向贝叶斯排名系统添加额外因素（点击次数）
我经营一个面向业余音乐家的音乐网站，我们有一个基于 10 分的评分系统，然后将其计算为满分 100 分的总分。我们有一个针对用户的“可信度”评分系统，它直接影响平均分在评级方面，但下一步是实施一个有效使用这些数据的图表系统。
我将尝试准确解释这一切是如何工作的，以便您可以看到我可以使用哪些数据。
- 网站成员对曲目的评分介于 1 到 10 之间。
- 该网站成员有一个“可信度”分数，该分数只是网站周围各种活动所累积的分数总和。例如，用户通过给出评级获得 100 分，因此他们给出的评级越多，他们的“可信度”分数就越高。仅总可信度分数保存在数据库中，每次用户执行附有积分奖励的活动时更新。这些个人活动不会被存储。
- 根据该用户与对曲目进行评分的其他用户相比的可信度，计算该曲目的加权平均值，然后将其作为 1 到 100 之间的数字存储在曲目表中。
- 在曲目表中，还存储曲目被收听的次数（即播放次数）。
因此，我必须使用的数据是：
- 曲目的总体评分（1 到 100 之间的数字）
- 曲目的评分数 曲目
- 的播放次数
在图表系统中，我想创建一个使用上述 3 组的排名数据，以在质量（总体评分，根据评分数量标准化）和流行度（播放次数）之间建立公平的平衡。但是系统应该更重视质量而不是受欢迎程度，因此例如质量方面占标准化排名的 75%，受欢迎程度占 25%。
在此网站上搜索后，我发现 IMDB 贝叶斯风格系统 这对于确定质量方面很有帮助，但是我如何添加受欢迎程度（播放次数）并使其按照我想要的方式平衡？
如果有帮助的话，该网站是用 PHP 和 MySQL 编写的。
编辑：标题说“点击次数”，但这基本上与“播放次数”直接等效。
I run a music website for amateur musicians where we have a rating system based on a score out of 10, which is then calculated into an overall score out of 100. We have a "credibility" points system for users which directly influences the average score at the point of rating, but the next step is to implement a chart system which uses this data effectively.
I'll try and explain exactly how it all works so you can see which data I have at my disposal.
- A site member rates a track between 1 and 10.
- That site member has a "credibility" score, which is just a total of points accumulated for various activities around the site. A user gains, for example, 100 points for giving a rating so the more ratings they give, the higher their "credibility" score. Only the total credibility score is saved in the database, updated each time a user performs an activity with a points reward attached. These individual activities are not stored.
- Based on the credibility of this user compared to other users who have rated the track, a weighted average is calculated for the track, which is then stored as a number between 1 and 100 in the tracks table.
- In the tracks table, the number of times a track is listened to (i.e. number of plays) is also stored as a total.
So the data I have to work with is:
- Overall rating for the track (number between 1 and 100)
- Number of ratings for the track
- Number of plays for the track
In the chart system I want to create a ranking that uses the above 3 sets of data to create a fair balance between quality (overall rating, normalized with number of ratings) and popularity (number of plays). BUT the system should factor quality more heavily than popularity, so for example the quality aspect makes up 75% of the normalized ranking and popularity 25%.
After a search on this site I found the IMDB Bayesian-style system which is helpful for working out the quality aspect, but how do I add in the popularity (number of plays) and have it balanced in the way I want?
The site is written in PHP and MySQL if that helps.
EDIT: the title says "number of clicks" but this is basically the direct equivalent of "number of plays".
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您可能想尝试以下操作。您提到的 IMDB 方程使用权重来倾向于电影的平均评分或所有电影的平均评分：
所以
和
这通常应该是公平的。根据播放次数计算 0 到 100 之间的受欢迎度分数非常棘手，除非您真正了解自己的数据。第一次尝试计算平均播放次数 avg(p) 和方差 var(p)，然后您可以使用这些数据来使用称为白化的技术来缩放播放次数：
这将为您提供 -1 到 1 之间的分数假设您的数据看起来像钟形曲线。然后，您可以通过再次缩放将其缩放到 0 - 100 的范围内：
要根据某个权重因子 w（例如 0.75）合并分数，您只需执行以下操作：
玩这些并让我知道您的进展如何。
注意：这并没有考虑到用户可以多次“玩弄”一首曲目的流行度。您可以通过惩罚单首歌曲的多次播放来解决此问题：
deltaP = (1 - (Puser - 1)/TPuser)
其中：
因此，用户仅播放一首曲目的次数越多，该曲目的计数就越少该曲目的总播放次数。如果用户的收听习惯多种多样，那么 TPuser 就会很大，因此 deltaP 将趋于回到 1。这仍然可以进行游戏，但这是一个好的开始。
You may want to try the following. The IMDB equation you mentioned uses weighing to lean toward either the average rating of the movie or the average rating of all movies:
So
and
This should generally be fair. Calculating a popularity score between 0 and 100 based on the number of plays is pretty tricky unless you really know your data. As a first try calculate the average number of plays avg(p) and the variance var(p) you can then use these to scale the number of plays using a technique call whitening:
This will give you a score between -1 and 1 by assuming your data looks like a bell curve. You can then scale this to be in the range 0 - 100 by scaling again:
To combine the score based on some weighting factor w (e.g. 0.75) you'd simply do:
Play with these and let me know how you get on.
NOTE: this does not account for the fact that a use can "game" the popularity buy playing a track many times. You could get around this by penalising multiple plays of a single song:
deltaP = (1 - (Puser - 1)/TPuser)
Where:
So the more times a user plays just the one track the less it counts toward the total number of plays for that track. If the users listening habits are diverse then TPuser will be large and so deltaP will tend back to 1. This still can be gamed but is a good start.