Having scrutinized the Fare Revision news release jointly issued by PTC and MOT , I fail to understand how there is an overall 2.5% reduction in fares in Singapore. If the change in fares can be modeled by a normal distribution, then for people who experience a fare increase of 43.8%, there must be a same number of people who experience a decrease in fare of a similar amount. The normal distribution is a symmetrical graph, and if the overall decrease is 2.5%, then it would suggest that there are people who will experience saving of more than 43.8%.

But given that fare structure is a lot more complicated than that, it would be overly simplistic to model fare changes using a normal distribution. At such, I am curious to the type of statistical model used to derive this 2.5%. I also question the sampling size used in their calculation as the press release did not mention anything about that. I also wonder about the huge standard deviation that could be inherent in the calculation. If there are people who experience a fare increase of 43.8%, it must indicate that the standard deviation is pretty big.

I think it is the big standard deviation that is worrying. And it is even more worrying that it is senior citizens who experienced a fare increase of 43.8%. A retiree traveled from Sengkang to Dhoby Ghaut. It used to cost her 73 cents. Now it cost her $1.05.  The difference of 32 cents brings about a fare increase of 43.8%. So let’s say this person travels on this route once a week. So $0.32 x 2 x 52 (return trip) = $33.28. If she travels on this route twice a week, the fare increase goes up to $66.56. I don’t think it’s very fair that senior citizens should bear the brunt of fare increase, especially since most of them are not working.

Unless of course such senior citizens are in the very rare minority, and that a lot of people experience fare reduction. But I don’t see how the sums add up. I also wonder why people who take buses to town centres would experience should experience fare increase of 17.4% as well. It used to cost me just 69 cents. Now it will cost 81 cents, with a fare increase of 12 cents. So for aunties who need to travel to town centres every morning to do their grocery shopping, this isn’t good news at all.

So, let’s talk about the tertiary student who travels to NUS from Bukit Batok. It used to cost him $0.88. Now it will cost him $1.01 per trip. That’s a fare increase of 13 cents or 14.77%. So he goes to school everyday. That’s a fare increase of $1.30 every week. This is 4.3 times that of the average increase ($0.30) that should be experienced by commuters. Again, the question is not fare increase, but the huge deviation involved, and who it impacts more.

The lowest increase in fare that I found is 1 cent. This person travels from Sembawang to a place in Newton every day. It used to cost this person $1.60. It costs this person $1.61 now. So that translates to an increase of 10 cents a week.

So let’s do some Math to find out the people required to experience fare increase of just 10 cents. Let that be y.

(0.1y + 1.3)/(y+1) = 0.3
0.1y+1.3=0.3y + 0.3
1=0.2y
y=5

So what that means is that for every person who experiences a fare increase of $1.30, 5 people must experience a fare increase of just $0.10 for us to get the average of $0.30. Although this is probable, it does suggest to me that the redistribution effect is quite large.

I hope more information could be released soon, otherwise there should be a centralized location for people to enter their old fares and current fares – and do a proper statistical model. I wouldn’t want to wait till the end of the year to read about huge profit gains for the transport companies in Singapore. Not that they shouldn’t make a profit at all, but the profit shouldn’t be so high. Anyway, they aren’t in the red last year.

Note: I do not have any real life example of people who experience reduction in fares, and thus this analysis is in itself limited. I suspect, however, that people who change bus/trains 2 times or more who may experience a fare reduction.