Sunday 13 February 2011

Partnerships that made big contributions

In an earlier post, A different kind of hundred partnership I looked at a number of partnerships ranked by how much they increased the Duckworth-Lewis expected score.

I have come up with a new method. If you want to skip the geekery of me explaining how it works, click here to go straight to the table.

There were a number of problems with the method I used in the hundred partnership post, some of which I outlined at the time. I spent some time thinking about it, and what could be done to give a more accurate description of the contribution a partnership made to a teams cause. Part of the idea of statistics is to find a way to make the numbers tell the story, and I didn't feel that these told the story accurately enough. There were a few glaring anomalies.

The first thing that I wanted to fix up was that shorter partnerships added more than longer ones. For example Amla and Duminy's partnership of 102 off 16.2 was worth much less than Misbah-ul-Haq and Younis Khan's partnership of 89 off 13.3. These partnerships seem like they are of a similar value to their respective teams. Also there was too much of an advantage for a partnership that came in after the fall of a couple of early wickets. It didn't seem correct that Sarwan and Bravo's epic 125 runs off 22.3 overs was worth 250 more than N McCullum and Styris's 120 off 14. It was a great recovery from 0/2 to 125/3, but it still felt a little off.

I came up with a couple of options to deal with this. Firstly I divided the DL prediction at the start and end by 50, then divided by the number of overs faced. This gave me a very interesting result. The numbers suddenly looked a lot more intuitive. It also eliminated the problems with a team getting off to a bad start, or a particularly good start. Clarke and Watson's 110 run partnership that came in at a ridiculous -75 with the old method was now a more sensible 94. They were still penalised for being a lot slower than the team had been going, but not nearly as much.

I also made a slight modification to the predicted score for anything less than 10 overs, by making it a little more moderate. Again I used the Duckworth Lewis g-score of 250, and multiplied the predicted score by the number of overs used, and then 250 by 10 minus the number of overs used, and then divided by 10. Under the old method if a team was on 34/1 off 2 overs, the predicted score would be 410, now it would be 282. This seems a more realistic platform to start with. Once the over calculation in the paragraph above was added in, the start went from 16 to 11. Not a big difference, but probably more fair. This can however cause a problem in the case of a long unbeaten partnership. If a 2nd wicket partnership went from 33/1 off 2 to 333/1 off 50, they would have added 300 runs, but this method would give them 322. However given that this situation is incredibly unlikely, I am happy to live with that issue for now.

Here are the top 15 partnerships under the new method.

Batsmen NamesScoreStartEndDL Adjusted
RR Sarwan, AB Barath16542/2, 12.4 Overs207/3, 43.2 Overs185
AB de Villiers, JP Duminy13182/3, 13.3 Overs213/4, 35.2 Overs171
MJ Guptill, JD Ryder12318/1, 3.4 Overs141/2, 24.5 Overs161
BJ Haddin, SR Watson110-110/1, 19.4 Overs156
MJ Prior, IJL Trott11323/1, 2.5 Overs136/2, 22.1 Overs156
RR Sarwan, DM Bravo1250/2, 1.6 Overs125/3, 24.3 Overs132
HM Amla, MN van Wyk9716/1, 2.3 Overs113/2, 22.2 Overs130
JP Duminy, F du Plessis11090/4, 23.2 Overs200/5, 44.5 Overs126
Misbah-ul-Haq, Mohd. Hafeez9456/3, 13.3 Overs150/4, 36.1 Overs123
SM Davies, AJ Strauss90-90/1, 12.1 Overs120
SE Marsh, CL White10033/4, 12.3 Overs133/5, 32.6 Overs117
DE Bollinger, SE Marsh88142/8, 36.5 Overs230/9, 48.1 Overs110
DJ Hussey, AC Voges95103/4, 25.2 Overs198/5, 39.1 Overs110
NL McCullum, SB Styris120190/5, 35.5 Overs310/6, 49.5 Overs110
SB Styris, KS Williamson8180/3, 14.5 Overs161/4, 33.1 Overs109

One interesting thing here is that there are three quite different partnerships all with DL adjusted results of 110. Each had a very different role in their game, but have all come out the same under this analysis. This feels good intuitively, as it is hard to separate them when the context of each game is taken into account.

Looking at this list, does this seem like a good method for ranking partnerships and their value. There aren't many that seem out of place to me here, and it seems to tell a better story than sorting them just by total runs scored.


  1. Interesting work! Nothing is jumping out at me as a glaring omission either!

    On a slightly unrelated note, how reasonable is the D/L assumption of 250? Have average scores changed appreciably since that figure was determined? What about adjustments for specific grounds?

  2. On the DL g-score of 250, the average batting first score over the last 3 years in matches between test playing nations is 265, so that suggests that the score isn't too far off. They had it at 230, and revised it up.

    The basic system that I use doesn't actually have any modification built in for the score (and so it's probably not ideal), but it is very easy to implement, and only slightly varies from the proper system.

    I think it is realistic to not take in account of the location, as the variation in pitches is often much more than the variation in countries when it comes to overall score. While the batting technique required to be successful in Auckland might be different to Karachi or Centurion, the average score at those grounds is almost the same. Also the system is designed to provide a fair and even contest between the two teams, so it's probably better if it is consistent.

    However, as I am using their system for a completely different purpose, it is fine for me to come up with a system that allows for those variations. (which I'm currently working on) My system is more for picking what a team is on track for, than for defining a target in case of rain.