As I have said before on this blog, the value of a batsman in cricket depends on how quickly they score runs relative to the average batsman and how long they stay in relative to the average batsman. Using these principles, we can look at the value of each batsman in one-day internationals, which last 50 overs, or 300 balls (‘no-balls’ excepted), per side. Let’s look at the value of how quickly they score runs first.

The value of how quickly a batsman score runs is the difference between the average runs per ball of that batsman (i.e. their strike rate) and the average runs per ball of all batsmen (i.e. the average strike rate) multiplied by the average amount of balls the batsman stays in. Using this very useful article from S Rajesh, we can look at the example of, say, Dean Jones:

Dean Jones: Average runs per out = 44.61; Average runs per ball = 0.7256; Average balls faced per out = 44.61/0.7256 = 61.48.

Average batsman during Jones’ era: Average runs per ball = 0.6656.

Therefore the value of Dean Jones from how quickly he scores runs is:

[0.7256 - 0.6656] * 61.48 = 3.69 runs over the average batsman.

What this result says is that, for every ball Dean Jones faced before he went out, if you were to replace him with average batsmen, the team’s score would be expected to be 3.69 runs lower. Batsmen who could score at the average rate would be expected to score 0.06 runs less per ball, and when that is multiplied over the 61.48 balls on average that Jones stayed in this equates to 3.69 runs.

Rajesh compared the strike rates and batting averages of 29 batsmen with the average strike rates and batting averages of all batsmen during their respective eras. Using these statistics, we can calculate the respective values of each of these batsmen from how quickly they score runs:

Viv Richards: +12.63

Virender Sehwag: +9.61

Adam Gilchrist: +8.46

Sachin Tendulkar: +6.56

Sanath Jayasuriya: +6.21

MS Dhoni: +5.95

Yuvraj Singh: +4.78

Saeed Anwar: +4.71

Aravinda de Silva: +4.65

Allan Lamb: +4.46

Chris Gayle: +3.75

Dean Jones: +3.69

Brian Lara: +3.65

Mark Waugh: +3.32

Matthew Hayden: +3.27

Ricky Ponting: +2.93

Graeme Smith: +2.40

Mohammad Azharuddin: +2.36

Allan Border: +2.32

Michael Bevan: +1.11

Inzamam-ul-Haq: +0.97

Michael Clarke: +0.70

Javed Miandad: +0.27

Mohammad Yousuf: -0.09

Sourav Ganguly: -0.12

Gary Kirsten: -0.15

Gordon Greenidge: -0.74

Jacques Kallis: -1.51

Desmond Haynes: -1.91

Looking at things in this way has the potential to lead to a huge re-evaluation of the value of some batsmen. Richards, Sehwag and Gilchrist all do particularly well, as they all scored much faster than the average batsman in their eras. Richards comes out on top because he stayed in longer on average than the other two and therefore his team got the extra value from his high strike rate for longer. On the other hand, batsmen like Greenidge, Kallis and Haynes do badly. Consider the case of Haynes: his average runs per ball were 0.6309, compared to an average runs per ball of all batsmen during his era of 0.66, and he stayed in on average for 65.57 balls. If one replaced Haynes with batsmen who could score at the average rate for those 65.57 balls, then on average his team would score almost 2 runs more.

To make this clearer, consider the respective cases of Michael Bevan and Adam Gilchrist. Gilchrist had a much higher strike rate than the average batsman, whereas Bevan had only a slightly higher strike rate than the average batsman, although his team received the benefit of that higher-than-average strike rate for more balls. Gilchrist though averaged 0.2285 runs per ball more than the average batsman, and so it took him, on average, only five balls to add one more run to his team than an average batsman would. Bevan, in contrast, averaged 0.0153 runs per ball more than the average batsman, and so it took him, on average sixty-five balls to add one more run to his team than an average batsman would. In other words, Gilchrist was much more efficient in adding extra runs for his team.

Clearly though there is some benefit from Bevan managing to stay in longer than Gilchrist, and benefits from Greenidge, Kallis and Haynes for managing to stick around for much longer than the average batsman. Part of that value would likely be the increase in the team’s strike rate that results from the team having one extra wicket in hand while the batsman stays in. However, I think that this value, while not negligible, would be small compared to the values given above. Some quick calculations I did over a small sample of games suggested that the average decrease in the strike rate for each wicket lost by a team during its innings was less than 10 per cent of the average strike rate. So if the average strike rate was 0.75 runs per ball, and a team on average lost 7 wickets in an innings, then a team that lost all 10 wickets would have an expected strike rate of no less than 0.525 runs per ball, and a team that lost 4 wickets would have an expected strike rate of no more than 0.975 runs per ball. These are pretty rough calculations, but they seem broadly plausible.

As I said though, this benefit is relatively small. For Michael Bevan, who stayed in on average for 72.24 balls, the expected value from him staying in compared to the average batsman is probably no more than 2.14 runs. This is calculated as the expected difference in the team’s strike rate from having lost one less wicket (no more than 10 per cent of 0.7224, or 0.0722 per cent), multiplied by the difference in the average number of balls Bevan faced and the average number of balls faced by all batsmen during his era (72.24 less 42.74 equals 29.50). Since Bevan stayed in on average longer than the other batsmen above, the respective values for other batsman will be less, in a lot of cases considerably less. No-one is going to overtake Richards simply based on that additional value.

There is another benefit from staying in longer than the average batsman, which is that your team is less likely to be all out, in which cases they will have unused balls. The cost of each unused ball will be the average strike rate of all batsmen (so if the average strike rate is 0.75 runs then the cost of each unused ball is in turn 0.75 runs). Note that, even if a batsman goes out first ball, you would expect on average a team would complete all of its 300 allotted balls, since there would be nine other wickets and the average batsman stays in for around 40 balls. But the probability of them having unused balls would be higher.

My idea for how to calculate this value would be first to create a frequency distribution of number of balls faced by batsmen before going out. Next, you could run a large number of simulations in which you draw from this distribution and insert the average number of balls faced by the batsman in question to work out the expected number of balls the team faces given the average number of balls that batsman faces. But again I expect this value to be relatively small. Say that a batsman averages only 5 balls per dismissal (a really bad No. 11 for instance): I reckon that the expected number of balls the team faces would still be around the 290 mark. If the average batsman faces 40 balls per dismissal, then that awful batsman is probably only costing his team less than 4 runs on average from the increased likelihood that his team will have unused balls. Taking this into account could substantially narrow the gap between batsmen like Bevan and Sehwag, given that Bevan averaged almost 40 more balls per dismissal, but I think Richards would still come out on top.

Note that the value from the change in likelihood that the team will have unused balls will probably vary considerably across the different forms of cricket. In Twenty20, where the team is unlikely to have unused balls the change in likelihood that the team will have unused balls from losing a wicket quickly is probably very small. Therefore, for Twenty20, a batsman’s strike rate is the best indicator of his value. In Test match cricket, however, which lasts for 5 days, the change in likelihood that the team will have unused balls from losing a wicket quickly would be quite large. Therefore, for Test match cricket, how long a batsman can stay in becomes quite important (and hence, why the batting average, which depends heavily on balls faced, becomes a better indicator of a batsman’s worth). In one-day cricket, the value is somewhere in between, but the results here suggest strike rate may be more important than often given credit for, and a batsman like Richards who can score really fast but still stay in a bit longer than the average batsman is king.

Note: I just worked out Rajesh's stats are based on Top 7 batsmen only, not all batsmen, but even if the numbers change a bit the general points would still stand.

## 2 comments:

Just finally, another factor that you've partially omitted - batting second, and playing conservatively.

You correctly note unused balls, and stretching the innings to use all available balls, but only in the context of scoring maximum runs. When batting second, and on track for an achievable target (run rate is above the required) then some batsmen - Bevan particularly comes to mind - begin to control the run rate, taking very considered runs and minimal risks.

Note that this behaviour is not intended to maximise the run rate. It is intended to only win the match. If I only need to get ten runs to win the match, and I have ten overs to do so, it makes sense to wait for the safest opportunities rather than attempt to get those runs in an over or two.

Because of this I believe you would ultimately need to include some significant weighting for whether the match was won or lost when batting second; and whether the batsman was still at the crease at the end of the match.

That's a good point - I guess to determine if it was significant enough to be factored in one could first look at how a batsman performed when his team batted first to how he performed when his team batted second. It could be for some batsmen that the situation described is uncommon enough not to worry about it. But for other batsmen, like Bevan, if they often find themselves in a situation where they are sticking around to guide the team to a win their strike rate might be lower and balls faced may be higher when their team bats second.

Another option is just to remove all innings when the team batted second but that seems a bit drastic.

Post a Comment