Tuesday 3 July 2018

Using Added Value to assess cricket performances - Part 3 ODI all rounders

Viv Richards - by Aditya Naikdesai
Growing up in the 1980's, cricket was all about three things: the mighty West Indies, Lance Cairns biffing 6's and the "Big 4" all rounders.

I remember sitting on the school bus as someone was sharing the updates of a match that they'd been listening to on the radio: Viv Richards hit a century, Malcolm Marshall took 3 wickets, Lance Cairns hit a ball onto the roof. I may have been mixing up 3 different games, but that's what every match report felt like.

Other matches were all about the battle between Imran Khan and Ian Botham, or Richard Hadlee vs Kapil Dev. Those 4 players transfixed a generation - each of them had the ability to win a match with either the bat or the ball.

Throughout history, all rounders have been both highly sought after, and incredibly rare. To find a player who was capable of playing as a batsman or a bowler was unusual. To find someone who was a star with both was phenomenal.

There are 43 players who took more than 100 wickets and scored more than 2000 runs in ODI cricket. Some of them were batsmen who bowled a bit, some bowlers who occasionally contributed with the bat, some were "bit's and pieces players." An interesting question is if any were truly all rounders. Were any players both above average batsmen and bowlers?

To answer that, we'd first need to get a gauge on what average looks like.

I first of all used batting and bowling index. I looked at the overall average batting and bowling averages, and took them as the cut off. For batting, I just looked at top 6 batsmen, because an averge batsman is still likely to bat in the top 6.

I came out with these values: The average batting index is 24.4 while the average bowling index is 25.2. The difference between these is caused by run outs and extras.

The next thing that I did was graph them, and break them into 4 quadrants.

I've categorized the players based on what quadrant they are in. Those of you outside New Zealand may not have heard the term "Cunis" - it's used for something that "not one thing nor another." In this case a "bits and pieces" player, who doesn't quite do the job of a batsman or a bowler, but contributes at times with either.

The 4 players who make it into the All-rounder category using this method are: Mohammad Nabi, Andy Flintoff, Shakib Al Hasan and Lance Klusener. There are 3 players who just miss out: Imran Khan and Abdul Razaq are just to the lest of the batting line and Mohammed Hafeez had a bowling index that was only 0.1 off crossing the line. Hansie Cronje and Jacques Kallis also got close.

Here's the table of the top few, ordered by difference between batting index and bowling index:

However, it is surprising that none of the "Big 4" made the grade as All-rounders. Hadlee hadn't scored enough runs to make the 2000 runs criteria, but if the criteria was lowered to 1500 runs to let him it, he'd still have been in the "Bowler" category, rather than the "All-rounder." Kapil, Imran and Botham all, likewise, were categorized under "Bowler."  This made me wonder if it was a moving target. Perhaps the averages had changed over time.

To get a quick gauge on that, I coloured the players above by the middle decade that their career most overlapped with.

Looking at this, it seems clear that the line is moving. In the 1980's it seems to have been about 23, while for the 2010's it is more like 27.

Another issue here is that if we reduce the criteria to 50 wickets and 1000 runs, Ryan ten Doeschate stands out as the greatest all rounder in the history of the game, by quite a margin. I have no problem saying that he was a very good batsman, and a handy bowler, but his stats are somewhat skewed by the opponents that he played, and I'm not sure that there's enough evidence in contextless numbers to be confident saying that he deserves that spot, without looking into it a little bit more.

So I decided to add in some context by combining the Added Value results from my previous two posts.

First I'll look at 2 ways of looking at the best individual performances. To consider how all-round a performance is, we can look at what the minimum contribution is between batting and bowling.

Here's the table:

Paul Collingwood's remarkable single-handed demolition of Bangladesh in 2005 takes the top spot. 9 of the 12 complete performances have come in the past 18 years, but 60% of all ODI matches have been played in that period, so 75% of the performances coming in recently isn't a major problem.

The other option is to look at Total Added Value. These won't all be all-round performances, but they will be the biggest all-round contributions.

3 of the performances on the previous table also make this one. Rohit Sharma's ridiculous 264 again tops the table, but the best actual all-round performance was Shahid Afridi's 76(55) and 7/12 vs the West Indies at Providence.

The next question to answer is "Who is the greatest all-rounder in ODI cricket?"

For this I wanted to look at three things. Who has made the most total contribution per match? Who has the highest minimum average contribution of each skill, and who made a contribution with both skills most often.

Total contribution per match finds out effectively the best ODI players. These are the players who made their teams better than if they didn't play by the biggest margin.

Bond, Starc, Flintoff and Garner would be a fairly handy bowling quartet.

Add in one spinner, and you could make a very good team out of these players.

It is a bit strange that there are not many players from the middle 2 decades of ODI cricket. That may, in part, be because players often have a reasonably slow start and a poor patch at the end of their careers, and as a result their overall numbers aren't so great. Richards, Garner and Abbas had already been through their early career phase when ODI cricket started to be played regularly, and Dhawan, Warner, Starc, Amla and Kohli have yet to have their end-of-career slump.

Perhaps another post looking at the players with the best 50 consecutive matches might be more revealing on this front.

Now to the minimum contribution

This table suggests that it would be fair to call Andrew Flintoff the greatest all rounder in ODI history, using this method. He's in all 3 top lists so far, making a contribution of 4 runs with the bat per match, and 8 runs with the ball. Effectively, this suggests that if England effectively had one player who was better than the average specialist batsman and better than the average specialist bowler, and by at least 4 runs with each skill. That makes it even more remarkable that they couldn't win much while he was there.

Three of the Big 4 make it into this list, only Hadlee misses out.

Finally, an under-looked at statistic, reliability. Who were the players who most regularly made a contribution with the bat and the ball.

This list throws up some interesting names. Firstly, top of the list is Bangladesh's favourite son: Shakib Al Hasan. Again we see Flintoff near the top, and we have 3 of the 80's Big 4 represented, with only Imran missing this time. However, the more interesting names are Santner, Marsh and Chappell.

Santner was a surprising pick when he was plucked out of nowhere to play for New Zealand, but he's started to show an ability to do the basic things very well.

Chappell was more of a batsman who bowled, but when he did bowl, he was quite effective. One of the greatest batsmen to have ever played, his bowling was more efficient than memorable. He averaged 7 overs per match, so he genuinely played as an all-rounder for a lot of his career. Making a positive contribution with both bat and ball in over 20% of matches is quite remarkable.

Mitchell Marsh is a player who is quite widely criticized by Australian fans. Yet his numbers say that he's a very important member of Australia's ODI team. Interestingly his probability of making a contribution with both the bat and the ball is much higher than the two individual components multiplied together.

I've heard various theories about players batting better after they've bowled well and vise-versa. I've also heard the opposite. Conversely, one former player told me that he felt that if he hit a hundred, he was too tired to bowl well, and if he'd bowled well, then he was often too confident and tended to get caught on the boundary early in his innings when he batted. However, most of the player in this table have their success rates looking fairly independent.

To see if Marsh's difference between what we would expect and what actually happened was significant I constructed a parametric bootstrap confidence interval using the Bernoulli distribution. I calculated an outcome for each match for either contributed with the ball or contributed with the bat, using the probabilities in the above chart. I then compared the expected with those outcomes to the actual, and saw the difference. We would expect that a player with 52 matches and those probabilities to have both happen within about 6.5% of the two multiplied together if it was independent (with 95% confidence). Given that Marsh's difference is 4.2% we don't have any evidence of his batting influencing his bowling, from this statistic.

The next step would be to look at his AV values for each, rather than just asking if they are positive or negative.

Looking at the graph it's clear that there isn't any particular pattern.

This suggests that it's probably just randomness that has seen his "Both"% be so much higher than expected.

I then looked through all of the top 82 all rounders by consistency, and only one, Ashantha de Mel, had statistical evidence of dependence. However, looking closer at his numbers, there was also no evidence of dependence there either.

It seems that for anyone who has played 50+ matches and has played as an all-rounder for at least some of those, doing well with the bat or ball doesn't make them more or less likely to do well with the other discipline in ODI cricket.

The overwhelming conclusion to this investigation is that there is one player who, without doubt, was a star all rounder in ODI cricket: Andrew Flintoff. Others can make a good claim for that title, but none as consistently as Flintoff.

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