**Intro**

While a pool is small it’s hard to understand how many blocks are typically lost to height battles (ghosted) and slot battles. Being Part of the xSPO Alliance (Link: https://www.xspo-alliance.org/) I want to share my idea of this in the hope new pool operators can get a better understanding of how Cardano works.

**Disclaimer:**

The included calculations are assumption-based. I do not have mathematical proof or 100% evidence that my calculations are correct. If you see any mistakes in the calculation or the idea behind it please let me know!

**Pre-Knowledge**

If you want to know what a ghosted block is, please take a look here: Ghosted Blocks - How to optimize Propagation Times - Action Required

Slot battles mean in simple words that multiple pools have the same slot assigned and only one can be kept, the other is lost.

Both scenarios are as per design and nothing to be afraid of. It’s just good to know how often this typically occurs.

Lost blocks influence the Network Density. Theoretically, it is 5% as on average every 20s a block is produced. Based on the lost blocks this theoretical average is not reached.

**Numbers**

Let’s get straight away to the numbers:

**Details and explanations**

- The 5% Slot battle is not 100% mathematically correct. The underlying logic is that the chance that any pool got a slot assigned is 5%. Now, this is not exact because it ignores the fact that your own pools slots cannot be overlap and slightly reduce that risk.
- It’s assumed that 50% of slot battles are won. In reality, this depends on the pool size. Lower Saturated pools tendentially win more battles.
- Ghosted slots depend on Propagation times which are varying between pools based on their setup and network latency towards connected peers. If you did not receive a previously generated block before minting your own block your block will be discarded.
- Also for ghosted the calculation is not 100% accurate as there are different factors influencing which block is in the end discarded. Anyways, the assumption is that every 1s Propagation Delay leads to a ~5% risk of one block being dropped. Increased propagation times heavily impact the risk of ghosted blocks. The given percentages for (% 1s, %2s, …) are based on typical stats which are reported by CNODE. It’s just an example
- There is a chance of slots and height battles occurring at the same time. This is not considered in the calculation.

**High-Level Validation**

To validate the results on a high level I took a look at the Network Density.

Based on the calculations it should be around 4.72% with the current Propagation Times.

**Details and explanations**

- The network Density is around the expected number of 4.72%
- In Epoch 313 there was a drop in network density.
- This drop is related to two reasons.
- Release of Node 1.33.0 → In this version the rewards calculation time period was extended. Before it was 1 day which led to 1 day of 1-3s propagation times, the rest <1s. Now a bigger portion of blocks exceeds the 1s border.
- Increased Network Usage: Based on e.g. SundaeSwap related Transactions. Bigger blocks means a longer time to Propagate.