Have number 11's gotten better?

I recently read an article about the impact of DRS and technology on umpiring by Jarrod Kimber. like most of Kimber's articles, it's both informative and readable.

He asked the question in there if number 11's were getting out more or less now to lbws. Umpires seem to be more generous to the bowlers now than they used to be, but they also seem less likely to give horrendous decisions against tail enders now, where it used to seem that if a number 11 got hit on the pad, then it only had to be close for the umpire to give it.

There's also a thought that number 11s are more likely to stay in line now than they used to be.

I decided to have a quick look into it, and found that they were really getting about the same number of lbws now as they were in the pre-DRS days.

I used dismissals per hour, because it tells us more about how likely they were to be given out, as opposed to just looking at proportion of dismissals.

One thing that struck me, however, was how long number 11's actually tend to survive. On average they bat about 40 minutes or so per dismissal. That's much, much longer than I would have expected.

Part of this is due to the large rat of not outs. There have been 9 players left not out on 45 or more occasions, 7 of them were generally number 11's, including a few famously bad batsmen, such as Chris Martin, Glenn McGrath and Courtney Walsh.

I had generally been under the impression that number 11's had been improving over time, so I was surprised to see the numbers increasing. That led me to see if there was a trend of number 11's getting better or worse. 

I decided to use series averages, and use exponential smoothing to adjust for the different number of matches played per series, and the natural variability of situations that number 11s find themselves in.

Exponential smoothing is a technique that spreads out any peaks or troughs across a number of observations. It's a way of finding an average that works well for fluctuating data. It does have a tendency to get extreme at the edges, however, so any peak at either end needs to be interpreted carefully.

Here's the result:

This is displayed in series, rather than in time, so there's no labels on the x-axis, as they are not arranged evenly.

There has been an increase at the end, but there have only been series where the smoothed average has gone above 15, and in the last 5 test series, number 11 batsmen have only batted 28 times, with 18 not outs, meaning that there have only been 10 completed innings in 5 test series by number 11 batsmen. 

There were a couple of fairly recent golden eras for number 11's, with the two peaks being from 2003 to 2005 and from 2012 to 2015. The latest peak started in about 2018. 

What has happened, however, is the normal range has moved from about 8 runs per dismissal to about 10 runs per dismissal.

This made me wonder if there was a change in strike rates or dismissal rates. I've used runs per 100 balls and dismissals per 100 balls, so that the graph makes sense in terms of direction. Up means more frequent for both situations.

I've taken since 1991, as that's the first year that we have full ball-by-ball data for every number 11 innings.

There's no evidence here for a change in the dismissal rate, but the strike rate is going up. This signifies a change in approach, from the traditional one where a number 11 was supposed to have a solid defense, but they were not expected to contribute much with the bat, to now where they're often asked to go out and try to score runs while they can. 

There doesn't seem to be a big difference in the rate of getting lbws, but in the rate of number 11's scoring, there has certainly been a change.