Working out a formula to bring Test matches within the scope of Glickoblog-cricket is difficult. First, we've got to work out how much more important a Test success is against a one-day win. Our naive estimate is that it's roughly, but not quite, twice as important. We propose to make it 1.8 times as rewarding.
The basic concept is similar to the existing one-day formula: a tied match splits 9:9, an innings victory scoops all 18 points.
Victory by wickets
Where victories are taken by the side batting last, they're given by the number of wickets remaining. Award points as follows:
Win by 10 wickets - 17 points
9 or 8 wickets - 16 points
7w - 15p
6w - 14p
5w - 13p
4w or 3w - 12p
2w or 1w - 11p
Victory by runs
Where victories are made by the side bowling last, the margin is runs. Calculate the margin of victory as a percentage of the total score of the losing side, as follows:
>50% - 17p
35-50% - 16p
20-35% - 15p
15-20% - 14p
10-15% - 13p
5-10% - 12p
<=5% - 11p
In the rare event that the side batting last scores fewer runs in their two innings than the other side made in their first innings, treat as an Innings Victory. For instance, India 295 and 150; Bangladesh 100 and 100 is officially a win for India by 245 runs; we treat it as an innings.
Draws
So far, so simple. Drawn matches present a problem - how do we come up with a simple method of adjudicating draws? We need to scale up the incomplete innings to completion, factor in any unstarted innings, and then adjudicate upon the result.
Now, we're not aware of any research that says on average, when a side loses its second wicket, it will go on to increase its score by %%so much%%. In the absence of such research, we reach for the Duckworth-Lewis tables, read across the very top line - resource remaining with all overs left - double it, and add on the runs scored already:
Wickets lost - scale factor
0 - 300%
1 - 286.8%
2 - 270.2%
3 - 249.8%
4 - 225.5%
5 - 198.0%
6 - 169.8%
7 - 144.0%
8 - 123.8%
9 - 109.4%
So, for instance, if the match ends with the final side on 100/6, we estimate that they will have increase their score to 169.8% of the current total, and finish on 170 all out.
That's fine for matches where the fourth innings begins; where it doesn't, we assume that the side batting last will have done so at the same rate-per-over as they did in their first innings, and will bat for the same number of overs as the presumptive duration of the third innings. For instance: Aus 400 and 100/6 (35 overs); NZ 300 (100 overs). We scale up the Australian second innings to 170, and award the New Zealand side (runs/overs)*opp_overs*scale = (300/100)*35*1.698 = 178.
(Sidebar) It has been observed that test match wickets are lost at the approximate rate of one every 15 overs, and that the run-rate per over decreases approximately linearly with the number of wickets lost. In a study of one-day cricket, and ignoring the term relating to balls remaining, Carter and Guthrie implicitly propose a run-per-ball rate of 0.85-0.1028w where w wickets have fallen. If implemented, and assuming that wickets are lost exactly every 90 balls, this gives flat rates as follows:
Wickets lost - Additional runs
0 - 355
1 - 279
2 - 212
3 - 154
4 - 105
5 - 65
6 - 35
7 - 14
8 - 3
9 - 0This does not appear to tally with the evidence, particularly with three or four wickets lost. It is entirely possible that a better model can be produced.
Back with the main thread, where we have estimated total scores for the sides. Now work out the margin of victory (in runs), divided into the winner's score - we use the winner, rather than the loser, because we're less certain about the result than before, and want to introduce a larger margin of error. Award points as follows:
Margin - points
<=5% - 9
5-15% - 10
15-25% - 11
25-40% - 12
40-75% - 13
>75% - 14
Where the second innings is incomplete, but has lasted at least 50 overs, scale that up and adjudicate on a single-innings match, for a maximum of 13 points. Where the second innings is incomplete and has not lasted 50 overs, declare a No Result, and award no points.
A side securing a draw is guaranteed 4 points; generally, the leader will receive a couple of points fewer than they would have done if the match had concluded.
Some recent worked examples:
Bangladesh -v- India, 18-22 May: IND 387 and 100/6d, BAN 238 and 104/2. Match drawn.
Computed totals: IND 487, BAN 238+104*2.702 = 238+281 = 519.
Margin of victory: (519-487) = 32 runs, 6.2% of BAN score.
Result: Bangladesh 10, India 8
In this Test, just over two days were lost to rain and bad light. Bangladesh had been set a total of 250 to win in 20 overs, and clearly held the upper hand in the chase. Would they have reached it? It's difficult to say; we reckon they would have more likely won than not.
Bangladesh -v- India, 25-27 May: IND 610, BAN 118 and 253.
Margin of victory: Innings.
Result: India 18, Bangladesh 0.
Series result: India 26, Bangladesh 10.
For the purposes of Glickoblog expected results (0 a comprehensive ODI loss, 1 a comprehensive ODI win), work out the ratio of points per game, then work out the signed difference between the side's result and expectation, and multiply by 1.8. India's result in this series was 26/36 = 0.72; its expectation was 0.61, so the side is credited with a win by 0.22; this translates to 23 points. Bangladesh is punished for its poor performance in the second test, and loses 15 points.
England -v- West Indies, 17-21 May: ENG 553/5d and 284/8d; WI 437 and 89/0.
Computed totals: ENG 837, WI 437+89*3 = 437+267 = 704.
Margin of victory: (837-704) = 133 runs, 15.8% of ENG score.
Result: England 11, West Indies 7.
Slightly more than a day was lost to rain in this match, mostly on the final day; England had set the West Indies a near-impossible 401 to win.
25-28 May: ENG 570/7d; WI 146 and 141.
Margin of victory: Innings.
Result: England 18, West Indies 0.
7-11 June: ENG 370 and 313; WI 229 and 394.
Margin of victory: 60 runs, 9.6% of loser's score.
Result: England 12, West Indies 6.
15-19 June: WI 287 and 222; ENG 400 and 111/3.
Margin of victory: 7 wickets.
Result: England 15, West Indies 3.
Series result: England 56, West Indies 16.
The expected score was England 43, West Indies 29, so England advances by a good margin.
Adding in these two series results gives:
AUS 1285 119.7 BAN 845 117.4 ENG 977 129.3 IND 966 145.4 NZ 1057 121.5 PAK 996 172.2 SA 989 123.9 SL 1121 115.2 WI 875 124.1
For 20/20 matches, we propose awarding 2 points to the winner, 0 to the loser, 1 each for a tie, regardless of the margin; each match will (effectively) count as slightly less than half a full ODI.
Coming up before the end of August:
25 Jun - 15 Jul – Sri Lanka v Bangladesh (3 tests) Expected result: SL 39, Ban 9 - three crushing victories
26 Jun - 1 Jul – India v South Africa (3 ODI) Expected result: Ind 8½, SA 9½ - a slight edge to SA
28-29 Jun – England v West Indies (2 20-20) Expected result: Eng 2.5, WI 1.5.
1-7 Jul – England v West Indies (3 ODI) Expected result, approximate figure: Eng 12, WI 6 - almost exactly a 2-1 series win.
19 Jul - 13 Aug – England v India (3 Tests)
20-24 Jul – Sri Lanka v Bangladesh (3 ODI)
21 Aug - 8 Sep – England v India (7 ODI)
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