Using Added Value to measure cricket performances - Part 1

The palpable drop in air pressure from 41000 people collectively inhaling is something that is hard to understand unless you've experienced it. Dale Steyn was bowling to Grant Elliott.

Eden Park in full World Cup mode.

Elliott had been a controversial selection. In the first 5 matches he averaged 19.25 at a strike rate just below 82. That's hardly justifying the selectors faith in you.  However, an important innings against Bangladesh, followed by a breathtaking 27 off 11 against West Indies gave him momentum going into this match. Often the concept of momentum is a case of us over-fitting. We see a couple of good performances back to back and assume a causative effect, where there really probably isn't one. However, regardless of the causes, Elliott was playing the sort of innings that quickly made the critics forget that they had been calling for the coach's head for selecting him before the tournament.

There was a significant obstacle in his road to glory. Dale Steyn. Quite possibly the best bowler to have ever strapped on a pair of boots. Throughout history there have been terrifying bowlers. Fred Spofforth, Jeff Thompson, Andy Roberts, Waqar Younis and Brett Lee are examples. There have also been bowlers who could work a batsman out and exploit weaknesses unmercifully. Alec Bedser, Richard Hadlee, Wasim Akram and Glenn McGrath all shared this trait. In Steyn, South Africa had someone who was in both camps. Possibly only Larwood, Truman, Lillee, Holding and Marshall have been there like Steyn.

But now there was 2 balls left, and 5 needed. Steyn with his tail up bowling to Elliott on 78 off 72. Elliott had previously hit a bouncer for 6, and Steyn's last yorker had gone for 4. Eden Park's short straight boundary meant that bowling full was risky, and bowling short could ask for a top edge carrying for 6. Better instead to try to get him to hit to the longest boundary so Steyn opted for a length ball....

The palpable increase in air pressure from 41000 people collectively screaming with exhilaration as the ball clears the boundary is something hard to understand unless you've experienced it.




Performances like Elliott's on that damp March night are bigger than the sum of the parts. It was much more than a quick 50. It was a career defining innings. It spawned memes, and even had New Zealand's largest talk radio network sharing them.

Elliott the superhero.

It existed in its context, and can't really be understood without knowing the history of NZ and South Africa at World Cups. It may have been his most memorable ever innings. But an interesting question it, if it was stripped of that context, how would it stack up? Would it be his best ever innings?

It's an interesting question, and one that has both an easy and a difficult answer. The easy answer is to look at the total runs scored, and say: his highest score was 115. 84 is less than 115. Therefore it was not his best innings. This simplistic approach is both completely inadequate and yet remarkable common.

An alternative approach is to divide the square of the number of runs by the number of balls faced. This is based off the concept of the batting index.

Grant Elliott's 4 highest scores, with their Index.

This approach makes sense, as a score of 48 off 80 is probably not as good as a score of 45 off 15.  The first score has probably cost the team, while the other has effectively seen the team score more runs because it hasn't used up as many deliveries.

This method would say that Elliott's supporting innings of 104 (96) in the match where Luke Ronchi scored his ridiculous 170 (99) was better than the 115 against Australia. But there are a couple of things that are different here, and possibly need to be taken into account. Australia in 2009 had 4 very good bowlers. Sri Lanka in 2009 had one bowler who would have made that Australia team. The SCG is a much larger ground than the University of Otago Oval, and so you'd realistically expect bigger scores at Dunedin.

None of those factors, the opponent, the era or the location, are factored into the equation when using the index approach. It feels like that approach could be improved.

One of the questions that needs to be answered is "what would we expect someone to do in this situation?" To look at how good a performance is, we could compare it to the expected result, for the average player in that situation. If we are able to do that, we could then ask how much value this player had added.

I first came across this approach in a controversial article by economist Nicholas Rohde, who, in a rather un-Australian move, decided that Tendulkar had eclipsed Bradman. It was an article that got him a lot of ridicule on twitter, but an approach that fascinated me, and one that I'd attempted to use previously.

However, I lacked the analytic skills to do a reasonable job of it. As my skills have improved, my target of being able to do a good job of this has become nearer, so I felt like it might be a good idea to have another attempt.

To assess each innings I decided that first of all I had to know what the expected runs per innings and runs per ball were. To do this I looked at the overall averages over the 5 years either side of the match that were against that opponent, or that were in that country. I was initially going to average those, but I felt that the opponent was more important than the venue, so I gave the opponent a weighting of 0.7 and the country a weighting of 0.3. Hence the expected runs per innings was 0.7 times the runs per innings against that opponent over the 5 years either side of the match, plus 0.3 times the runs per innings in that country over the 5 years either side of the match.

To put that in context, this is what those values looked like for the 4 Grant Elliott innings:

ARPI is Average Runs Per Innings, and ARPB is Average Runs Per Ball.

Teams score more runs, more often now than they did 10 years ago. Hence the ARPI and ARPB for the innings in 2009 is lower than for the ones in 2015.

Teams tended to score less against the South African bowling attack than the Australian or Sri Lankan, so their numbers are lower than the other two.

Basically would would expect an average batsman to score 22 (28) vs Australia in Australia in 2008. By 2015, that would increase to 25 (29).

To calculate the difference between this innings and the expected, I found the difference from the average runs per innings, and the difference expected runs from that number of balls, and found the number in the middle.

For example, with the first innings, he score 92.79 more than expected per innings, but we would have expected him to have scored 95.85 runs from that number of balls. He scored 19.15 more than that. So his added value for that innings is halfway between 92.79 and 19.15 or 55.97 - (55.95 if you don't round prematurely).

Here's how the added value table looks now:

Added value per innings. The innings against Australia goes back on top.

For not outs, the added value is the maximum of the average of the two numbers, or just the runs per ball. This doesn't make much difference for large scores, but stops players getting penalized for a score of 4*(2), where they've really done their job.

The next question, therefore, is what are the best 10 innings of all time?

Using this method to analyse all ODI innings, which one comes out on top? The answer will probably not be a surprise to anyone who follows cricket.

The 10 innings with the highest added value. 

Rohit Sharma's 264 was such a ridiculous score that it has to be at the top. He's the only one to have more than one score in the top 10, and he has 3.

It also shows up an issue with the method. There is no adjustment for the time that the player came in. The expected score should be lower for players who arrive in later in the innings. However, that was a limitation in the database that I was using.

A modifications along those lines would see players coming in later to be expected to score slightly fewer runs, but to score them faster. Those two factors should cancel themselves out to an extent, but AB de Villiers 162 (66) would probably be in the top 10 with that modification. However, the overall results would probably not change too much.

The final question to answer, then is who was the batsmen who added the most value in total, and per innings throughout their careers. Again, the answer for the highest total is not a huge surprise:

Most added value with the bat in a career

Sachin Tendulkar is head and shoulders ahead of anyone else. Effectively India scored 5530 more runs because of Tendulkar than they would have if he'd been replaced with an average batsman.

In 5th place is a name that will possibly end up challenging Tendulkar at the top. Virat Kohli is not yet even 30, and is already roughly half way to where Tendulkar got. He will need to maintain his run scoring feats, and India will need to keep playing a lot of ODI matches, neither of which are a certainty, but if they do happen, he could very well take over the top spot in 8 years or so.

More interesting, however, is the next table, with the most per innings.

For this, I've set a minimum number of innings at 50. I would normally use 30, but I felt that given that this adds extra uncertainty, it was too unreliable to look at only 30 innings.

Average runs added per innings.

The top two names are two genuine greats of the game from the 70's and 80's. Both averaged 47 with strike rates that were roughly 20 runs per ball more than most of their contemporaries.

The newest addition to the list is Jason Roy. His impressive recent form has seen him start to put his hand up as a player to be regarded alongside the likes of Warner and Kohli as a modern day great. He will need to maintain it for a bit longer to be really universally accepted as belonging in this company, however.

Over the next few posts, I will use this method to look at a number of different formats, and see what interesting conclusions can be reached.

No statistical method can ever calculate the emotion that Grant Elliott's innings created. The best innings in people's memories will possibly never make it onto a list of statistically great innings. But that doesn't mean that there is no value in looking at those performances that are statistically the greatest.

Go to part 2 - ODI Bowling