This is rather complicated, but it gives a general and neat solution.
import numpy as np
value1 = 3
xvalues = [0, 1, 2, 3, 4]
line1 = [2.0, 3.0, 2.0, 5.0, 4.0]
stdev1 = [0.1, 0.2, 0.1, 0.4, 0.3]
line2 = [1.7, 3.1, 2.5, 4.8, 4.2]
stdev2 = [0.12, 0.18, 0.12, 0.3, 0.35]
max_times = [max(line1+stdev1),max(line2+stdev2)]
min_times = [min(line1+stdev1),min(line2+stdev2)]
font_size = 25
max_total = max(max_times)
min_total = min(min_times)
max_minus_min = max_total - min_total
step_size = max_minus_min/10
head_space = (step_size*3)
plt.figure(figsize=(15, 15))
plt.errorbar(xvalues, line1, yerr=stdev1, fmt='', color='b')
plt.errorbar(xvalues, line2, yerr=stdev2, fmt='', color='r')
plt.xlabel("xvalues", fontsize=font_size)
plt.ylabel("lines 1 and 2 Test "+str(value1), fontsize=font_size)
plt.title("Let's leave space for the legend Experiment"+ str(value1), fontsize=font_size)
plt.legend(("Line1", "Line2"), loc="upper left", fontsize=font_size)
plt.tick_params(labelsize=font_size)
plt.yticks(np.arange(min_total, max_total+head_space, step=step_size) )
plt.grid()
plt.tight_layout()
Result:
