## Why being on time is a wonderful thing

This post is NOT about Indigo airlines, though I do fly them fairly frequently (approximately once a month). It is about the general culture of timeliness, and how it can help all of us save time and money.

If you and I decide to meet at say, 1 pm tomorrow, what time are you likely to turn up? There are two factors to consider here – you don’t want to be too late since that will create a bad impression in my mind, and you wouldn’t want that. You don’t want to turn up too early, either, for you don’t want to end up waiting for me. So when you plan your travel to the place we are meeting, you will first estimate what time I’m likely to show up and then plan to turn up such that you’ll maximize the probability of turning up between the time I’m expected to show up and five minutes earlier.

Notice how this can change depending upon the culture of timeliness. If you and I know each other, and I know that you are a punctual person and vice versa, we will both make an attempt to time our travel so that we maximize our probability of being there before 1 pm (the appointed time). What if I think that you are perennially late? The problem here is that I need to not only shift the “mean” of when I want to get to the place, but the variance also changes!

Notice that in case I know you are habitually late, I’m unlikely to know precisely when you’re going to arrive. Say I estimate based on our past record that you might turn up any time between ten and twenty minutes after the appointed time. How will I now plan to arrive so that I arrive between five and zero minutes of the time when I expect you to arrive? My travel time to get to the place already creates one level of uncertainty and to that I need to add another level of uncertainty in terms of when you are expected to arrive! Thus, these two sources of variation end up adding up and I will either be late (in case I’m okay wtih that) or end up spending more time just waiting for you!

Essentially, because I know that I cannot precisely determine when you are likely to get there, I assume a variance of when you are likely to get there, and that variance will add to the variance of my travel time and thus I’ll have to give myself a larger buffer so that I need to be on time while not waiting for too long!

This is similar to what people in quantitative finance call “market price of risk”. Let me illustrate that again using travel time as an example. In case 1, travel time from my office to yours has a mean of 40 minutes and a variance of 10 minutes (let us assume it is normally distributed). In case 2, travel time from my office to yours has a mean of 40 minutes (same as above) but a variance of only 5 minutes. Let us assume I want to be on time for the meeting at least 97.5% of the time. What time should I leave in each case?

In the first case, the one sided 97.5% confidence interval for my travel time is 40 + 2 * 10 = 60 minutes, or I expect to take no more than 60 minutes 97.5% of the time. In the second case, however, it is only 50 (40  + 2 * 5) minutes! In the first case, if I want to ensure a 97.5% chance of being on time for our 1 pm meeting, I’ll need to leave my office at 12 noon, while in the second case I can leave a full ten minutes later!

You need to notice here is that in both cases, the average travel time is the same. The only thing that has changed is the variance. In the first case, because the variance of the travel time is larger, I need to leave earlier! Leaving ten minutes earlier is essentially the price I have to pay because of the larger variance!

Similarly, when there is a variance in my estimate of when you will arrive for the meeting, it adds to the variance of my travel time, and the total variance I need to consider for when I need to leave goes up! In other words, simply because there is a variance in when you will arrive for the meeting,  i will have to leave earlier to compensate for your variance!

What if we had a culture of being on time? Then, I would know that with a very high probability you would be there on time for the meeting, and that would reduce my overall variance, and make it easier for me to also be on time for the meeting!

Essentially, a culture of being on time can save time for both of us – simply because it eliminates the variability of when we will end up arriving for the meeting, and this saved time is reason enough to build a culture of punctuality.

Yet you have people who schedule back-to-back meetings that invariably cascade and ruin their reputations of being on time, and thus inconvenience themselves and their counterparties!