Give and take

In one of my favourite Hagar the Horrible cartoons, Hagar is explaining to young Hamlet “Son, in our fast-paced society … stress is unavoidable” and then goes on to say “But when you grow up, it’s better to be a giver of stress than a taker”. There are, of course, suggestions that in general it is better to give than to receive. But, this is not a Philosophy and Ethics lecture, and I am not going to get into that here. I suspect, dear reader, that you will have seen thousands of wickets fall so you will know instinctively that some wickets are given and some are taken. We always, however, refer to wickets being ‘taken’ rather than ‘given’, e.g. “Joe Soap took 3 for 56”. This is fair enough in the cold reporting of the facts. We wouldn’t want a report to make a subjective judgement: “Joe Soap took one and was given two for 56” would be silly. Steve Finn ‘took’ a hat-trick against Australia in the 2015 World Cup. They were off the last three balls of the 50^th over as the batters swung for the fences. He was clearly ‘given’ the hat-trick as opposed to ‘taking’ it, whatever the terminology implies.

Having seen the thousands of wickets that you have seen, you will probably also have noticed that wickets fall more often the shorter the game is. This is not surprising as batters are under more pressure to score quicker the less time they have, and therefore play more shots, which increases their chances of getting out. While you may have simply noticed this, I, for reasons mysterious even to me, want to quantify it. How many wickets fall as a result of the over-limit? Here are the calculations:

Most modern professional games are played as 20-over games. There are also a substantial number played over 50 overs. To calculate the number of wickets that fall because of the over restriction, we need what researchers call a ‘control’ group. These researchers would probably be surprised and delighted to discover that cricket already has a control group for the purposes of this study. Control groups are rare in the real world. Some games of cricket are played without an over limit, most of these last three or more days. So, we have a control group that can tell us how many wickets fall when there isn’t an over limit. The sample I will use for this calculation is men’s professional cricket in the 2020s. (There have been only 33 women’s first-class matches played in the 2020s; there is not a lot that you can glean from that).

On average, a wicket falls every 53.49 balls in first-class cricket. This means that in 50 overs of first-class cricket, we would expect 5.61 wickets to fall. In matches with a 50 over limit, wickets fall on average once every 33.29 balls, a rate of 9.01 wickets every 50 overs. This suggests that 3.40 of the 9.01 wickets that fall can be attributed to the over limit, or 37.76%. Not surprisingly, wickets fall more often in 20-over matches. At the rate wickets fall in first-class cricket we would expect 2.24 to go down in 20 overs, but in T20 matches the average is 6.99 wickets per 20 overs. The difference (4.75) suggests that 67.91% of T20 wickets fall due to the over-limit. For those less beholden to decimal points than the Notcher’s Natter is, it is fair to say that about one of every three wickets that fall in 50-over matches can be attributed to the over limit, and about two of every three wickets in T20s are because of that over-limit.

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