100 from hits where denomination not in ('5','200') group by 1;
+--------------+------------------------+----------------------------------------------------------------+
| denomination | count(distinct serial) | 100-( log(count(distinct serial) - 846) / log(559156-846))*100 |
+--------------+------------------------+----------------------------------------------------------------+
| 10           |                 159650 |                                              9.501058064713135 |
| 20           |                 141445 |                                             10.421196432291310 |
| 50           |                  38525 |                                             20.372392921419873 |
| 100          |                   4219 |                                             38.609834187384350 |
| 500          |                   1040 |                                             60.190511050902900 |
+--------------+------------------------+----------------------------------------------------------------+

In this scenario 5e notes would (also) get zero and 200e notes 100 points.

I don't like the zeroes here, for two reasons:
  • it's easy for me to think of this as the value of a hit and zero would mean they are of zero value, when in fact they are better than not having a hit (zero value)
  • for multiplication purposes, zeros aren't good; for division purposes (I can't think of any use for this but anyway) they're terrible
On the log scale, although better than the first one, I also don't like the big difference between :note-500: and :note-200: nor the big difference between :note-5: and :note-10: or :note-20: .


I tried to derive values related to the real rarity (inverse of usualness = frequency). For each denomination, this would be the inverse of [ (hits for that denomination) divided by (total hits) ]. Here's my first attempt:

Code: Select all

=SUM(B$2:B$8)/B2
+--------------+------------------------+-------------------------------------------------+
| denomination | count(distinct serial) | 1 / ( ( count(distinct serial) / (sum(hits) ) ) |
+--------------+------------------------+-------------------------------------------------+
|   5          |                 559156 |                                   1.61829793474 |
|  10          |                 159650 |                                   5.66790479173 |
|  20          |                 141445 |                                   6.39740535190 |
|  50          |                  38525 |                                  23.48815055159 |
| 100          |                   4219 |                                 214.47760132733 |
| 200          |                    846 |                                1069.59929078014 |
| 500          |                   1040 |                                 870.07788461539 |
+--------------+------------------------+-------------------------------------------------+

Now, I don't like the huge number, although I prefer this proportion: 1069.599… is around 660 times more than 1.618…, just as it is 660 times less likely to have a hit with a :note-200: then with a :note-5:

So, my next attempt was to reduce this scale to a maximum of 100:

Code: Select all

 =100*C2/MAX(C$2:C$8)
+--------------+------------------------+-------------------------------------------------+
| denomination | count(distinct serial) | 100 * (previous result) / max(previous results) |
+--------------+------------------------+-------------------------------------------------+
|   5          |                 559156 |                                  0.151299458470 |
|  10          |                 159650 |                                  0.529909176323 |
|  20          |                 141445 |                                  0.598112340486 |
|  50          |                  38525 |                                  2.195976638546 |
| 100          |                   4219 |                                 20.052145058071 |
| 200          |                    846 |                                100.000000000000 |
| 500          |                   1040 |                                 81.346153846154 |
+--------------+------------------------+-------------------------------------------------+

Now I'm not sure if I like the smallest numbers: being below 1, when used on some multiplication, might reduce the interestingness instead of adding. Which might not be bad per se but I'm not sure about it.

So, my next attempt was to raise the minimum to 1 and keep the maximum at 100. This will reduce the variation (maximum will be now 100/1 = 100) but will keep the values on a fair scale. Here are the results of compressing the scale from [1.618… to 1069.599…] to [1 to 100]:

Code: Select all

 (I messed up with this formula but I know the results are correct :)
+--------------+------------------------+------------------------------------------------+
| denomination | count(distinct serial) |  math guys, please derive this formula, sorry  |
+--------------+------------------------+------------------------------------------------+
|   5          |                 559156 |                                1.0000000000000 |
|  10          |                 159650 |                                1.3753915861121 |
|  20          |                 141445 |                                1.4430150325412 |
|  50          |                  38525 |                                3.0272976987158 |
| 100          |                   4219 |                               20.7316910853641 |
| 200          |                    846 |                              100.0000000000000 |
| 500          |                   1040 |                               81.5047090326163 |
+--------------+------------------------+------------------------------------------------+

To me, these last figures feel much closer to how much I instinctively think each denomination should have: about the same for fivers to 20-euro notes, a little more for :note-50: , much more for :note-100: , very much more for both :note-200: and :note-500: , which shouldn't be that apart from each other, the same way as their rarity is not very different. Anyway, I'm fine if anyone says that my feelings are completely wrong and even that not a single thing of what I wrote makes any mathematical sense. :)

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Re: Hit interestingness scores (phase 2)

Postby avij » Sun Mar 17, 2013 9:44 am

Yes, your final results look fine (but we'd need the formula). For this case using 1 as the lowest value may indeed make sense, because that allows us to say things like "hits with 100e notes are 20.73169.. more interesting than hits with fivers".

Generally speaking, people shouldn't be afraid of the zero. If the hit has travelled zero kilometres, it's fair and logical to give it zero points for the distance metric, for example. It's very likely that the hit would get non-zero points from other metrics. On the other hand, if the method for calculating a score for an individual metric "works better" with a range of 1-100, using a scale of 1-100 is alright. Whether the lowest value is 0 or 1 is not significant.

I've been thinking of using a weighted average for combining these individual metrics into one number, with some grouping depending on if the metric is related to the entire hit, one leg of the hit's path or one single point along the path. The zeroes wouldn't be harmful in that kind of a setup. If it turns out that we need to get rid of zeroes after all, it's just a matter of x=x*99/100+1 to convert from the 0-100 scale to the 1-100 scale. It's unnecessary to award "pity points" in any of these individual metrics, it will only cause unnecessary score inflation which will need to be taken into account when we have the final score for the hit.
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Re: Hit interestingness scores (phase 2)

Postby an-148 » Sun Mar 17, 2013 10:18 am

the frequency of a hit with a specific denomination should not be seen as a percentage of the total amount of hits: therefore you arrive to disproportionnal numbers: it should be calculated with regards on the amoount of bills of that denomination really entered :wink:

the place in the scale should reflect the difficulty to have a hit with a :note-5: :note-10: :note-20: :note-50: :note-100: :note-200: :note-500: in regard of the number of :note-5: :note-10: :note-20: :note-50: :note-100: :note-200: :note-500: entered and not as a percentage of all hits : you would have no "zero" and a better scale of importance

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Re: Hit interestingness scores (phase 2)

Postby avij » Sun Mar 17, 2013 10:35 am

So what would be the formula you'd use? You can see the current amount of notes by denomination here.

Granted, using the "entered notes" as the comparison value would also allow us to take into account how many notes of each denomination each user has entered.
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Re: Hit interestingness scores (phase 2)

Postby an-148 » Sun Mar 17, 2013 11:57 am

The software allows to show the number of bills/value as soon as one new bill is entered; it also shows the number of hits/value as soon as one hit occurs. (you would be surprised that the bills of :note-200: have a better hit-ratio than the bills of :note-500: :idea: and don't deserve the factor 100 !)
I guess it is possible to have a hit ratio/value continuously updated: if yes, there is a possibility to decide about an interrestingness factor of the hits by value that corresponds better to the real frequency.
The ranking of the hits (regarding value) would depend of the hit-ratio of this specific value and not of the overall amount of hits (which is distorded by the fact that power users register more :note-5: or :note-10: than normally used in daily life).

Discussion about a formula to take this fact in account is open and still to be decided (but in this specific case, I would avoid the complete range from 0 (or 1) to 100 : it doesn't reflect enough the difficulty to have a hit anyway!).

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Re: Hit interestingness scores (phase 2)

Postby lmviterbo » Sun Mar 17, 2013 12:25 pm

The remark made by an-148 might make sense in fact. Here's a new experiment:

Code: Select all

 taking into account rarity of hits per denomination, as suggested by an-148
+--------------+-----------|--------+------------------|----------------------+
| denomination |   notes   |  hits  |   notes / hits   | =100*D2/MAX(D$2:D$8) |
+--------------+-----------|--------+------------------|----------------------+
|            5 |  46025746 | 559156 |  82.312889426207 |     16.7415696556489 |
|           10 |  27569367 | 159650 | 172.686295020357 |     35.1225629037242 |
|           20 |  24223518 | 141445 | 171.257506451271 |     34.8319624458943 |
|           50 |  14774917 |  38525 | 383.515042180402 |     78.0028964772086 |
|          100 |   2074346 |   4219 | 491.667693766295 |    100.0000000000000 |
|          200 |    275461 |    846 | 325.604018912530 |     66.2244078756371 |
|          500 |    430090 |   1040 | 413.548076923077 |     84.1112975626275 |
+--------------+-----------|--------+------------------|----------------------+

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an-148
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Re: Hit interestingness scores (phase 2)

Postby an-148 » Sun Mar 17, 2013 12:34 pm

this looks effectively much better :wink: :wink:

(suprise, surprise : :note-100: have the biggest difficulty to make a hit!!!)

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Re: Hit interestingness scores (phase 2)

Postby avij » Sun Mar 17, 2013 1:38 pm

Cool. I'd be happy using those figures for our calculations. We'd still probably need to calculate those numbers on a per-country basis, because different countries can have a somewhat different denomination distribution due to various factors. I can take care of that, there's no need to calculate those numbers for the various countries right now.
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Re: Hit interestingness scores (phase 2)

Postby an-148 » Sun Mar 17, 2013 2:11 pm

avij wrote:Cool. I'd be happy using those figures for our calculations. We'd still probably need to calculate those numbers on a per-country basis, because different countries can have a somewhat different denomination distribution due to various factors. I can take care of that, there's no need to calculate those numbers for the various countries right now.


right !! in Portugal, for example, the "axial" bill is the :note-20: (even oversea: I saw it in the Açores last January: :note-20: everywhere: in atm's, in shops, etc : when you pay 15€ with a :note-100: instead of receiving :note-5: :note-10: :note-20: :note-50: as exange, you receive :note-5: :note-20: :note-20: :note-20: :note-20: )

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Re: Hit interestingness scores (phase 2)

Postby lmviterbo » Sun Mar 17, 2013 3:39 pm

avij wrote:We'd still probably need to calculate those numbers on a per-country basis, because different countries can have a somewhat different denomination distribution due to various factors.
I would bet it's true that there are national variations over the denomination distribution. As an-148 noted, in Portugal the 20-euro note is pervasive.

I have computed the hits per denomination of Portugal's top ebter, Leofer40, totaling 1518, which happens to be very close to 1/600 of all EBT hits:

Code: Select all

+--------------+------------+-----------------+------------------+
| denomination | total hits | Leofer40’s hits | total / Leofer40 |
+--------------+------------+-----------------+------------------+
|            5 |     559156 |             447 | 1250.90827740492 |
|           10 |     159650 |             467 |  341.86295503212 |
|           20 |     141445 |             531 |  266.37476459510 |
|           50 |      38525 |              53 |  726.88679245283 |
|          100 |       4219 |              10 | *421,90000000000 |
|          200 |        846 |               6 | *141.00000000000 |
|          500 |       1040 |               4 | *260.00000000000 |
+--------------+------------+-----------------+------------------+
|      totals: |     904881 |            1518 |  596.10079051383 |
+--------------+------------+-----------------+------------------+

Hits with :note-100: , :note-200: and :note-500: are too few to be statistically relevant but you can clearly see that :note-50: is around average, while hits with :note-5: are twice as rare for Leofer40 (and in Portugal, in general?), and hits with both :note-10: and :note-20: are twice as common.

Now let's do the same for the second Portuguese hitman :roll:

Code: Select all

+--------------+------------+------------------+---------------------+
| denomination | total hits | Eureka.72’s hits |  total / Eureka.72  |
+--------------+------------+------------------+---------------------+
|            5 |     559156 |              195 |    2867.46666666667 |
|           10 |     159650 |               71 |    2248.59154929577 |
|           20 |     141445 |               50 |    2828.90000000000 |
|           50 |      38525 |                9 |   *4280.55555555556 |
|          100 |       4219 |                4 |   *1054.75000000000 |
|          200 |        846 |                1 |    *846.00000000000 |
|          500 |       1040 |                2 |    *520.00000000000 |
+--------------+------------+------------------+---------------------+
|      totals: |     904881 |              332 |    2725.54518072289 |
+--------------+------------+------------------+---------------------+

Now we can't compare denominations equal or greater than :note-50: . As for the rest, :note-5: and :note-20: are around average now, and hits with :note-10: are just a little below average.


In face of this, I wonder if there are also relevant regional variations. I believe that can be checked with relative ease.

However, this might also be showing a need for another metric: rarity per denomination per user. This will only be of some value for heavy users but let's say we arrive to the conclusion that Portugal's hit per denomination averages are close to total EBT averages. Then Leofer40 is unlucky with fivers, so that denomination should be more valued for his hits.

Or… maybe he just doesn't enter many :note-5: notes. In that case, the personal metric has to be different, reflecting personal denomination entering weights.


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