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Definitions relating to the Trending screen available via the Sidebar on the Rated Network Explorer.
The definitions in this page are separated by theme in the order that these appear on the explorer. All screens are modulated by the master "time window" toggle at the top right of the screen.
It is normal to see differences in the effectiveness ratings on the Landing Page and the Treding page. This is because the data in the former refreshes on an hourly basis while the latter refreshes on a daily basis.

By Effectiveness 🔖

A collection of trending operators and validator keys according to their respective effectiveness scores. Read more about the Effectiveness Rating in the Rated Effectiveness Rating section of the docs.
The trending view of the top-5 and bottom-5 identified operators on Ethereum.
For the All-time calculation in this section, we are only considering validators that have been active for more than 30 days so that we reduce noise. This is equally true for Trending validator indices, as well as for operator groupings (we exclude validators younger than the 30day window from the calculation).

By MEV facilitated 🔖

A collection of trending operators in terms of how much MEV they have facilitated. We are only considering operators that facilitated some MEV; that means we are excluding all validators that only produced locally built blocks and are not subscribed to any MEV Relays.
We have introduced a couple new toggles below the screens, namely Average and Total. These filter the rankings for operators that score at the very top or bottom of the distribution in terms of Total MEV (whole operation) or on a per validator basis (Average).
The "By MEV facilitate" view in Trending.
You can learn more about MEV Relays in the Relayer landscape section of the docs. For a deeper dive into how we go about calculating MEV facilitated, take a closer look at Baseline MEV computation.

By Slashing history 🔖

A collection of trending operators in terms of how many times they have been slashed or how many times they produced a block with a slashing proof included. The frame of view has been limited to 30d and All-time to make the analysis a little more comprehensive as slashings are not a frequent phenomenon on the Beacon Chain.
The "By Slashing history" view in Trending.

Median slash time

This is the subtitle to the slashing counter under "Top 5 entities by times slashed" and represents the median time at which an entity was slashed. The purpose of this is to show how recently or not recently the majority of those incidents took place which offers a proxy for how each operator has performed since.

Slasher pedigree

This is the subtitle to the slashing counter under "Top 5 entities by slashes collected" and is a direct reference to how @eth2REKT attributes titles to the top slashers by slashing proofs included.
Every time a validator slashes another, eth2REKT adds a +1 on the lifetime count of slashes executed to the entity associated with said validator. For more information on how Rated approaches building entities out of validator keys, please refer to Classes of aggregation.
The following naming conventions apply to the different classes of lifetime slashes executed:
Noob Saibot
Sub Zero
Prince Goro
Shang Tsung
Shao Khan