## Free hits

We're on the eve of what should be another fantastic battle of Test cricket, but this evening I finally got around to a simple study of the effect of the free hit rule in the IPL. The IPL's the only ball-by-ball database I have, otherwise I'd see if the results are the same in ODI's as well.

Anyway, I went through the tournament and found the run rate on the ball immediately following a no-ball (there might be some non-front-foot no-balls in there, but whatever...). The result was 140 runs off 82 balls, a run rate of 10.2 per over.

To work out how many runs you'd expect to have been scored if it wasn't a free hit, I used the overall run rates by over (actually I did a bit of smoothing first, fitting quadratic trends to the first six overs and remaining 14 overs). The graph looks like this:

So, e.g., if there was a free hit in the 10th over, you'd assume that if it was a normal ball, 7.0/6 = 1.17 runs would have been scored off that ball. Doing this for each of the free hits, you end up with an expected score of 111 runs coming off those free hits, a run rate of 8.1 per over. So the batsmen are scoring more than usual off the free hits, but not by a lot. An extra third of a run per free hit, on average.

It is a nice check that the average run rate in the 20th over (when you're batting like they're all free hits anyway) was 10.1.

Presumably free hits in ODI's also go at about 10/over (or 1.7 per ball), so proportionally speaking, the punishment is greater in the 50-over form of the game.

That graph above is pretty interesting. There's a bit of noise, but the end of the fielding restrictions is very clear. It's interesting that the acceleration is gradual.

The batsmen are circumspect (relatively speaking) in the first over, and the effect certainly muhc larger than just the first over being just bowled by the best bowler (no-one had an economy rate as low as 5.2 in the IPL). Perhaps it is worth opening with your "fifth" bowler. I don't know.

No Australian has done this much research on the IPL before.

Perhaps no white man.

Your like an explorer in the jungle right now.

Heh. The funny thing is, I can't even remember who lost the final, only that Dhoni was the captain. I'm pretty sure that Marsh's team came second but they lost their semi.

One of the things I looked forward to with the IPL was the league format giving good amounts of data to play with.

Free hits in the first six overs would have only two fielders on the boundary therefore you would expect more runs. Is that the case Dave?

The graph illustrates exactly what you would expect in a T20 match. And I suspect that before powerplays a 50 over match would appear much the same.

Spot on there Nesta - in the first 6 overs, the free hits were worth 50 runs in 21 balls, or a bit over 14/over.

In fact, if you look at only the free hits without field restrictions, the runs scored is only barely above the prevailing run rates.

That's a rather curious result. I guess batsmen are being too ambitious with their free hitting to defensive fields.

nice analysis.

The graph illustrates exactly what you would expect in a T20 match

Really unexpected as anything can happen.....................

wow, did that take a lot of effort. opening with the 5th bowler now that adds an interesting twist.

keep your best till the end overs to cut the runs out that way...

send this to warney, he might jst try it out in a game

"That's a rather curious result. I guess batsmen are being too ambitious with their free hitting to defensive fields."

An alternative that it might be worthwhile to investigate is that there is a selective sampling problem.

It's possible that the opening bowlers/"real quicks" will bowl more no-balls than the 4th choice "trundlers" and that these bowlers also bowl a disproportionate number of the overs with fielding restrictions.

As you say, it makes sense that a free hit is like the last over, although as has been pointed out, the fielding restrictions affect things.

Is there enough data to make a similar study of wickets, rather than strike rate, meaningful?

I hadn't thought of doing wickets. When I next remember, I'll have a look at it.

It occurred to me that your data would probably not include the "wickets" that would have fallen if the balls had not been free hits.

Are you referring to (eg) catches taken off free hits? They're not interesting, because on the free hit the batsman chooses his shot knowing that the catch won't matter.

So we would probably expect to see more catches from free hits than at any point in the match. The same is not necessarily true of being bowled on a free hit, etc.

You'd expect that "pseudo" caught, bowled, stumped, and possibly LBW to all increase in frequency on free hits. The only question mark is the LBW, because the batsmen are often giving themselves room.

When you completely remove incentive to defend, there will be more dismissals.

The incentive to defend is gone, it is simply a matter of shot placement for boundaries or maximum running time.

In this situation, being "bowled" is much more of a failure than being "caught", so it would be interesting to look for a difference if the data were available.

The fact that ball-by-ball run maximisation is the only concern also explains why the fielding restrictions make such a big difference. With the defensive fields, perhaps it is not that the batsmen are too ambitious, so much as that most of the restraints affecting them are not affected by the free hit. This might be different in 50 over games.

Hey where did you get eh ball by ball database...and also apart from mean the other interesting stat would be to look at the median..

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