Twenty20 World Rankings

[Neil Pickup]

Hi all,

A little mathematically-driven project I've had a crack at over the Christmas break - trying to come up with a model for the T20 World Rankings, which I don't believe exist anywhere else.

I have adapted the chess model of Elo Ratings, where the idea is as follows:

Match Points = K factor * (result - expected result).

The result is either 1 (win), 0.5 (tie) or 0 (loss), and the expected result is calculated based on the rankings of the sides before the match, and home advantage - for example, taking the third match of the NZ-Pak series just completed, the expectation was 0.63 for an NZ win, and 0.37 for a Pakistan win.

The K factor is 10 for a bilateral or series game involving an associate, 20 for a bilateral or series game involving proper teams, 30 for a WC game, 35 for a WC semi and 40 for a final. The K factor is then affected by the margin of victory - multiplied by R/160 for a win batting first, or by [(W-2)/20+BR/100] for a win batting second.

Pakistan beat New Zealand by 103 runs, so the K factor was multiplied by ~1.64.

This meant the match points were 33 * (1 - 0.37) = 21 points.

Before the game, NZ had 997 points and Pakistan 1007 (NZ were favourites due to home advantage), so afterwards they were ranked on 976 and 1028 respectively.

The rankings at present stand as follows:

1 ENG 1093
2 SA 1087
3 AUS 1057
4 SL 1037
5 PAK 1027
6 IND 1022
7 NZ 976
8 WI 939
9 ZIM 859
10 NED 831
11 BAN 812
12 AFG 792
13 IRE 791
14 BER 780
15 CAN 773
16 KEN 769
17 SCO 749

Test nations started on 1000, Ban/Zim on 900 and associates on 800.

Don't complain about Bangladesh being ranked below Holland. Bangladesh haven't won a T20 in three and a half years, and ranking systems must be based on results. Otherwise, let me know what you think, but please make feedback constructive and relevant to the mathematical model.

 

[Prince EWS]

Gun.

I'm not sure I like the methodology that has you start Bangladesh off with 900 rather than 1000 just because you say so, but the results look good.

 

[Quaggas]

Nice. How did you come up with the adjustment factors? For example: the 1/160, the base K for bilateral vs WC, etc?

 

[Howe_zat]

Interesting stuff. I expected Pakistan to be much higher, 2nd or 3rd, after doing so well in World Cups.

 

[centurymaker]

Hi all,

A little mathematically-driven project I've had a crack at over the Christmas break - trying to come up with a model for the T20 World Rankings, which I don't believe exist anywhere else.

I have adapted the chess model of Elo Ratings, where the idea is as follows:

Match Points = K factor * (result - expected result).

The result is either 1 (win), 0.5 (tie) or 0 (loss), and the expected result is calculated based on the rankings of the sides before the match, and home advantage - for example, taking the third match of the NZ-Pak series just completed, the expectation was 0.63 for an NZ win, and 0.37 for a Pakistan win.

The K factor is 10 for a bilateral or series game involving an associate, 20 for a bilateral or series game involving proper teams, 30 for a WC game, 35 for a WC semi and 40 for a final. The K factor is then affected by the margin of victory - multiplied by R/160 for a win batting first, or by [(W-2)/20+BR/100] for a win batting second.

Pakistan beat New Zealand by 103 runs, so the K factor was multiplied by ~1.64.

This meant the match points were 33 * (1 - 0.37) = 21 points.

Before the game, NZ had 997 points and Pakistan 1007 (NZ were favourites due to home advantage), so afterwards they were ranked on 976 and 1028 respectively.

The rankings at present stand as follows:

1 ENG 1093
2 SA 1087
3 AUS 1057
4 SL 1037
5 PAK 1027
6 IND 1022
7 NZ 976
8 WI 939
9 ZIM 859
10 NED 831
11 BAN 812
12 AFG 792
13 IRE 791
14 BER 780
15 CAN 773
16 KEN 769
17 SCO 749

Test nations started on 1000, Ban/Zim on 900 and associates on 800.

Don't complain about Bangladesh being ranked below Holland. Bangladesh haven't won a T20 in three and a half years, and ranking systems must be based on results. Otherwise, let me know what you think, but please make feedback constructive and relevant to the mathematical model.

Isn't the bolded part supposed to be 0.64? or did you add 1 to the margin of victory-

[1 + (margin of victory) ] * K Factor ??

Otherwise

 

[Neil Pickup]

Isn't the bolded part supposed to be 0.64? or did you add 1 to the margin of victory-

[1 + (margin of victory) ] * K Factor ??

Otherwise

Yep, that's what I meant! Blame the jet-lag...

Pakistan were right up in the top 2/3 until they lost six in a row against England, SA (at "home") and then in New Zealand.

Over the long term, the starting points will prove irrelevant as teams find their own level: it is something of a fudge as a beginning, but dating back to 2005 and the birth of International T20, I think 900 is a fair reflection of Bangladesh's beginning.

The adjustment factors and K values are inspired by the football Elo ratings, and a bit of fiddling around and guesswork to think about what margins of victory are broadly equivalent to the margins they use.

I've just noticed India beat SA this afternoon, which shakes things up: India's win expectancy was only 28% given the home advantage. This means a ranking change of 0.72 * 23 = 16 points. The K factor of 23 comes from 20 * 1.13 from the 21-run margin.

This adjusts the top six as follows:
1 ENG 1093
2 SA 1071
3 AUS 1057
4 IND 1038
5 SL 1037
6 PAK 1027

 

[Prince EWS]

Over the long term, the starting points will prove irrelevant as teams find their own level: it is something of a fudge as a beginning, but dating back to 2005 and the birth of International T20, I think 900 is a fair reflection of Bangladesh's beginning

I don't really disagree, but my issue is that it's entirely subjective. It's just based on your (IMO correct) opinion of their starting quality rather than anything properly calculated. At least with the associates you have an official difference between the teams' classifications - Bangladesh aren't actually any different to Australia in theory; they've just performed worse.

I'd be interested, as long as the way you have it set up would make it easy to do, on what the rankings would look like if you denied the existence of a level difference between any of the teams and just let the rankings work their magic - ie. start every team on 1000 and remove the difference in K factor for associate games. Associate teams tend to play each other more than they do proper teams so I reckon we'd see some pretty out-there rankings, but I'm genuinely interested to see what it'd come up with.

 

[Neil Pickup]

I don't really disagree, but my issue is that it's entirely subjective. It's just based on your (IMO correct) opinion of their starting quality rather than anything properly calculated. At least with the associates you have an official difference between the teams' classifications - Bangladesh aren't actually any different to Australia in theory; they've just performed worse.

I'd be interested, as long as the way you have it set up would make it easy to do, on what the rankings would look like if you denied the existence of a level difference between any of the teams and just let the rankings work their magic - ie. start every team on 1000 and remove the difference in K factor for associate games. Associate teams tend to play each other more than they do proper teams so I reckon we'd see some pretty out-there rankings, but I'm genuinely interested to see what it'd come up with.

1 ENG 1116
2 SA 1103
3 AUS 1080
4 IND 1072.3
5 SL 1071.8
6 PAK 1064
7 NED 1025
8 NZ 1012
9 AFG 979
10 WI 963
11 BER 960
12 IRE 959
13 ZIM 937
14 KEN 936
15 CAN 929
16 SCO 898
17 BAN 887

All teams start at 1000; all games worth 20 except WC games which remain 30-35-40

 

[Prince EWS]

1 ENG 1116
2 SA 1103
3 AUS 1080
4 IND 1072.3
5 SL 1071.8
6 PAK 1064
7 NED 1025
8 NZ 1012
9 AFG 979
10 WI 963
11 BER 960
12 IRE 959
13 ZIM 937
14 KEN 936
15 CAN 929
16 SCO 898
17 BAN 887

All teams start at 1000; all games worth 20 except WC games which remain 30-35-40

Haha well that certainly makes the case for not starting Bangladesh on 1000.
Thanks for that.

 

[morgieb]

lol @ how dire Bangladesh are at T20 cricket.

 

[benchmark00]

Hi all,

A little mathematically-driven project I've had a crack at over the Christmas break - trying to come up with a model for the T20 World Rankings, which I don't believe exist anywhere else.

I have adapted the chess model of Elo Ratings, where the idea is as follows:

Match Points = K factor * (result - expected result).

The result is either 1 (win), 0.5 (tie) or 0 (loss), and the expected result is calculated based on the rankings of the sides before the match, and home advantage - for example, taking the third match of the NZ-Pak series just completed, the expectation was 0.63 for an NZ win, and 0.37 for a Pakistan win.

The K factor is 10 for a bilateral or series game involving an associate, 20 for a bilateral or series game involving proper teams, 30 for a WC game, 35 for a WC semi and 40 for a final. The K factor is then affected by the margin of victory - multiplied by R/160 for a win batting first, or by [(W-2)/20+BR/100] for a win batting second.

Pakistan beat New Zealand by 103 runs, so the K factor was multiplied by ~1.64.

This meant the match points were 33 * (1 - 0.37) = 21 points.

Before the game, NZ had 997 points and Pakistan 1007 (NZ were favourites due to home advantage), so afterwards they were ranked on 976 and 1028 respectively.

The rankings at present stand as follows:

1 ENG 1093
2 SA 1087
3 AUS 1057
4 SL 1037
5 PAK 1027
6 IND 1022
7 NZ 976
8 WI 939
9 ZIM 859
10 NED 831
11 BAN 812
12 AFG 792
13 IRE 791
14 BER 780
15 CAN 773
16 KEN 769
17 SCO 749

Test nations started on 1000, Ban/Zim on 900 and associates on 800.

Don't complain about Bangladesh being ranked below Holland. Bangladesh haven't won a T20 in three and a half years, and ranking systems must be based on results. Otherwise, let me know what you think, but please make feedback constructive and relevant to the mathematical model.

Good to see you make your holidays overseas well worth it.

 

[centurymaker]

lol @ how dire Bangladesh are at T20 cricket.

Their players are too small and appear to be weak

Edit- physically weak.

 

[Uppercut]

Haha, I was quite offended by the fact that Ireland were placed below Bangladesh based on their arbitrarily larger starting point..

 

[Athlai]

Has Bangers played the lesser teams very often?

 

[Prince EWS]

Has Bangers played the lesser teams very often?

Given the true rankings have them last, I'm going to take a guess and say no.

 

[juro]

Not really understanding the complexities involved with rankings, why doesn't the ICC have an official rankings for T20? Given that there have already been 3 world cups, surely there is enough data for them to apply their ODI model...

 

[jashan83]

Hi, I believe someone has already been working on a similar model. The ranking in that is as follows

[CODE]Rank 	Team 	Points 	Membership
1. 	South Africa 	6095 	Full
2. 	Australia 	6086 	Full
3. 	England 	6074 	Full
4. 	Sri Lanka 	6027 	Full
5. 	Pakistan 	6020 	Full
6. 	India 	6000 	Full
7. 	New Zealand 	5930 	Full
8. 	West Indies 	5887 	Full
9. 	Afghanistan 	5633 	Affil
10. 	Netherlands 	5598 	Assoc
11. 	Oman 	5549 	Affil
12. 	Zimbabwe 	5529 	Full
13. 	Bangladesh 	5498 	Full
14. 	Ireland 	5436 	Assoc
15. 	United Arab Emirates 	5276 	Assoc
16. 	Nepal 	4906 	Assoc
17. 	Kuwait 	4811 	Assoc
18. 	Malaysia 	4677 	Assoc
19. 	Canada 	4495 	Assoc
20. 	Singapore 	4453 	Assoc
21. 	Qatar 	4417 	Affil
22. 	Kenya 	4369 	Assoc
23. 	Belgium 	4180 	Assoc
24. 	Saudi Arabia 	4128 	Affil
25. 	Scotland 	4124 	Assoc
26. 	Hong Kong 	4098 	Assoc
27. 	Uganda 	3953 	Assoc
28. 	Bermuda 	3931 	Assoc[/CODE]

the ranking can be found here

 

[morgieb]

Oman getting 11th is itstl.

 

[smash84]

Interesting stuff. I expected Pakistan to be much higher, 2nd or 3rd, after doing so well in World Cups.

I thought Pak were a fantastic T20 side. Maybe they are just good in t20 WCs and dire otherwise

 

[biased indian]

what happened to the test ranking that we had..is it still going ???