more simplification

content/validator-trust-score.md

@@ -2,14 +2,66 @@
 
 The Nimiq's Validator Trust Score is a metric that helps users to evaluate the trustworthiness of a validator. It is a value between 0 and 1, where 0 means that the validator is not trustworthy at all and 1 means that the validator behaves well and is trustworthy.
 
-> The score is just a value used to help users evaluate the trustworthiness of a validator. It is not a guarantee that the validator is trustworthy and the value of the score can change over time. The value of the score won't affect the protocol in any way.
-
 The score is reactive and changes over time as the validator behaves well or poorly.
 
-This score is a combination of several factors that we believe are important for a validator to be trustworthy. These factors include liveness, uptime and age. In this document, we will explain how the score is calculated and what each factor means.
+The factors are, respectively: reliability, liveness and size. All of the factors are in the range $$[0; 1]$$, so the trust score naturally is also in the range (that then we can transform into whichever range we want of course).
 
-Feel free to share your feedback and suggestions on how to improve the trust score calculation.
+$$
+T = R \times L \times S
+$$
+
+## Reliability
 
 ## Liveness
 
-This factor measures how often the validator is online and producing blocks. A validator that is offline for a long time is not trustworthy. The liveness factor is calculated as follows:
+The Reliability factor penalizes validators that inconsistently produce blocks when expected, assessing their active contribution to the network.
+
+```text
+For a single batch, take the number of slots that the validator owns and received a reward for and divide it by the number of slots that the validator owns.
+```
+
+We calculate each observation (data point) of the reliability like this:
+
+To calculate the factor we do a weighted moving average over the past $n$ batches:
+
+$$
+\bar{R} = \frac{\sum_{i=0}^{n-1} \left( 1-a\frac{i}{n-1} \right) x_i}{\sum_{i=0}^{n-1} \left( 1-a\frac{i}{n-1} \right)}
+$$
+
+Where $x_i$ is the observation at batch number $i$ with $i=0$ representing the most recent batch. And $a$ is a parameter determining how much the observation of the oldest batch is worth relative to the observation of the newest batch.
+
+We decided the parameters to be:
+
+$$
+a=0.5
+batches\_in\_a\_day = 60 * 60 * 24;
+d = 9 * 30; \text{ 9 months in days}
+$$
+
+$$
+
+n = batches_in_a_day \* d
+
+$$
+
+### **Adjusting for High-Reliability Expectations**
+
+The previous formula provides a weighted moving average score for server reliability in block production, where a score of $0.9$ indicates a significant downtime of 10%, highlighting recent performance and the need for improved consistency. (This is not entirely true, but it is a good approximation)
+
+As one block is missing, this is a significant shortfall. To better reflect the high standards required, we will plot the value on a circle, having $c$ as the parameter defining the slope of the arc.
+
+$$
+
+R=-c+1-\sqrt{-\bar{R}^{2}+2c\bar{R}+\left(c-1\right)^{2}}
+\\~\\
+\text{Center of circle at (c,-c+1), where }
+c=-0.16
+
+$$
+
+<iframe src="https://www.desmos.com/calculator/zqemsh7yay" width="100%" height="500px"></iframe>
+
+Feel free to share your feedback and suggestions on how to improve the trust score calculation.
+
+$$
+$$

nuxt.config.ts

@@ -104,5 +104,12 @@ export default defineNuxtConfig({
         type: true,
       },
     ]
+  },
+
+  content: {
+    markdown: {
+      remarkPlugins: ['remark-math'],
+      rehypePlugins: ['rehype-mathjax'],
+    }
   }
 })

package.json

@@ -44,6 +44,8 @@
     "eslint": "^9.2.0",
     "eslint-plugin-format": "^0.1.1",
     "nimiq-css": "^0.0.96",
+    "rehype-mathjax": "^6.0.0",
+    "remark-math": "^6.0.0",
     "vite-plugin-top-level-await": "^1.4.1",
     "vite-plugin-wasm": "^3.3.0",
     "wrangler": "^3.56.0"