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My new T20 cricket formulae

July 12, 2012

On a number of times in the last year I have lamented the fact that many cricket statistics are becoming a bit outdated and don’t do the best job at reflecting why a match turned out as it did. This is most apparent in the T20 game. You can’t just look at a T20 scorecard and hand man of the match to the guy that scored the most runs, there are lots of other factors that need to be taken into account and the next column of the scorecard, balls faced, is just one of those things.

The most valuable commodity in T20 cricket isn’t wickets, it is deliveries. There are less wickets than balls available to the batting side but in 18 games this year featuring the top nations the batting side were only dismissed 20% of the time which means 80% of the time it is deliveries that are the biggest restriction. On 15 of 18 occasions the team with the lowest amount of dot balls wins the game. Two of the exceptions the difference was a solitary dot ball, the third we will get to shortly.

Making use of scoring opportunities is important but we hardly ever hear about dot ball rates because it isn’t sexy and the value of dot balls seems to fly under the radar.

Another way to highlight the importance of scoring opportunities is to consider two identical scores – 35 runs coming from 20 balls – under all traditional measures these represent the same contribution but the truth could be more fuzzy. Let’s pretend the first player scores his 35 runs mainly by hitting boundaries and has 10 dot balls along the way while the second player hits some boundaries and a lot of singles and only has three dot balls. I believe the second player has contributed more to his side because he has used the team’s opportunities more efficiently. Cricket doesn’t happen in isolation and every dot ball not only loses an opportunity to score it takes away what the guy at the other end could have done. Cricket can be a remarkably simple game when the strike is ticking over regularly, the second innings helped that happen while the first didn’t.

Statistical revolutions are in full swing in American sports and considering cricket’s great statistical history it is a shame it is left behind. I am doing my part though with my first, albeit not that complicated, advanced statistic. To try to measure what players are bringing or taking off the table and how their efforts contribute to an outcome I have devised two formula and along the way come up with a pretty compelling reason why our T20 team is struggling all the way back to when we were smashing Zimbabwe.

These formula don’t currently extend to bowling. I have noted a few things that the stats highlight with regard to bowling teams just not bowling individuals. I know that the bowling side is just as important and I’d like to do something similar for that aspect in the near future.

Now to the formulae.

Opportunity score

I like to call the first opportunity score (OS) and this measures what a player did with the opportunities they had. Strike rate is an opportunity score but as I have already shown it can be a little bit flawed and hence though it is a good starting point it  needs a few modifications. The first modification is to subtract dot ball rate (dot balls over balls faced), as we know every ball is important and there has to be some sort of penalty for playing a forward defensive shot.

The second modification takes into account the fact that a few dot balls early can lead to explosion late, otherwise known as the Chris Gayle factor, though ideally players score at a high tempo throughout an innings there are a lot of players that need to get their eye in. To reflect this we add the boundary rate (boundaries over balls faced) to minimise the hit on players that get themselves in before they explode. As the boundary rate is usually much less than the dot ball rate I have multiplied it by 1.5 to negate some of that weighting while not completely offsetting the dot ball penalty.

These three factors give the OS and this can be represented as:

Strike rate – dot ball rate + (boundary rate x 1.5) = OS

A good OS is generally around 1 (or 100% if you are into percentages, I prefer just working in real numbers) while a bad OS is generally less than 1. The lowest OS is -1 which creates its own mini issue in that a one ball duck scores -1 and so does a ten ball duck. It is just a glitch in the formula that needs to be adjusted at some point.

When you look at my example of two different scores of 35 off 20 balls – the one with ten dots would score a 1.78 contribution score, which is still very good, but the one with three dot balls gets a 1.98 which is better but not significantly better which feels about right.

Contribution score

I really wanted to call this the Nico Factor but instead settled for the less dynamic contribution score (CS). The contribution score is an effort to measure how a batsman’s efforts contribute to the winning or losing of a game while bringing a bit of context to the table. Not every pitch is a 200 run wicket and scoring 30 for 35 balls is pretty acceptable when chasing down 90 on a slow turning wicket.

Really this one is pretty straight forward in that we take the opposition team’s OS and subtract it from the batsman’s individual OS. Represented by:

OS – Opposition OS = CS

If you contributed positively you have a positive number and lo and behold if you contributed negatively you get a negative number. Basically it represents what a player did less what they needed to do to win the game.

The main weakness of this is a smaller sample size can give more opportunity for a higher CS. What I mean by this is that it is much easier to sustain a strike rate of 400 from one ball compared to 400 from 20. I think the answer to this is you can’t look at it in isolation – the highest CS might not mean the best or biggest contribution but when it is high for a score of 20 or 30 then it could well be much more meaningful.

Putting it into practice

Having put every T20 international between the main nations this year into my database there are a few interesting results.

The first is the match between South Africa and India that was impacted by rain and won by South Africa under Duckworth Lewis. Colin Ingram was man of the match for his 78 off 50 balls with support from Jacques Kallis (61 off 42) and cameos from Levi, Behardian, Ontong and Morkel. India didn’t lose any wickets in their chase but fell 11 runs short of the D/L target. When you examine the numbers Ingram and Kallis had the least valuable contributions to South Africa’s innings in everything but runs scored. Justin Ontong scored 22 from 7 balls for an OS of 3.86 and a CS of 2.40 which was topped by Albie Morkel who sent all three deliveries he faced to the fence for an OS of 6.83 (the best this year) and a CS of 5.37 (remember the sample size issue above though). On the other hand Ingram had a CS of 0.13 and Kallis was a perfect zero – though they both contributed their contributions weren’t quite as valuable as they would seem and take the cameos and if Robin Uthappa had done a bit more than a CS of -1.27 South Africa could very well have lost the game despite Ingram and Kallis’ apparently strong contributions.

The second interesting example is the recent game between England and the West Indies. This is interesting because it was such a tight game and threw up a couple of interesting stats. England won the game with two balls to spare despite hitting four fewer boundaries than the West Indies. On one other occassion this year the winning team hit less boundaries and on four occasions the number of boundaries hit was the same by both teams. The way England offset this was to score 18 less dot balls than the West Indies did. The highest run scorer for the West Indies was Dwayne Smith’s 70 but he ate up 27 dot balls and only had a CS of -0.28. In fact the West Indies only had two positive contributions, Dwayne Bravo’s barely positive 54 at 0.03 and Kieron Pollard (who the formula seems to love) scoring 23 at 0.37. England’s Alex Hales was man of the match for his 99 and this is justified by his 0.16 CS which considering the amount of runs he scored and the tightness of the match but it is hardly an overwhelming performance despite the fact he almost became the seventh player with an international T20 hundred.

I mentioned above about the third occasion that a team had more dot balls than the opposition and still won, that was the 2nd T20 between the Black Caps and Zimbabwe. This game blows up my system somewhat. That day the Black Caps had 47 dot balls compared to Zimbabwe’s 33 while both teams hit the same number of boundaries (NZ one more 6 and Zimbabwe one more 4). Despite losing the Zimbabweans overall team OS of 1.72 was better than what the Black Caps had at 1.64 – the only time a losing team exceeded a winning team. Part of this was because of extras but the rest was Kane Williamson. On the face of it New Zealand had good contributions from Nicol (56 off 37), Franklin (man of the match with 60 off 37) and McCullum (38 off 24) but each of these innings got a negative CS based on the fact they were worse than what Zimbabwe did. The Black Caps won the game because Kane Williamson scored 20 from the 5 balls he faced for a CS of 3.48, without that effort the Black Caps lose the game because Nicol, Franklin and McCullum didn’t make the most of the opportunities they had compared to what the Zimbabweans did.

What is wrong with the Black Caps?

If my answer can’t be everything then it has to be the top four batsman who are absolutely killing us compared to what the opposition is doing. In seven T20 games in which the top four batted they have contributed just four positive innings. That is four out of 28. As a comparison the West Indies had 6 in just two games against us last week! Overall the opposition top order has produced three times as many positive innings as ours. Teams that win are more likely to have players get positive scores but our record is 3 wins and 4 losses so it shouldn’t be that lopsided.

The four positive innings from the Black Caps come from Martin Guptill and Rob Nicol with two each. Nicol has combined those two positive scores (12 against Zimbabwe and 33 against South Africa) with five negative scores, and we will get to how bad some of those negatives are shortly. Guptill has four negative efforts to go with the two positives scores (91 against Zimbabwe and 78 against South Africa) despite the fact that in this time period he has averaged 37.8 at a strike rate of 142.

The other batsman used in the top four were McCullum (5 negative scores), Williamson (5 negative scores, his positive score against Zimbabwe was further down the order), Franklin, de Grandhomme , Ryder, Southee and Taylor have all chipped in with a negative score each. Considering McCullum is one of the premier T20 batsman the fact he hasn’t produced one positive innings for us is pretty shocking.

Picking on Rob Nicol now. Using 30 runs as a qualifying point Nicol has the worst and fourth to worst CS so far this year. His recent 32 off 31 against the West Indies is the worst at -0.91 and his 56 off 37 against Zimbabwe was fourth worst at -0.45. Even if you drop the qualifier a bit Nicol’s effort against the West Indies would still be the worst. When you throw in that Martin Guptill has the second worst CS score for his 47 off 35 against South Africa which got a -0.61 you can see why we are struggling, there are too many poor efforts at the top of the order compared to what the opposition is doing.

A line-up of Guptill, McCullum, Taylor and Ryder should be one of the most destructive top orders in world cricket but this year they aren’t even close. Taylor and Ryder have been out for most of the year which doesn’t help but if we are to improve our big money players need to play more big money innings, right now they are letting us down or letting Rob Nicol fill in for them.

On the flip side three of the top five CS have come against the Black Caps which suggests the bowling isn’t flash either (keep in mind we have played more games than anyone else). Number five is Richard Levi’s phenomenal 117 off 51 balls which got a 1.18 CS, while his raw OS was 2.47 and the second best so far this year. As I mentioned the more the runs the harder to keep the OS and CS up and the fact that no other score over 75 could get more than a 0.48 highlights how good that innings was. Kieron Pollard has the third best CS with a 1.38 for his 63 off 29 balls in the 1st T20 against us and Dwayne Bravo has the best CS and OS for his 35 off 11 balls which got a CS of 3.28 and an OS of 3.86.

Another way to pin some of the blame on the bowling would be that of the 10 highest team OS half of them have come against New Zealand. That is a bit biased as we haven’t played in Dubai or Abu Dhabi where some of the lower scores have happened. But still….

We can’t bowl tight and we can’t score quick. Did I mention we are horrible against spin and on slow wickets, and a T20 World Cup is coming up in Sri Lanka on slow turning wickets and we are in a pool with Bangladesh and Pakistan, teams with no shortage of slow bowlers…

And that’s it

So there are the formulae, a bit of discussion and the numbers that show how bad the Black Caps have been this year. As much as I would love to do something more sophisticated and situational I don’t have anywhere near the time that is required so this will have to be sufficient until that day comes.

With the T20 World Cup coming up there will be lots of opportunity for me to play with the formula and gather some more data in a more controlled and consistent environment. Hopefully the winner will justify my stats and be the team that faced the least number of dot balls…and hopefully that team is the Black Caps….and hopefully my ’97 Bluebird turns into a Aston Martin DB7 just while we are dreaming big.

For the three people (hi Dad!) that managed to get through this all I would love to hear your thoughts either good or bad. And if you wanted a copy of my database (it is just an excel sheet) let me know I will happily share it. It isn’t copyrighted, yet, so I am happy for any tinkerers or stats buffs to have at it. Enjoy!


From → Cricket

  1. The intelligent Uncle permalink

    So the three pple that got through all this are your Dad, me and who? Lol

    Actually very interesting stuff and will attempt an analysis myself sometime. However it’s not all about the batting and sometimes a dot ball is a dot ball for a very good reason….. A bowler in T20 with a lot of dot balls is a valuable a player as is one who can have dot balls and limit scoring to ones and twos rather than boundaries. I see you acknowledged the bowler thing so be interesting to see how you can sort that out.

    • Well I read it myself too…
      Though I haven’t done it yet I am assuming I can do the same sort of analysis on bowlers – reward dots and penalise boundaries the opposite of what batsman get. As you said a bowler who bowls a lot of dot balls is valuable but right now I have no idea who those guys are. Other then the occassional maiden we never hear a thing about bowlers that have lots of dot balls just their RPO.

  2. Dabusiness permalink

    Maybe you could be the Paul DePodesta of cricket…. If I have his name correct. Pick people based on these stats

    • Yep you do.
      England actually already has someone doing that sort of thing to the same sort of Moneyball level. Lots of English county teams do it and I am guessing some of John Buchanan’s stuff is similar. It just hasn’t filtered out to the media or public yet.
      I can’t find the actual article but this blog talks about it (
      It is part scouting and part analysis and another part maths. It doesn’t replace anything but top level sport is all about gaining a miniscule advantage over the opposition so if you can do that by say minimising the amount of dot balls you face and score an extra 10-15 runs you will probably win a few more games. It should be imperative for a team like us that lacks the talent of some of the other countries, you have to be smarter.

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