Measuring the Internal Resistance of Battery
Figure 1 shows a controlled current regulator attached to the battery through a switch. Standard capacity testing for NiMH used Ic = 30{A}. The clock starts when the switch closes, measures time in seconds, and it stops when measured battery terminal voltage Vt = Vc, the cutoff voltage. The standard cutoff Vc = 0.9 volts per cell in the series stack.
Notice source voltage Vs and source resistance Rs in the "lumped parameter" battery circuit model are variables. In the short run these values depend on the State of Charge / Depth of Discharge and battery temperature. In the long run there are also changes in the chemicals that impact State of Health.
Since both Vs and Rs can change independently during discharge inside the battery, and one only measures Vt and Ic, one cannot really measure source parameters during continous discharge, either on a test bench or out on the track.
To get a curve for Vs and Rs the technique is to chop the switch at specified time intervals, measure Vs at the terminals with zero current, then apply Ic again and measure voltage drop Vt. If you standardize this test and use good precision in the current regulator and voltmeter, you get a curve of Vs and Rs over the depth of discharge given the state of health of the unit under test (UUT - actual battery).
This link shows one effort to produce the Vs and Rs curves for older batteries:
http://www.slkelectronics.com/ecalc/gen4a.htm
John's curves of Voltage versus Amps compare Vt to Im during a Dyno run. The simplest equivalent circuit model appears in Figure 2.
Rm is the motor resistance, which primarily varies a function of temperature due to the resistivity of copper. Vbe is the reverse voltage which increases with motor shaft speed due to generator feedback in the coils. It also varies a bit due to changes in air gap temperature.
There are four variable circuit parameters which impact the measured Vt and Im, so it is very doubtful one is measuring Rs in any accurate way.
However, if the peak power on the flywheel is much greater with a battery swap, other factors kept equal, and both batteries have roughly the same initial open circuit voltage Vs, and the same motor/ESC/Dyno combination is used at roughly the same starting temperatures, then the gain in peak flywheel power is very likely due to a reduction in internal source resistance Rs for the battery that supplies more power to the flywheel.
This should show up as more raw electrical power output at the terminals, where John could multiply each line Pe = Vt*Im and get a battery power curve. The better battery would supply more electrical power at its terminals compared to the lesser battery as measured on the Dyno. This power crosses the air gap and produces a bit more peak mechanical power.