For the alternative points format, the differences between Season 1 and the current Season, Season 12, is that their are no: Customer championships, Nelson Piquet Jr Trophy, nor Manufacturer championship as this season a spec powertrain is used by all competitors and this is the first season of the championship, so all competitors have 1 or less podium in the sport.
For current real life format, the differences between Season 1 and the current Season, Season 12, is that along with no Manufacturers' championship (due to the use of spec powertrains) the fastest lap is worth 2 points and is earned by the driver who sets the fastest lap regardless of their eventual finishing position. Also, dropped scores exist for drivers this season, meaning you drop your worst finish, excluding disqualifications.

For the Drivers' Championship the point of Mathematical ineligibility begins during the 2015 Berlin ePrix, the 8th race of the season, with it specifically beginning after qualifying. This is because the championship leader after round 7 in Monaco, Lucas di Grassi, has 92 points and that is exactly the same amount of points available but he only has 1 win so it possible to beat him after Monaco. Lucas, however, does not win the championship as his chances are immediately scuppered by his disqualification from the Berlin ePrix (a race he had won on the road) and ends up finishing 3rd in the standings. The eventual champion is Nelson Piquet Jr, who was 2nd in the standings at the point of mathematical ineligibility with 91 points, with his winning points total being 140.
For the Teams' Championship the point of mathematical ineligibility also begins during the 2015 Berlin ePrix, although it only begins after its conclusion due to the way points are scored in this championship compared to the Drivers'. The championship leader at this point is Team e.dams Renault who lead on 169 points and continue to lead until season's end where they win the Teams' championship with 230 points.

For the Drivers' Championship the point of mathematical ineligibility is the conclusion of 2015 Berlin ePrix and the championship leader at this point being Nelson Piquet Jr with 103 points, a position he inherits after Lucas di Grassi's disqualification. Nelson eventually wins the Drivers' championship by 1 point over Sebastien Buemi with a points total of 144.
For the Teams' Championship the point of mathematical ineligibility is also the conclusion of the 2015 Berlin ePrix and the championship leader for this championship at this point is Team e.dams Renault, who lead on 179 points. They continue to lead until the end of the season, even sealing the title with a race to spare, to win with 232 points.

With the opening of development on powertrains, a manufacturers' championship is available for both formats although it will be hypothetical for real life format as Formula E would not implement such championship until partway through season 10.
Specifically for the alternative format, as 3 teams do not build their powertrain and instead are supplied by a registered manufacturer (Dragon Racing) or are supplied by an unregistered manufacturer (Amlin Andretti Formula E Team and Team Aguri); we have Customer championships for those 3 teams and their drivers. Also we have Nelson Piquet Jr Trophy (NPJT), which has different eligibility rules compared to today (at the time of posting) as for this season in order to be eligible for the NPJT you must not have made a start in Formula E prior to this season. The championships are scored the same way as they are today.
For the real life format, the points system in place is the same as last season minus existence of dropped scores.

For the Overall Drivers' Championship, the point of Mathematical ineligibility is after the Paris ePrix, the 7th race of the season. The championship leader at this point with 103 points is Lucas di Grassi and unlike Season 1, he doesn't choke it away and he goes on to win the Drivers' Championship with 141 points.
For the Customer Trophy for Drivers Championship, the point of Mathematical ineligibility is after the Long Beach ePrix, the 6th race of the season. The leader at this point is Jerome d'Ambrosio, who leads with 103 points, before going on to win the Customer Trophy at season's end with 168 points.
For the Nelson Piquet Jr Trophy Championship, the point of Mathematical ineligibility is also after the Long Beach ePrix, with the leader being Robin Frijns, who leads on 114 points. Robin seals the title a round later and ends the season on 154 points.
For the Overall Teams' Championship, the point of Mathematical ineligibility is also after the Paris ePrix, with ABT Schaeffler Audi Sport leading the standings at this point with 164 points, however, they are not leading at season's end as the championship winning team is Renault e.Dams. Dams win the title with 238 points and were 2nd on 154 points at the point of Mathematical ineligibility, while ABT drop to 2nd. The deciding factor is that Nico Prost is better driver this season compared to Daniel Abt.
For the Customer Teams' Championship, the point of Mathematical ineligibility is also after the Long Beach ePrix, with Dragon Racing leading the standings on 113 points and win the championship with 178 points.
For the Manufacturers' Cup, the point of Mathematical ineligibility is also after the Long Beach ePrix, with ABT Schaeffler leading the Cup standings on 156 points, but they do not go on to win the theCup as instead it goes to Renault. Renault, who were 2nd at the point of Mathematical ineligibility with 147 points, win the Cup with 259 points for the same reason that Renault e.Dams won the Overall Teams' Championship - Nico Prost > Daniel Abt.

For the Drivers' Championship, the point of Mathematical ineligibility is after the Paris ePrix, the 7th race of the season. At this point the leader is Lucas di Grassi, who has 126 points, but he unfortunately does not win the title as he loses a fastest lap shoot-out with Sebastien Buemi during the final race. Sebastien wins with 155 points after being 2nd with 115 points at the point of Mathematical ineligibility.
For the Teams' Championship, the point of Mathematical ineligibility is also after the Paris ePrix, with the leading team being Renault e.Dams who have 165 points at this point. e.Dams go on to win the Teams' Championship with 270 points.
For the hypothetical Manufacturers' Cup, the point of Mathematical ineligibility would have also been after the Paris ePrix and the leader would have been ABT Schaeffler, with 173 points. They, however, would have not won the Manufacturers' Cup had it run this season, as instead it would go to Renault as they would win with 254 points despite being 3rd with 158 points at the point of Mathematical ineligibility.

Regarding the alternative format: as there is only 1 customer team, Techeetah, the customer championships will not run this season.
Regarding the format used in real life: the fastest lap is now worth 1 point instead of 2 like last season. This brings the maximum points available from a race down to 29.

For the Overall Drivers' Championship, the point of Mathematical ineligibility is after race 2 of Berlin ePrix, the 8th race of the season. The leader at this point is Sebastien Buemi, who leads with 131 points before he had to miss 2 races in New York due clashing commitments with Toyota in the World Endurance Championship. When he returns for the Montreal ePrix doubleheader, he no longer leads the standings and his disqualification in race 1 hands the title to Lucas di Grassi, who wins it with 172 points. Lucas was 2nd in the points at the point of Mathematical ineligibility.
For the Nelson Piquet Jr Trophy Championship, the point of Mathematical ineligibility is after race 1 of Berlin ePrix, the 7th race of the season. Felix Rosenqvist is leading at this point with 113 points and he goes on to win the the Trophy with a race to spare with 203 points.
For the Overall Teams' Championship, the point of Mathematical ineligibility is also after race 2 of Berlin ePrix, with Renault e.dams at the top of the standings with 210 points. e.dams defend this lead and win the Overall Teams' Championship with 264 points.
For the Manufacturers' Cup, the point of Mathematical ineligibility is also after race 1 of Berlin ePrix, which at this point sees Renault lead with 188 points. Renault go on to win the Manufacturer's Cup with 281 points.

For the Drivers' Championship, the point of Mathematical ineligibility is after race 2 of Berlin ePrix, the 8th race of the season. Sebastien Buemi leads at this point with 157 points, but does not go on to win the championship as instead the winner is Lucas di Grassi with 181 points.
For the Teams' Championship, the point of Mathematical ineligibility is also after race 2 of Berlin ePrix, with Renault e.dams leading the championship with 229 points This is a position they maintain for the rest of the season as they win the Teams' Championship with 268 points.
For the hypothetical Manufacturers' Cup, the point of Mathematical ineligibility is after race 1 of Berlin ePrix, the 7th race of the season. At this point, the leader would be Renault with 223 points and they would go on to win the hypothetical Manufacturers' Cup 2 races early with 367 points. Their advantage is so great because they are the only manufacturer this season to supply 2 teams - Renault e.dams and Techeetah.

For the alternative format, the eligibility rules for the Nelson Piquet Jr Trophy have changed to match the changes made to the eligibility rules for the Jack Sears Trophy in the BTCC for 2018. So rather than having never made a start in the series prior to the season like before, now you must have no podiums prior to the season start (although podiums achieved after post-race penalty for a fellow competitor do not count against your eligibility) or have never won the Trophy before.
For the format used in real life, the eligibility for the fastest lap have changed from the driver who sets the fastest race lap to the driver who sets the fastest lap amongst the top 10 finishers for a race.

For the Overall Drivers' Championship, the point of Mathematical ineligibility is after the Paris ePrix, the 8th race of the season. At this point, the leader is Jean-Eric Vergne with 131 points and the eventual winner is also Jean-Eric Vergne, who winning points total is 184.
For the Nelson Piquet Jr Trophy Championship, the point of Mathematical ineligibility is after the Rome ePrix, the 7th race of the season. Mitch Evans leads the class at this point with 114 points and continues to do so until the end, winning the Trophy with 178 points.
For the Overall Teams' Championship, the point of Mathematical ineligibility is also after the Paris ePrix, with Techeetah leading at this point with 167 points They would go on to win the Overall Teams' Championship with 263 points.
For the Manufacturers' Cup, the point of Mathematical ineligibility is also after the Paris ePrix and DS Automobiles (remember they are with Virgin Racing this season and not Techeetah) are at the top of the standings with 165 points, but are not there come season's end as Audi beat them to it to win with 275 points. The differing factor is probably line-up as Alex Lynn regresses quickly and hard in terms of results, while Daniel Abt has a career year and helps Audi recover from their poor start that saw them last in the standings after race 4 (Santiago ePrix).

For the Drivers' Championship, the point of Mathematical ineligibility is after the Paris ePrix, the 8th race of the season. Jean-Eric Vergne leads the standings at this point with 147 points and goes on to win the championship a race early, with his final points tally being 198.
For the Teams' Championship, the point of Mathematical ineligibility is after qualifying for the Berlin ePrix, the 9th race of the season. This is because upon the conclusion of the previous round, Techeetah, who lead the standings, have 188 points which the exact amount left available for teams to score and thus must wait until the points left shrinks down to 185 after qualifying for the race in Berlin. Techeetah, however, do not win the Teams' championship as instead Audi Sport ABT Schaeffler take the title in the final round with 264 points. The deciding factor? Daniel Abt is better than Andre Lotterer.
For the hypothetical Manufacturers' Cup, the point of Mathematical ineligibility would have been after the Berlin ePrix, the 9th race of the season. The leader at this point would have been Renault, who would lead with 242 points and they would have won the title a round early with 326 points.

For the alternative points format, this season sees the return of the Customer Trophy for Drivers and Customer Teams' Championship after a 2 season absence, otherwise the format used last season is still continued to be used.
For the format used in real life, the format is the same as was used last season.

For the Overall Drivers' Championship, the point of Mathematical ineligibility is at the end of the Monaco ePrix, the 9th round of the season. At this point the championship leader is Andre Lotterer, who leads with 98 points. However, he does not win the championship as he fails to finish 2 of the last 4 races and has best finish of 14th, so he falls to 9th in the standings (this is less choke and more straight-up lung collapse). His teammate, Jean-Eric Vergne, wins the championship with 139 points and was 2nd at the point of Mathematical ineligibility with 91 points.
For the Customer Trophy for Drivers Championship, the point of Mathematical ineligibility is at the end of the Rome ePrix, the 7th round of the season. The Championship leader at this point point is Robin Frijns who has 128 points and leads thanks to his teammate's DNF at the prior ePrix in Sanya. However, it is DNFs that cost Robin as back-to-back DNFs at the Swiss ePrix and race 1 of the New York ePrix, allow his teammate, Sam Bird, close in and overtake him for the championship. Sam Bird, who 2nd at the point of Mathematical ineligibility with 109 points, wins the championship with a points total of 213 points.
For the Nelson Piquet Jr Trophy Championship, the point of Mathematical ineligibility is also at the end of the Monaco ePrix and the leader for this championship at this point is Oliver Rowland with 111 points. Oliver does end up winning the Trophy in the end with 154 points, but ends up losing the lead to Felipe Massa with 2 rounds to go after retiring from the Swiss ePrix and only reclaims after the final round, after Felipe suffers his worst classified finish in the class.
For the Overall Teams' Championship, the point of Mathematical ineligibility is also at the end of the Monaco ePrix and the leader for this championship at that point is DS Techeetah who leads with 179 points. However, like their driver Andre Lotterer, they don't win the championship as they can only score 226 points and instead the winning team is Audi Sport ABT Schaeffler, who wins with 234 points despite having 155 points and in 2nd place at the point of Mathematical ineligibility. Of the remaining 4 races, Techeetah only outscore ABT in 1 of them, the Swiss ePrix, but is only 5 points while ABT outscore them by 37 in the other 3, thanks to a 2nd driver who actually finishes well (shout-out to Lucas di Grassi - Daniel Abt outscores him over the final 4 races).
For the Customer Teams' Championship, the point of Mathematical ineligibility is at the same point as the Customer Trophy for Drivers, end of the Rome ePrix, with the leader for this championship being Envision Virgin Racing, who lead with 137 points. Unlike all of other championships this season, the leader of the championship doesn't choke it away at any point(or in Oliver's case, nearly) and in fact Virgin seal the Customer Teams' title with 3 races to spare, such was their advantage over HWA Racelab.
For the Manufacturers' Cup, the point of Mathematical ineligibility is also at the end of the Monaco ePrix and it is being lead by DS Automobiles with 202 points. However, DS Automobiles cannot maintain this lead and lose it in the final race to Audi who win with a points total of 264, compared to DS Automobiles' total of 259. Audi, at the point of Mathematical ineligibility, were 2nd in the standings with 176 points. The deciding factor in this championship is the same as Overall Teams' Championship - better 2nd drivers and finishing records.

For the Drivers' Championship, the point of Mathematical ineligibility is at the end of the Berlin ePrix, the 10th round of the season. The championship leader at this point is Jean-Eric Vergne, with 102 points and goes on to win the championship with 136 points.
For the Teams' Championship, the point of Mathematical ineligibility is also at the end of the Berlin ePrix and the leader is DS Techeetah, who leads with 188 points. Techeetah go on to win the Teams' Championship with 222 points.
For the hypothetical Manufacturers' Championship, the point of Mathematical ineligibility is after the Monaco ePrix, the 9th round of the season. The leader at this point is Audi, who would lead with 207 point and would maintain that lead until the end as they seal the championship with 2 rounds to go and have winning points total of 315.

While the break in the calendar caused by the Covid-19 pandemic may make obvious start for a run to the title, one must also remember that we spend the majority of the season in Berlin so the title contenders aren't obvious going into those 6 races. For example, 2nd place under alternative format, Sebastien Buemi, was 10th in the standings going into the 6 Berlin races.
Under the alternative format, there is no change compared to last season and it will stay that way until season 11. In real life, a point is now awarded to the driver who sets the fastest time in the group stage of qualifying, bringing the maximum points available from a race up to 30.

For the Overall Drivers' Championship, the point of Mathematical ineligibility is after race 2 of the Berlin ePrix, the 7th race of the season. Antonio Felix da Costa leads the standings at this point with 111 points and continues to do so as he wins the championship 2 races early and has a winning points total of 149.
For the Customer Trophy for Drivers Championship, the point of Mathematical ineligibility is also after race 2 of the Berlin ePrix and the leader at this point is Edoardo Mortara, who leads with 107 points and he goes on to win the Customer Trophy with a race to spare.
For the Nelson Piquet Jr Trophy Championship, the point of Mathematical ineligibility is also after race 2 of the Berlin ePrix and Max Guenther leads the championship at this point with 88 points, although 2nd place (James Calado) does tie him in points. However, neither would win the Trophy as Nyck de Vries would win it with a points total of 149 after being 3rd at the point of Mathematical ineligibility with 85 points.
For the Overall Teams' Championship, the point of Mathematical ineligibility is after race 3 of the Berlin ePrix, the 8th race of the season. The leader at this point is DS Techeetah, who lead with 172 points and they go on win the championship with 225 points.
For the Customer Teams' Championship, the point of Mathematical ineligibility is after race 1 of the Berlin ePrix, the 6th race of the season. At this point the championship leader is ROKiT Venturi Racing, who lead with 112 points, and they maintain this lead for the rest of season, even sealing the title with a race to spare. Their winning points total is 196 points.
For the Manufacturers' Cup, the point of Mathematical ineligibility is also after race 2 of the Berlin ePrix and at this point the leader is DS Automobiles, who lead with 153 points. DS Automobiles go on to win the Manufacturers' Cup with 241 points.

For the Drivers' Championship, the point of Mathematical ineligibility is after race 2 of the Berlin ePrix, the 7th race of the season. Antonio Felix da Costa leads the standings at this point with 125 points and continues to do so as he wins the championship 2 races early and has a winning points total of 158.
For the Teams' Championship, the point of Mathematical ineligibility is after race 3 of the Berlin ePrix, the 8th race of the season. The leading team at this point is DS Techeetah with 188 points and they go on to win the championship, sealing it with 2 rounds to and finishing the season with 244 points.
For the hypothetical Manufacturers' Cup, the point of Mathematical ineligibility is also after race 3 of the Berlin ePrix and the leader at this point is DS Automobiles, who lead with 172 points and would go on to win the Manufacturers' Championship, if it existed back then, with 227 points.