Irrelevant numbers: Lambert may not keep his job for long

According to a new article from the Birmingham Mail, Paul Lambert can expect to be around for only 1.2 years once new owners are found for Aston Villa. To get to that number, they've taken a look at how long managers have remained at a club following a takeover since Villa were last bought in 2006. 

It's an interesting argument, but statistically speaking it doesn't make a whole lot of sense. Given that there are only fourteen examples, the trends really don't tell us too much. One of the first issues is that there are a number of outliers here. It appears as if five of the managers were fired almost immediately, which to me signals that the new owners already had the idea of sacking the manager in mind. One of the managers, Martin O'Neill at Villa, was kept around for four years (and that number would have been larger had he not quit). The spread here is huge, and there doesn't really seem to be much of a pattern. In light of these facts, it's easy to argue convincingly that the numbers should not be taken as a group. Doing so implies that there is a pattern and that there is some degree of correlative relationship between the numbers, when no such thing seems to be true. 

The Mail also compares these numbers to the average tenure of Premier League managers, which is a faulty comparison for two reasons. First, we are comparing the time that a sitting manager is allowed to carry on at a club to the average of an entire tenure. Alan Pardew was at West Ham for nearly three years, but on the chart he registers as only one tenth of a year. Why are we comparing that number to average tenure, then? Pardew's time at West Ham wasn't .1 years, it was 3. I would offer a better alternative, but there isn't one.

The second problem here is that even if we accept a comparison between the 14 managers who got sacked after new ownership arrived and the average tenure of Premier League managers, even the latter number doesn't make a whole lot of sense. There have been 194 managers in the Premier League, which seems like a substantial sample. But when you realize that simply removing Alex Ferguson from the equation changes the average tenure from 2.03 years to 1.9 years, you see how volatile the set is. 

In reality, Lambert's time at the club will be determined by the circumstances at the time of purchase. For instance, imagine that someone buys Aston Villa right now. They've got plenty of money and the compensation package for Lambert's sacking won't be an issue. At that point, given his record, it would make sense to sack Lambert and find a new manager immediately. That way the new manager would have time to mold the squad the way they would like for next season.

Now imagine the very same person purchasing Aston Villa in September. Paul Lambert has crafted a squad on a shoestring budget and has put together his philosophy for the season. Are you as eager to sack him now? Would changing owners at that point only lead to more trouble? Even answering this question requires knowing how well the first few weeks went. It's all about context.

This isn't the first time the Birmingham Mail have used numbers to make points that make no sense. There is useful information to be gleaned by statistically crunching numbers, but determining how long Paul Lambert has to stay around once new owners are found isn't an example of that. Lambert may very well last only 1.2 years at Villa once new owners arrive (though that seems unlikely, given that it would mean getting a contract extension and almost immediately having it terminated), but it won't be because that's the average in the situation. It will an event independent of all others.