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How Zeta's leaderboard and PnL calculations function

Zeta's global trading leaderboard shows the ranking of all traders based on their PnL (Profit and Loss) and ROI (Return on Investment a.k.a. PnL %). These rankings can be viewed currently over both a 24hr and 7d window.
Trade profitably to climb the leaderboard to cement yourself in the Zeta halls of fame! ## How we calculate rankings

It's recommended to read through as a primer in order to understand some of the terminology used in PnL calculations.

### PnL

PnL is calculated as the total account equity net of any deposits and withdrawals into the account. To calculate the change in PnL over say a 24hr period one would simply subtract the users current PnL from their PnL 24 hours ago.
$AE = AB + UPnL$
$PnL = AE - \sum_{t=t_0}^{T}{(D-W)}$
where:
• AE = Account Equity
• D = Deposits
• W = Withdrawals
• $t_0$
and T are start and end times of the PnL evaluation period, measured at 1hr intervals

### ROI

ROI is a more complex calculation based on the Modified Dietz Method for calculating investment returns in the presence of external cashflows. Intuitively, ROI is the change in PnL over a period of time divided by the estimated value of the account over the time period (taken to be the starting equity of the account adjusted by the time weighted cashflows into that account).
$ROI = \frac{PnL_T - PnL_{t_0}}{100 + AE_{t_0} + TWD}$
$TWD = \sum{(D_i * \frac{T-t_i}{T-t_0})}$
where:
• i = index of the individual deposit used to calculate the time-weighted deposits (TWD)