Predicting Growth in L2 Chains

class: center, middle, inverse, title-slide

.title[
# Predicting Growth in L2 Chains <br> <br> <br> <br> <br>
]
.author[
### Omni Analytics Group
]

---

## Introduction

A Layer 2 chain, or L2 chain, helps to keep in check the growth of L1 chains such as Ethereum.

![](l2.png)

---

## Goals

As L2 chains continue to grow, it is worth devoting some statistical expertise to attempting to forecast their growth.

In this case study, we will focus on two: `Polygon` and `Optimism`, and use a Brownian Motion based forecasting technique in order to forecast the growth.

Let's get started!

---

## The Data

First, let's begin by loading in our two sources of data. We'll start with `Polygon`:

```r
pol <- read_csv("data/polygon.csv")

pol %>%
    head %>%
    kable
```

<table>
 <thead>
  <tr>
   <th style="text-align:left;"> Date(UTC) </th>
   <th style="text-align:right;"> UnixTimeStamp </th>
   <th style="text-align:right;"> No. of Verified Contracts </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> 2021-05-12 </td>
   <td style="text-align:right;"> 1620777600 </td>
   <td style="text-align:right;"> 2 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2021-05-17 </td>
   <td style="text-align:right;"> 1621209600 </td>
   <td style="text-align:right;"> 1 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2021-05-18 </td>
   <td style="text-align:right;"> 1621296000 </td>
   <td style="text-align:right;"> 6 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2021-05-28 </td>
   <td style="text-align:right;"> 1622160000 </td>
   <td style="text-align:right;"> 1 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2021-06-09 </td>
   <td style="text-align:right;"> 1623196800 </td>
   <td style="text-align:right;"> 468 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2021-06-10 </td>
   <td style="text-align:right;"> 1623283200 </td>
   <td style="text-align:right;"> 228 </td>
  </tr>
</tbody>
</table>

---

## Optimism Data

Next, the `Optimism` data:

```r
optim <- read_csv("data/optimistic.csv")

optim %>%
    head %>%
    kable
```

<table>
 <thead>
  <tr>
   <th style="text-align:left;"> Date(UTC) </th>
   <th style="text-align:right;"> UnixTimeStamp </th>
   <th style="text-align:right;"> No. of Verified Contracts </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> 2021-01-14 </td>
   <td style="text-align:right;"> 1610582400 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2021-01-15 </td>
   <td style="text-align:right;"> 1610668800 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2021-01-16 </td>
   <td style="text-align:right;"> 1610755200 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2021-01-17 </td>
   <td style="text-align:right;"> 1610841600 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2021-01-18 </td>
   <td style="text-align:right;"> 1610928000 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2021-01-19 </td>
   <td style="text-align:right;"> 1611014400 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
</tbody>
</table>

---

## A First Glance at the Polygon Data

We do some minor data cleaning below:

```r
## Day of week
pol$Day <- weekdays(pol$`Date(UTC)`)
pol$Day <- factor(pol$Day, levels=weekdays(pol$`Date(UTC)`[2]+0:6))
pol$Contracts <- pol$`No. of Verified Contracts`
optim$Day <- weekdays(optim$`Date(UTC)`)
optim$Day <- factor(optim$Day, levels=weekdays(pol$`Date(UTC)`[2]+0:6))
optim$Contracts <- optim$`No. of Verified Contracts`

## Weekday wise Contracts Deployed
pol_pld <- pol[pol$Contracts>0,]
pol_plot <- pol_pld %>%
			ggplot(aes(x=Day, y=Contracts, fill=Day)) +
			geom_boxplot() +
			scale_fill_viridis(discrete = TRUE, alpha=0.6) +
			geom_jitter(color="black", size=0.4, alpha=0.9) +
			theme(legend.position="none",plot.title = element_text(size=11)) +
			ggtitle("Contracts Verified Weekday Wise (Polygon Chain)") +
			xlab("Weekday")+
			scale_y_continuous(limits = quantile(pol_pld$Contracts, c(0.01, 0.99)))
```

---

We immediately see a strong weekend effect in the number of contracts verified for Polygon

---

## A First Glance at the Optimism Data

We perform a similar routine for the optimism data

```r
optim_pld <- optim[optim$Contracts>0,]
optim_plot <- optim_pld %>%
			ggplot(aes(x=Day, y=Contracts, fill=Day)) +
			geom_boxplot() +
			scale_fill_viridis(discrete = TRUE, alpha=0.6) +
			geom_jitter(color="black", size=0.4, alpha=0.9) +
			theme(legend.position="none",plot.title = element_text(size=11)) +
			ggtitle("Contracts Verified Weekday Wise (Optimistic Chain)") +
			xlab("Weekday")+
			scale_y_continuous(limits = quantile(optim_pld$Contracts, c(0.01, 0.99)))
```

---

The weekend effect is much less pronounced for the Optimism chain, though there still remains a noticeable dropoff in verified contracts on Sundays.

---

## Polygon Calendar (2022)

We can visualize a calendar of the 2022 Polygon data using the following code:

```r
pol22d <- data.frame(Date = seq(ymd('2022-01-01'),ymd('2022-12-31'), by = 'days'), Contracts = 0)
pol22d$Contracts <- pol$Contracts[match(pol22d$Date,pol$`Date(UTC)`)]
pol22d$ContractsCuts <- as.character(cut(pol22d$Contracts, c(0:6*100),right=FALSE))
pol22d$ContractsCuts <- fct_reorder(pol22d$ContractsCuts, pol22d$Contracts)
pol22 <- calendR(
					title = "Polygon 2022",title.size = 20,mbg.col = 2,weeknames = c("M","T","W","T","F","S","S"),subtitle = "Contracts Verified",subtitle.size = 10,months.col = "white",
					year = 2022,special.days = as.character(pol22d$ContractsCuts),special.col = brewer.pal(length(levels(pol22d$ContractsCuts)), "Oranges")[order(levels(pol22d$ContractsCuts))],legend.pos = "bottom"
				)
```

---

---

## Polygon Calendar (2021 + 2022)

And for 2021 + 2022 combined:

```r
pol21d <- data.frame(Date = seq(ymd('2021-01-01'),ymd('2021-12-31'), by = 'days'), Contracts = 0)
pol21d$Contracts <- pol$Contracts[match(pol21d$Date,pol$`Date(UTC)`)]
pol21d$ContractsCuts <- as.character(cut(pol21d$Contracts, c(0:5*100,3900,4000),right=FALSE,dig.lab=10))
pol21d$ContractsCuts <- fct_reorder(pol21d$ContractsCuts, pol21d$Contracts)
pol21 <- calendR(
					title = "Polygon 2021",,title.size = 20,mbg.col = 2,weeknames = c("M","T","W","T","F","S","S"),subtitle = "Contracts Verified",subtitle.size = 10,months.col = "white",
					year = 2021,special.days = as.character(pol21d$ContractsCuts),special.col = brewer.pal(length(levels(pol21d$ContractsCuts)), "Oranges")[order(levels(pol21d$ContractsCuts))],legend.pos = "bottom"
				)
pol_calplot <- pol21+pol22
```

---

---

## Optimism Calendar (2022)

A similar routine allows us to compute the calendar for Optimism:

```r
opt22d <- data.frame(Date = seq(ymd('2022-01-01'),ymd('2022-12-31'), by = 'days'), Contracts = 0)
opt22d$Contracts <- optim$Contracts[match(opt22d$Date,optim$`Date(UTC)`)]
opt22d$ContractsCuts <- as.character(cut(opt22d$Contracts, c(0,1,1:4*20),right=FALSE))
opt22d$ContractsCuts <- fct_reorder(opt22d$ContractsCuts, opt22d$Contracts)
opt22 <- calendR(
					title = "Optimistic 2022",,title.size = 20,mbg.col = 2,weeknames = c("M","T","W","T","F","S","S"),subtitle = "Contracts Verified",subtitle.size = 10,months.col = "white",
					year = 2022,special.days = as.character(opt22d$ContractsCuts),special.col = brewer.pal(length(levels(opt22d$ContractsCuts)), "Oranges")[order(levels(opt22d$ContractsCuts))],legend.pos = "bottom"
				)
```

---

---

## Optimism Calendar (2021 + 2022)

And for 2021 + 2022 combined:

```r
opt21d <- data.frame(Date = seq(ymd('2021-01-01'),ymd('2021-12-31'), by = 'days'), Contracts = 0)
opt21d$Contracts <- optim$Contracts[match(opt21d$Date,optim$`Date(UTC)`)]
opt21d$ContractsCuts <- as.character(cut(opt21d$Contracts, c(0,1,1:4*10),right=FALSE))
opt21d$ContractsCuts <- fct_reorder(opt21d$ContractsCuts, opt21d$Contracts)
opt21 <- calendR(	
					title = "Optimistic 2021",,title.size = 20,mbg.col = 2,weeknames = c("M","T","W","T","F","S","S"),subtitle = "Contracts Verified",subtitle.size = 10,months.col = "white",
					year = 2021,special.days = as.character(opt21d$ContractsCuts),special.col = brewer.pal(length(levels(opt21d$ContractsCuts)), "Oranges")[order(levels(opt21d$ContractsCuts))],legend.pos = "bottom"
				)
optim_calplot <- opt21+opt22
```

---

---

## Brownian Motion

Lastly, we use brownian motion in order to forecast each

```r
## Brownian Motion
polbd <- pol[5:nrow(pol),]
polbd$Date <- polbd$`Date(UTC)`
polbd <- polbd[,c("Date","Contracts")]
optimbd <- optim
optimbd$Date <- optimbd$`Date(UTC)`
optimbd <- optimbd[,c("Date","Contracts")]
polbd_n <- data.frame(Date = max(polbd$Date)+1:30)
pol_forecast <- brownian_forecast(polbd,polbd_n)
optimbd_n <- data.frame(Date = max(optimbd$Date)+1:30)
optim_forecast <- brownian_forecast(optimbd,optimbd_n)
```

---

## Polygon Forecast

```r
pol_forecast %>%
    head %>%
    kable
```

<table>
 <thead>
  <tr>
   <th style="text-align:left;"> Date </th>
   <th style="text-align:right;"> Prediction </th>
   <th style="text-align:right;"> Upper </th>
   <th style="text-align:right;"> Lower </th>
   <th style="text-align:left;"> Method </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> 2022-06-09 </td>
   <td style="text-align:right;"> 350.0542 </td>
   <td style="text-align:right;"> 722.9660 </td>
   <td style="text-align:right;"> 159.82879 </td>
   <td style="text-align:left;"> Brownian Motion </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2022-06-10 </td>
   <td style="text-align:right;"> 373.3307 </td>
   <td style="text-align:right;"> 935.5918 </td>
   <td style="text-align:right;"> 131.22131 </td>
   <td style="text-align:left;"> Brownian Motion </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2022-06-11 </td>
   <td style="text-align:right;"> 394.7485 </td>
   <td style="text-align:right;"> 1109.2994 </td>
   <td style="text-align:right;"> 112.10611 </td>
   <td style="text-align:left;"> Brownian Motion </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2022-06-12 </td>
   <td style="text-align:right;"> 422.6976 </td>
   <td style="text-align:right;"> 1444.3612 </td>
   <td style="text-align:right;"> 89.16038 </td>
   <td style="text-align:left;"> Brownian Motion </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2022-06-13 </td>
   <td style="text-align:right;"> 451.6471 </td>
   <td style="text-align:right;"> 1709.9363 </td>
   <td style="text-align:right;"> 71.10531 </td>
   <td style="text-align:left;"> Brownian Motion </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2022-06-14 </td>
   <td style="text-align:right;"> 485.0554 </td>
   <td style="text-align:right;"> 2157.0793 </td>
   <td style="text-align:right;"> 62.26108 </td>
   <td style="text-align:left;"> Brownian Motion </td>
  </tr>
</tbody>
</table>

---

## Optimism Forecast

```r
optim_forecast %>%
    head %>%
    kable
```

<table>
 <thead>
  <tr>
   <th style="text-align:left;"> Date </th>
   <th style="text-align:right;"> Prediction </th>
   <th style="text-align:right;"> Upper </th>
   <th style="text-align:right;"> Lower </th>
   <th style="text-align:left;"> Method </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> 2022-06-08 </td>
   <td style="text-align:right;"> 73.08083 </td>
   <td style="text-align:right;"> 300.000 </td>
   <td style="text-align:right;"> 3.0000000 </td>
   <td style="text-align:left;"> Brownian Motion </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2022-06-09 </td>
   <td style="text-align:right;"> 190.82595 </td>
   <td style="text-align:right;"> 1801.875 </td>
   <td style="text-align:right;"> 0.4272321 </td>
   <td style="text-align:left;"> Brownian Motion </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2022-06-10 </td>
   <td style="text-align:right;"> 503.55897 </td>
   <td style="text-align:right;"> 4259.135 </td>
   <td style="text-align:right;"> 0.1996875 </td>
   <td style="text-align:left;"> Brownian Motion </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2022-06-11 </td>
   <td style="text-align:right;"> 1301.39791 </td>
   <td style="text-align:right;"> 7035.469 </td>
   <td style="text-align:right;"> 0.1049063 </td>
   <td style="text-align:left;"> Brownian Motion </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2022-06-12 </td>
   <td style="text-align:right;"> 2740.34046 </td>
   <td style="text-align:right;"> 20576.374 </td>
   <td style="text-align:right;"> 0.0644000 </td>
   <td style="text-align:left;"> Brownian Motion </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2022-06-13 </td>
   <td style="text-align:right;"> 5409.50414 </td>
   <td style="text-align:right;"> 32827.902 </td>
   <td style="text-align:right;"> 0.0419925 </td>
   <td style="text-align:left;"> Brownian Motion </td>
  </tr>
</tbody>
</table>