When EPS growth is entirely due to profits from retained earnings, the increased EPS percentage measures the impact of ROE on those retained earnings.
For instance,
Half of profit is retained: If ROE is 20 percent, half the profit is retained and ROE in the following year remains steady at 20 percent, EPS will increase by 10 percent.
All profit is retained: If all profit is retained and reinvested at 20 percent, EPS will increase by 20 per cent.
All profit is distributed: If all profit were distributed, irrespective of ROE, EPS growth would be zero.