normalization – Pertinent Observations

Has Manchester United Really Been a Disaster This Season?

The talk of this English Premier League season so far has been the poor performance of defending champions Manchester United. After six rounds of matches, the Red Devils lie twelfth, with only seven points from six games. While we are barely one sixth our way into the season (where each team plays 38 games), people are talking about the loss of the United “magic” following the departure of its long-standing coach Sir Alex Ferguson last season break. Other analysts, however, are quick to point out that United started off with a rather tough fixture list this year, having visited Liverpool and Manchester City and hosted Chelsea already.

A snapshot of the Premier League Table, thus, does not paint a particularly accurate picture. It is possible that at a particular interval in the season you can go through a series of tough games, or easy games. The fixture schedule each year is different and thus early league positions can be deceptive.

On this page, we will try to adjust for that. This post is going to be updated every week, and what we will do is to compare this season to the earlier one and see how teams are performing relative to the same set of fixtures last year. Thus far this season, Manchester United have played Chelsea, West Bromwich and Crystal Palace, all at home and have traveled to Swansea, Liverpool and Manchester City. What we do is to compare the performance of Manchester United in these six games to the corresponding six fixtures last season.

To adjust for relegation and promotion, the teams that placed 18th to 20th last season are respectively replaced by the three qualifiers (in order) from the Championship. Thus, we will assume that Cardiff City will replicate Wigan’s performance, Hull City Reading’s and Crystal Palace has taken QPR’s place.

Thus, we get table 1 – the “points change graph”, which shows how many additional points each team has got so far relative to the corresponding fixtures last year.

This table confirms that irrespective of the fixture list, Manchester United’s performance so far this season is significantly inferior to that of last year. At the other end, Southampton and Tottenham Hotspur have vastly improved from last season.

Next, we will assume that the rest of the season would go as it did last season, and see how the table has changed taking into account this season’s performance.

Again, it is early in the season yet, but if the rest of this season were to go as it did last year, Manchester United is likely to still win the title, but only just. Interestingly, Tottenham will be second if the rest of the season goes as per last season’s performances.

Journal of Bad Statistics: Road Accidents in India

Occasionally, this blog takes a break from presenting interesting data to critiquing data-related journalism in the media. Our object of attention for this post is a report in the Hindustan Times that states that “Maharashtra has highest number of road accidents in the country”. The headline is factually correct, if you go by the data on the website of the Ministry of Road Transportation and Highways. The problem, however, is that it is a meaningless statistic.

It might be intuitive to you that one cannot compare the number of accidents in a large state like Maharashtra to that of a small state of Manipur – the former is so much larger than the latter that it is bound to have more accidents. Extending this argument, does it makes sense to compare states on the basis of sheer number of accidents? Does the statistic of “state with highest number of accidents” make sense? If not, what is a good metric to compare road safety in various states?

Comparing values that are measured in ‘absolute numbers’ across geographies makes no sense, for it doesn’t take into account the difference in size of the various geographies. In order to get a good comparison we need to “normalize” the measure that takes into account the relative sizes of the geographies. And it is important that we use the right metric in order to normalize the measures.

So how do we compare the accident rates in Maharashtra and Manipur, given their different sizes? An intuitive normalizing factor is the state population. Population might be a good metric for comparing birth rates or disease incidence rates, but road accidents? Population doesn’t account for people in one state driving more than in another state. We need a better metric.

Going back to the basics, what are we trying to achieve here by comparing accident rates across states? The accident rates is probably going to be used as a proxy for road safety. So how would you compare road safety across two different regions? A good metric, I would argue, is the likelihood of having an accident if you were to drive 1 kilometer. Or the number of accidents per vehicle kilometer. Notice that this at once takes care of both problems we have discussed above – sizes of states as well as propensity of people in various states to drive.

However, whether this is the best metric is debatable. For example, this metric ignores the “vehicle mix” in various states – so would “passenger kilometer” (rather than “vehicle kilometer”) be better? Perhaps. Again, this metric assumes that all kinds of roads are similar, and treats traveling along a kilometer of a highway as equivalent to traveling a kilometer on a village road. There are no “perfect” metrics or “normalizing factors” – so we have to choose one that is “good enough” and go with it.

Now, let us compare states based on their likelihood of accidents. Unfortunately, data on “vehicle kilometers” is hard to come by – in the absence of tolled roads, no one really keeps track of this. So we need to use a proxy. Again, it is debatable about what is the best proxy (remember there was already a debate on what is the best measure), but for ease of data capture (if not anything else) let us use “accidents per total road length” as a metric here. Drawbacks of this metric is that it doesn’t capture how busy these roads are, and are only a loose proxy for how much people drive.

The graph below shows the relative safety of roads in Indian states. Based on accidents per 10000 kilometers of roads, we see that Maharashtra (green) is quite close to the national average (blue). It turns out that it is the union territory of Lakshadweep that is the clear outlier on number of accidents per kilometer of road.

Road accidents per 10000 Km of roads, per state (2008). Source: Ministry of Road Transportation and Highways

Based on this, we can say that the article in the Hindustan Times quoted at the beginning of this piece, while factually correct, does not present a correct picture.

The Necktie Index

I’m currently reading Roger Lowenstein’s When Genius Failed – about the rise and fall of the hedge fund LTCM. So when LTCM was in trouble, the employees there came up with a measure called the “necktie index”. I’m not able to find a good link to it, and unfortunately physical books don’t offer an efficient “Ctrl+F” option so I’ll have to paraphrase and put it here.

The necktie index states that the more senior officers of the company wear neckties, and the more the meetings they attend, the more trouble the company is in.

I think this concept is generally true, and applicable more widely and to all companies. The more the number of employees wear neckties (compared to normal business days), the more the trouble the company is in. The indexing to “normal business days” is important because different companies have different normal dress codes, so normalization is required.

On a related note, I read somewhere that sometime in the beginning of this decade, when most other investment banks had a business casual dress policy, Lehman Brothers insisted that all its employees wear suits and ties to office. And you know what happened to the firm.

Now UBS has released a 43 page dress code, insisting its employees wear ties, among other things. It probably gives you an indication of where the company is headed.

On a less related note, I used to work for a startup hedge fund whose first office was a room inside the office of a fairly large BPO/KPO company in Gurgaon. And every week, “inspirational quotes” from the founders of the BPO/KPO would go up on the walls, along with their photos. And this was fairly well correlated with the decline of the stock price of that company.