We observe. We measure. We try to be accurate. Assuming we have enough reliable observations we measure centrality of the data. The central value (or average) can be computed in a number of ways so we choose the most appropriate method. The central value need not be the most frequent observation. In fact it need not match any observation. Still it offers a benchmark which can be used beneficially.
Representing a whole set by a single value is bare bones modelling. Models are used to reduce an object. The object may or may not be complex. Complexity is stripped by focussing on essentials to understand what lies beneath. Earth is not a perfect sphere but its model will be spherical.
Of course we need more than a basic model. We observe a system; we understand its guiding principles; we try to find the chief causes that affect its core behaviour. And then we try to build a model that mimics most of whatever happens.
George Box said:
Now it would be very remarkable if any system existing in the real world could be exactly represented by any simple model. However, cunningly chosen parsimonious models often do provide remarkably useful approximations. For example, the law PV = RT relating pressure P, volume V and temperature T of an “ideal” gas via a constant R is not exactly true for any real gas, but it frequently provides a useful approximation and furthermore its structure is informative since it springs from a physical view of the behavior of gas molecules.
For such a model there is no need to ask the question “Is the model true?”. If “truth” is to be the “whole truth” the answer must be “No”. The only question of interest is “Is the model illuminating and useful?”.
The Relative Value Model to determine player contributions in a limited overs match is wrong. But is it useful?
The model is driven by:
- Actual values only. No predictive element.
- Most of the matches are equal. A select few are more equal. A bilateral between any two teams is equal. The same encounter in a World Cup tournament is more equal.
- Total points for a match will be same irrespective of who played whom in an uniterrupted match. Fewer match points when matches interrupted.
- A uniform margin of victory will determine the share for each team. Points will be shared equally in tied matches.
- The difference in scoring rate of two teams and ‘averaged‘ scores from earlier matches determine whether batting unit contributed more towards margin of victory (or defeat) or bowling. This ‘advantage’ will be used to calculate the share of total team batting points out of total team points. In tight matches, whether low scoring or not, this advantage will be close to zero as both sides found it equally easy(or difficult) to score. In one sided matches, the entire credit may go to bowling or batting unit but usually it will be shared proportionately.
- Team batting points will be divided amongst all batsmen based on runs scored and scoring rate when the team bats through an innings. Otherwise it will be based on runs scored.
- Team bowling points will be determined using number of overs bowled, runs conceded, wickets taken and when the wickets were taken by each bowler. The value for wickets is higher if opposition is bowled out and even higher when it is bowled out early. Wickets are valued less when the top order bats till the end but a bit more when the lower order batsmen are facing the final delivery.
The current Relative Value model relies solely on information recorded in scorecards. The model is called Relative because Value of every performance is measured against remaining 21. It does not scan the scorecard against a set of tests to create an index by allocating weights to each measure. In future ball by ball data will also be used to determine Relative Value. This is required to measure runs scored or conceded based on match situation. When plenty of wickets fall too soon, the absolute number of runs added will matter and not the rate of scoring those runs. Which brings us to the topic of this post. The value of taking the 10th wicket vis-a-vis the price paid for not taking all ten.
The longer version played in two innings format is won by bowling out the opposition twice and scoring an extra run. It does not matter whether runs were scored quickly or not. Margin of victory is determined by extra runs scored or innings/wickets saved. A limited overs match, on the other hand, is won by scoring an extra run in fewest possible deliveries. It does not matter how many wickets were lost. For example a bonus point is awarded when a side batting second wins by more than 10 overs. Teams are willing to sacrifice wickets to achieve this objective.
A specialist batsman does not bowl but every bowler must bat. In the longer format bowlers do not have a choice because an innings will not come to an end until the 10th wicket falls (or the captain forfeits remaining wickets) but in the limited overs edition a typical tailender often does not have to face bowling when batsmen do their job well. McGrath had to face a delivery in about 25% ODI matches only.
Openers have an advantage. A bowler is restricted by the maximum overs allowed in a match. An opening batsman can bat through the innings without any restriction on number of balls faced. In general, the top 4 batsmen will get a chance to bat and it is their job to bat for bulk of the innings. Others may not get a chance and when they do, it should be for fewer overs. Best to send your best early.
Of course some teams choose to play their best batsman much lower. Think Brian Lara. Misbah-ul-Haq is a more recent case. I think Shaiman Anwar should bat higher for UAE. Does the team’s best batsman need protection? The answer is NO if it is understood that failure is certain but the odds of a longer innings are higher. In any case a team needs more than one good batsman. Anything may happen but playing the strongest quartet at the top means they are more likely to survive collectively as a unit despite individual failures.
The lower order batsmen usually bat towards the end of an innings and are expected to score quickly. It is a different responsibility when a lot of overs remain. An in-form bowler (or a pair) may have done bulk of the damage. The primary task at hand is to see off that spell even if scoring remains attritional for an extended period. When wickets remain in hand then lesser bowlers will have to bowl.
If a team gets bowled out for 120 it does not matter whether they got there in 40, 30 or 20 overs scoring at 3, 4 or 6 Runs Per Over. The effective run rate will be 2.4 in all these cases. On a difficult surface both sides will struggle when the contest is between near equals. Then there are times when bowlers earn bagful of wickets. This is about the times when wickets are gifted while trying to unnecessarily attack.
There is no value in re-iterating common knowledge. Here is a handy guide for a team keen on giving its entire XI a chance to demonstrate its batting prowess. If you are in a situation similar to Pakistan (4 wickets down after 3.1 overs) then the task for 5th wicket is to bat until 34th over. If a wicket falls earlier then the task in hand for 6th wicket partnership is to last until 39th over.
Pakistan scored 160 despite losing 4 wickets for 1 run. Bunch of wickets can fall at any point. England scored 123 after losing 4 wickets for 104 runs. Relative Value model does not use predictive element in allocating points at present. It will continue to use actual match data in future. Pulse, WARR & FIPS map current match status with projections based on past data. These models are getting tested during CWC 2015 to understand whether match situation is read properly. The next step involves deriving raw data for the Relative Value model after each delivery to replace the current macro model with its micro version.
What is a good first innings total? A team may win after scoring 150 and lose even after scoring 300. FIPS projects team score after each delivery against an ‘average’ score based on past first innings data. It makes 3 projections after each delivery out of which 2 are shown in the chart: one favouring batting side and another favouring bowling team. The model projects that batting team will initially aim to score 300 and bowling side will try to restrict them under 200. Model will reveal revised projections as we fill in the actual runs scored and wickets fallen after each delivery. The projections do not assume uniform scoring rate throughout the innings.
England lost 3 wickets before 15th over and the run rate was slightly below par. At 57-3, we can assume that bowling side had an advantage. Model projects restricting England to 175 after 13.1 overs. At half way stage the 4th wicket partnership has made a mini recovery lifting projected score to about 200. Two more quick wickets reduce England to 104-5 after 26.2 overs. projected score is down to 175. The main difference between 13.1 & 26.2 is that we have double the actual data and lost 5 of Top 7 batsmen. 70 more runs in about 24 more overs is possible and a decent partnership may take England further.
The next 8 overs witnessed an exceptional collapse. An exception means it is an uncommon event. It is unlikely to happen often.
Aussie fans wondered how England got in that tangle. A run fest making use of smaller boundaries was expected. There is no need to play a game if we can anticipate what happens next.
Australia started briskly. Lost an early wicket. Kept scoring at a rate healthier than par. Yet found themselves at 80-3 after 13.1 overs. Not much unlike England then. They continued to aim for batsman favoured ~300 instead of less than 200 favouring New Zealand. No 4th wicket partnership this time and soon it became 97-6 after 17.4 overs. Plenty of overs remain with Clarke and Haddin at crease. No doubts now that the match situation favoured bowling side. The projected score was under 150. A good partnership would certainly left Australia above 150 with 32 overs remaining. There was a partnership. It was for 10th wicket. Australia eventually bowled out for 151 with about 18 overs remaining.
There have been games where 10th wicket partnership rescued a side. There will be more such games in future. We can make very good projections about how a team will fare after losing bulk of the wickets. Projections get better once we have more data. Extra data comes in two forms: plenty of balls played without losing equivalent wickets OR plenty of wickets lost irrespective of balls played.
To differentiate between actuals and projections the very obvious rule must be kept in mind. Losing 9 wickets does not reduce the balls available resource. The fall of 10th wicket is the key event where remaining balls are forfeited. Try not to lose the first 9.
If the game halts suddenly then victorious team will be decided based on the match situation at the end of that delivery. The chasing team is expected to stay ahead of the par curve throughout the match. A typical successful above average score chase comprises of saving wickets in the middle overs and scoring just around or below required scoring rate and upping the tempo in the last lap. If sufficient wickets are in hand, it is expected that the team batting second will significantly increase the run rate once the target is in sight. It means the winning team stayed below the par curve for most of the match as part of a plan. A last ball six is sometimes sufficient to win the game even if scoring remains below par curve throughout the match.
McCullum scored 50 in 24 balls and took New Zealand to 78-2 after 7.4 overs, way above the par score. Fall of two more immediate wickets put them behind par. If the match stopped at that point, the game will be declared no result because 20 overs were not bowled. Since this is a low scoring game where more than 50% of target has been chased it is possible to call a winner within this blogspace. At 79-4 after 8.2 overs, Australia is ahead based on WARR and will be declared victorious if the game stops. This is based on the actual state of the match. The Pulse projection puts New Zealand firmly in command. With 6 wickets in hand, overs taken out of the equation and less than 75 runs remaining – an easy win with lots of balls to spare is projected. That is the projected state of the match.
PULSE allocates points out of 100 for both team after each delivery relying on projected scores. No projections required at the end of the match where points allocated by PULSE based on ball-by-ball data match the scorecard determined result values of Relative Value model.
I created the Pulse model based on my understanding of the game relying on fewest assumptions and recent historical data. One of my checks for the model is calling who is ahead during the game. I have my biases and I try not to conquer them. I rely on who is batting, who has overs left, recent form etc. The model does not care. It relies on runs remaining, wickets remaining, balls remaining and the recent historical trend. At 79-4 I told myself that the game will get interesting if Williamson departs. In other words I agree with the model even though we use different data.
5th wicket partnership secured the game. There was a wobble not unlike the Scotland match but it was too close to the target. Vettori departed at 145-7 and it still does not matter with only 7 runs needed. Model predicts a win for New Zealand with plenty of balls to spare and so did I.
World Cup 2007. Sri Lanka v South Africa. Chasing 210, South Africa sitting pretty at 206/5 after 44.4 overs. Malinga took 4-in-4 to leave them at 207-9 after 46.2 overs. Despite those 4 wickets, South Africa was ahead because WARR Par was 204. Sri Lanka needed the 10th wicket as Malinga tried to make if 5-in-5.
46.3 Malinga to Langeveldt,no run,beaten Just kissed past the off stump. Tremendous nerves out there. Full and just outside off, yorker-length, Langeveldt pokes at it and gets beaten
It did not happen. Eventually South Africa edged past Sri Lanka with 10 balls to spare. It was a tense finish to what should have been an easy one. Something similar although less dramatic happened in 23rd over bowled by Starc.
Williamson took a single on the second delivery. 146-7 with 6 needed. Next we get 2-in-2, both bowled by Starc making it 146-9. What if he made it 3-in-3?
A narrow 50.5-49.5 win for Australia, 7/28 by Starc would have fetched over 200 points relegating Boult’s 5/27 below 150 points. It is the magic of taking the 10th wicket. No need to guess what could have happened. The model was predicting a win for New Zealand until the hat trick delivery but updates values in favour of Australia once the improbable win is secured.
But the 10th wicket did not fall. Scoring a few runs is easier than taking a wicket. Wickets need to fall regularly while defending a low target. McCullum’s innings made the job easier for Williamson. New Zealand has stumbled twice while chasing an easy total. In these two cases the late clutter made the job tense without putting the chase in serious jeopardy. There will be other cases where a lot of wickets fall early and a late partnership secures a win with plenty of overs to spare.
A limited overs match is won by scoring an extra run in fewest possible deliveries. It does not matter how many wickets were lost. For example a bonus point is awarded when a side batting second wins by more than 10 overs. Teams are willing to sacrifice wickets to achieve this objective. Wickets play an important role during the match. The primary objective is reducing the run rate. Taking wickets is a good way to achieve that. Bowling out the opposition will limit the target. Bowling them out as early as possible is the best way to restrict runs. A side may not get bowled out. In general a team will score more runs if less than 5 wickets fall. Getting into the tail without getting the side out is helpful too. In a hypothetical scenario one team may set the target without losing any wicket. Side batting second can win the match while losing as many as 9 wickets. Wickets are secondary. It helps to take the 10th wicket which will happen only if the first 9 have fallen. Wickets are important. But it is extremely important to get the 10th wicket. It may decide whether a team wins or loses. Failing to do that and margin of victory gets decided by balls saved.
Relative Value model awards points by the size of victory. A narrow win or a loss conveys good performances by other team. The Relative Value of a very good performance can’t be significantly better than the rest in such matches.
How does one compare Starc’s figures with those by Boult? Relative Value model evaluates these on the basis that it is a team game. The bowling performance that helps in bundling the opposition is more valuable. The bowling performance that sets up a win is more valuable. The bowling performance that sets up a very big win is even more valuable. Boult’s 5 wickets helped his team to bundle Australia in less than 32 overs. Starc’c 6 didn’t. His performance would have fetched far more points if he took the 7th or his team took the 10th.
This is about the Paramount Utility of the 10th Wicket!