To closer align the outcome of cricket matches with skill, I propose to replace the toss with a scheme to decide which team bats first.
In brief, the scheme calls for both teams to submit sealed bids where each specify their preference to bat first or to field first and also specify the number of runs that each is willing to give to the other for getting their preference.
An average of the bids is awarded as incremental runs for the team that bids the lower number of runs while the other team gets their preference for batting or fielding as specified in their bid.
Settlement at the average of the two bids allows for both teams to be happy with the settlement in comparison to their respective bids.
According to ESPNCricinfo, the 2019 Cricket World Cup witnessed a pattern of both captains wanting to bat first after winning the toss – a habit also seen in the IPL.
The book Fairly Random: The Impact of Winning the Toss on the Probability of Winning by Gaurav Sood and Derek Willis, who noted the toss-winner had a 2.8% advantage over a 40,000-game data set. This is a material advantage in elite sport.
The toss therefore undermines the fundamental requirement of any sporting contest that is to have competing teams start on even footing on all known conditions except for skill.
In my proposal, both teams submit sealed bids for a certain number of runs, based on their analysis of the conditions, for the right to bat first. Then the team with the higher bid bats first and the team that bats second will have their score augmented by the average of the two teams bids.
Let’s use an example. Suppose team A’s analysis of the conditions led them to believe that batting first is worth an extra 31 runs. Accordingly, team A bids 31 runs to bat first.
Suppose team B bids 53 runs to bat first. Since team B’s bid is higher, they will bat first and team A will be awarded 42 runs – the average of both teams’ bids.
This is fair because the higher bidder bats first, team A will be happy to get 42 runs compared to 31 they thought as fair to bat second, team B is also happy to give away only 42 runs compared to 53 runs they bid to bat first, while both teams get a better bargain by 11 runs, compared to their bids.
In another case, let’s say neither team wants to bat first. In this case, both submit a bid to field first. Suppose A bids ten runs to field first and B bids 50 runs to field first, then team A will bat first, and get 30 runs to do so (the average of the two bids).
Both teams, again, are happy. Team A got 20 more runs and team B gave away 20 fewer runs than their respective bids.
Let’s examine a third case. Both teams bid identical values for right to bat first. To resolve this case, we use a coin toss and the team that loses the toss gets the bid value as compensation to bat second. Alternatively, we can ask for new bids.
In a fourth example, both teams bid identical values for right to field first. We resolve this in the same way as the third case, with either a coin toss or with new bids.
In a fifth hypothetical, one team bids to bat first while the other bids to field. In this case, both teams get their desired wish and we subtract half the lower value bid from half the higher value bid and award that many runs to the team with the lower value bid. See two examples below.
In the first example, team A bids 11 runs to bat first and team B bids seven runs to field first. Then team A bats first and B gets two runs to bat second. Again, everyone gets a better bargain than their bids, with team A conceding only two runs instead of 11 to bat first, and team B getting to field first and also getting two additional runs instead of having to give away seven runs.
In the second example, team A bids 11 runs to bat first and team B bids 41 runs to field first. Then team A bats first and also gets 15 runs to bat first. Again, everyone gets a better bargain than their bids.
For limited over games, the target for the team batting second equals the score of the team batting first plus any runs awarded to team A from the bidding process minus any runs awarded to team B from the bidding process.
The sealed bids of each team should be submitted at the time that is usually reserved for the coin toss – about 30 minutes before the match starts. The submitted bids are opened immediately and the batting order is determined.
Each team submits an odd number as a bid or zero. In case one of the bids is zero and the other is an odd number, we can round up the second number divided by two. This ensures that if both bids are greater than zero, the average of two bids will always be a whole number that is either odd or even.
Time to toss the toss? (Photo by Daniel Kalisz/Getty Images)
In rain-affected limited games, the bids are prorated to the number of overs for which the game is contested over. Sometimes we may have to round off the prorated number.
We compute the target for the team batting first by computing the prorated bids as the original bid multiplied by the revised number of overs divided by the original number of overs for the bids.
The target for the team batting second is the DLS equivalent score for the team batting first plus any runs awarded to team A from the prorated bidding process minus any runs awarded to team B from the prorated bidding process.
In a sixth case, say team A bids 13 and team B bids seven for the right to bat first in a 50-over game. The game is shortened to 20 overs after team A completed 50 overs.
The average bid was ten runs, and the game is shortened to 40% of its original length, so team B’s target becomes the DLS score minus four runs.
Can this scheme be gamed? As long as a team bids what they deem fair, then they cannot be gamed.
Let’s say team B, trying to game team A, somehow knows team A was thinking of bidding 19 runs so bids 21 runs to bat first. Then, of course, team B will win the bid. However, team A gets 20 runs – only one run more than what they thought was fair.
Let’s say team B – again somehow knowing that team A plans to bid 19 runs – bids five runs to bat first, then team A will bat first and give only 12 runs instead of 19 runs that team A bid.
Let’s say team B bids seven runs to field first and team A wants to bid 19 to bat first, then team A will bat first and give away only six runs.
In all cases, we see that team A – regardless of what team B bids – will be happy in relation to their evaluation of what’s fair. Team A is immune to team B’s behaviour or misbehaviour.
In terms of sensitivity to match-fixing, the sealed bids are opened at the scheduled time usually reserved for the toss – and at this time, regulators, media and the public can know the bids submitted by each captain. This introduces an element of transparency and potential scrutiny to the process.
Any bids intended to impart favour to the opposite team can potentially be discerned by observing abnormal differences of the two teams bids or perhaps by comparing each bid to historical bids for that ground or those conditions. Captains have a natural disincentive to make such bids since abnormal bids will invite questions from the public, officials, or the press and risk reputational loss.
Furthermore, it is likely that teams, their management and support staff will debate the relative value of batting first vis-a-vis fielding first. This will make it harder for a single bad actor to have undue influence on the bidding.
Does the toss add to the allure of the game?
Including a bias to favour the team that correctly calls the toss adds no more to the game’s charm than umpire bias.
Removing the toss eliminates some of the prose and retains the poetry of the game. The allure of the game is preserved in the unpredictable outcome of skillfully directed activity and has no additional need for an external source of randomness.
The most skilled of cricketers cannot consistently control where they can direct a ball while bowling or while batting. There are inches between a half volley and a yorker, between a ball that beats outstretched hands and one that is pouched, and between the blade’s outside edge and the sweet spot. This is the game’s timeless charm.
David Franklin, writing in The Cricketer last April, proposes a scheme where each teams bids a certain number of runs without specifying whether to bat first or field first to basically win the toss.
The team with the higher bid, in effect, wins the toss and chooses to either bat or bowl and in turn gives away runs corresponding to the winning bid to the other team.
But by settling the average of the two teams – as outlined in my scheme – both captains walk away happier than under Franklin’s proposal.
Arvind
Guest
Thanks Jeff. I've been ruminating about some of what you raised and will compose a more elaborate post that may address them. Re the idea of adding runs to a target, the practice is already prevalent and deemed fair in ODI's. Below is the link to the one day international concluded yesterday. West Indies played 35 overs. Because of rain, using projected scores, India's target was set about 20 runs higher for the same number of overs - 35. Re - toss, and a live example, do you want any compensation for the team that bats first at Lord's assuming that team that bowls first may have a reasonable advantage from rain yesterday. Arvind https://www.espncricinfo.com/series/19333/game/1188626/west-indies-vs-india-3rd-odi-india-in-west-indies-2019
Appu
Roar Rookie
It is a wonderful suggestion. Cricket game is becoming more and more complex. This simple method of bidding runs to bat first will eliminate many bais factors. Especially useful for removing home-ground basis for the team, which gets more cheers and encouragement from home-crowd. To start with, we may this method at country-level matches. Very useful suggestion. Let us try it out.
Arvind
Roar Rookie
Thanks for explaining. I see your argument more clearly now - they bear resemblance those made by purist friends of min. Here are somethings to consider. Decision making and forecasting is an integral part of cricket. "Whats a par score for this wicket" is a question that is routinely asked and almost always answered, by captains, cricketers and media presenters at the scheduled toss of an ODI. Anecdotally, as seen from comments during the recent world cup, teams seem to manage the first innings based on forecast from management and batsmen on the pitch. Another example, "Is the pitch going to turn later on and should we have an additional spinner therefore. " Second, in case you are overestimating (I am not saying you are) the difficulty of forecasting the value of conditions, consider how much progress has been made in cricket par score forecasting and win prediction while the ODI is underway. Or the phenomenal progress by Sabermetrics in baseball. It is simply a matter of time, and a few committed data analysts and fans, before we have a measurable and more reliable estimate of the value of a set of conditions that are available to public (at currently the toss time) and which captains can base their own tweaks on.
Old mate
Roar Rookie
Thanks Arvind. No-one would disagree with skill differences on the field being the key issue in deciding the outcome of a sports game. Your proposal however is not about skill differences on the field, rather, it is about skill about skill differences off the field, namely differences in the ability to forecast, barter, mathematics, and so on. That is why I would prefer to leave those skills to the business world and other areas (gambling?) and keep cricket match outcomes based on skills on the field, as far as possible ????
Jeff
Roar Rookie
Hi Arvind. Certainly my thoughts were singularly focused re Test cricket, being the multi-day format. I acknowledge re the odds of winning the toss many times in a row, though we do see it happen often; I think Finch had a bad run lately ? (My irregular ventures to the roulette table at the casino tell me that when I bet on black coming up, I'm surely likely to get 5 reds in a row!) Re Tests, it is a fact that the home side can (and will) produce wickets that suit the home side. I'm ok with that, but would like to see the toss outcome removed as a potential to further compound that advantage (i.e. home pitches prepared to suit the home team and then the home side regularly winning the toss). I don't like the idea of "artificially" changing the scorecard by adding runs in a game. I don't think we need to get to the point of eliminating all variables from a game that is played in the natural elements. Otherwise the easier solution would be to play on artificial surfaces and under a roof. But that goes against the grain of cricket which is an outdoors game. Regarding league stages in a WC tournament for example, personally I would just leave it to the "luck of the draw" re the toss. I just don't think you can eliminate the element of luck re conditions in a game played outdoors. Again, it's an intrinsic part of the game. The key point of cricket team selection is to choose a team that on balance can adapt to the changing conditions on hand; be it in one day or across four or five days. I don't know how far you can extend this discussion on "evening out" all the variables in a game, but if that were the intention, then arguably you could make sure that all games were played at a neutral venue so that the influence of "home crowd" atmosphere is neutralised; this is something that is difficult to qualify as an influence, but it no doubt is influential. So we could get to the point of a) playing on artificial surfaces (where natural wicket evolution is removed), b) playing under a roof (where natural elements were removed), c) playing at neutral venues (where home crowd atmosphere was removed). Plus I'm sure quite a few other things. Cricket is what it is and I don't think we need to try and aim for perfect equilibrium re all of these inputs? Isn't dealing with all these variable factors a part of the game and a test of the participating team to assess and plan for?
Arvind
Roar Rookie
Thanks Jeff. I appreciate your thoughtful comments. How would you propose to deal with one-offs such as league stage world cup games or elimination games. Also, just a quick note on the odds. In a 3 match series, theres a 25 pct chance of one of the two teams winning the toss three times in a row. So if the two teams are evenly matched on other counts, this may have a material impact on the series. Also, its unclear to me if the additional selection choice for the loser of the toss can materially affect the selection or is compensation enough. (Even in my proposal we don't know if the runs are compensation enough - but it is constructed to guarantee no captain can be unhappy with the decision of who gets to bat first so long as he or she bids what they deem to be fair. Over time data analyses will get more precise on what's the fair compensation for a given set of conditions.) Thanks for your input. Arvind Arvind
Arvind
Roar Rookie
Thank you Paul for your comments. I appreciate the time and vigor involved. For (1) and (2), other factors such as tv audience, determine starting times. Unlikely that things will change. Furthermore, the material change in condition could arise just a few hours before start, such as dampness or predicted rain for later, that may affect only one of the sides. The issue is that the winner of the coin toss enjoys the rub of the favorable condition and that seems to show up in increasing winning odds - as seen in the study I linked to. Let me address (4) first and then, (3)/(5). It is hard to know on a limited data set if the toss had any bearing on the data - no individual can claim to have keen insight on the counterfactual. However, consider the implications of an argument that "factor X did'nt have an impact on the result so its fine" - it would imply that giving Usain Bolt a 3 meter head start at the olympics is fine because the others would anyway lose to him; and it would also imply that it is fine for every other competitor, at least in Beijing 2008, to be given a 3m head start because Bolt would have won anyway. Another implication - Any perceived Russian tampering may not have affected the 2016 election, so it is fine for elections to allow external influence. So, I am not sure I agree with the structure of your argument. Re(3) and (5), if there's any perceived advantage to batting first or to avoid batting last in a test, the captain can bid a certain number of runs to bat first. If a captain perceives no such advantage he can simply bid 0. These perceived advantages are based on assessments a-priori and not post the event - your examples are post the event. If those perceived advantages don't materialize in the game, either due to poor execution or other factors including mis-judgement about the conditions, theres little that can be done about them. My proposal only attempts to mitigate any known biases in conditions by offsetting with runs that the captains decide among'st themselves. One of the upcoming Ashes tests is in Headingley where there seems to be some advantages to winning the toss. See: https://www.espncricinfo.com/story/_/id/22863861/win-toss-win-match. At Headingley, wouldn't you want, like me, to maximize Australia's chance to be 3-0 and like for them to be compensated additional runs in case they are put into bat first under unfavorable conditions or made to bat last in a foreseeably deteriorating pitch. Best Arvind
Jeff
Roar Rookie
Thanks for the article Arvind. In Test cricket, I do think the toss of the coin has always been a bit too influential, especially when in a 3, 4 or 5 match series, the same team wins all the tosses. That said, it has always been a game played in the elements and on natural surfaces, where both of these things are intrinsic to the concept of the long game format, so personally whilst I'd like to see some lessening of the impact of the toss, I'm still happy to have that element of luck (e.g. changing natural conditions) embedded within the game. I'm not sure I agree that your proposal is a "better" solution to the coin toss, but I enjoyed reading it and contemplating the approach as a hypothetical. Personally, for multiple game series, I would rather see some much simpler adjustments whereby the visiting side gets the choice to bat/field in the first game and the loser of that game gets the choice in the next game and so on. So e.g. in the current Ashes, Australia (as the visiting team and facing a pitch prepared by the home side) would have had the choice in the First Test. With Australia having won the First Test, England now has the choice in the Second Test (however if Australia had lost the First Test, Australia would again get the choice in the Second Test). It doesn't even out the advantage within the match, but does work towards evening it out across a series. My only qualifier is that the side which gets to make the choice has to nominate whether they bat/field prior to the other team having to confirm their final XI.
Paul
Roar Guru
Arvind 1) & 2) - the issue here is NOT the coin toss but the playing conditions, so if teams know the playing conditions are going to present a bias before a series/game starts, surely it's in everyone's interest to change the start time of games, to prevent things like dew becoming a factor? In an ODI/T20 series without significance, this is neither here nor there, but if it's a World Cup or a Test match, then surely the bias has to be taken put of the game, without resulting in a convoluted formula involving bids, sealed envelopes, etc. 3) "The advantages conferred by the existing toss can be mitigated through mechanisms such as what I describe". Tell me how Joe Root could have known what impact both the overhead & pitch conditions would have on England's first innings against Ireland? The different in scores between the 2 sides at the end of the first innings in that game was 122 - to Ireland , so Root would have to have bid at least that number under your system and there's no way he would have come up with that sort of number, which makes your system just as flawed as the toss. 4) "Captains routinely complain that the toss affected the outcome or at least indicate that the toss mattered to the result". The only time recently I've heard that discussed was in the World Cup but all I heard captains say was winning the toss gave their team/the opposition an advantage. No complaining, just stating the obvious. I also question whether the toss had ANY bearing on the outcome of the tournament? The best sides made it to the top 4 and the toss had exactly zero impact on the outcome of any of the finals games. 5) How does your formula work when the game's a Test match and the issue isn't what happens in the first innings, but what happens when the pitch deteriorates, as was the case in the First Ashes Test? Australia won the toss, batted first but ended up behind England on the first innings, so any sealed bids, etc would have been a waste of time. They then proceeded to outplay England over the next 2 innings, thus rendering both the toss and your suggestion meaningless.
Arvind
Roar Rookie
Thank you Bunratty for your kind comments.
Arvind
Roar Rookie
Thanks Les. I have an axiomatic preference for a contest to be settled largely by skill rather than by luck. Thats why I prefer the 100m at the olympics to watching the daily lotto. You may have more of a liking for a greater role for chance in determining outcome. I am glad that despite the axiomatic divergence, we still enjoy the same game of cricket.
Bunratty c
Roar Rookie
Excellent article Arvind! Your statement "However, the argument “make equitable whats possible” is a stronger argument than “we cannot have complete equity so lets ignore whats possible”." is especially apropos. I think a majority of people want to have a level playing field (excluding Lord's CG!) in sporting competition (and life!).
Old mate
Roar Rookie
A coin toss is fair because the outcome is based on luck and that is all. Luck forms an important part of the best game in the world, namely test cricket. Some examples: 1. one team is 9 for 100 chasing 400 and rain comes and the game is ultimately drawn 2. A star player is accidentally injured through no fault of his own on the eve of a game 3. A short leg fielder turns his back as he sees the batsman wind up for a full-blooded pull and the ball lodges in the fielder's legs and the batsman is out...and there are many more examples where luck alone can dramatically alter the course of the game or a series for that matter. Why leave the element of luck in the game? Because it is more interesting!
Arvind
Roar Rookie
Paul, thank you for your critique. To answer the some of your questions I reference the article linked to at the bottom below for reading more than my paraphrasing below. 1. The summary from the article linked to states "The data suggest that winning the toss increases the chance of winning by a small (∼ 2.8\%) but significant margin.". So the advantages translate to changes in win probability. 2. The above answers your second question to some extent. The study also notes "advantage varies heftily and systematically, by playing conditions" ... "winning the toss in conditions where the toss grants a greater advantage, for e.g., in day and night matches, has a larger impact on the probability of winning". So yes, the advantage seems to matter. 3. In a 100m dash, and for that matter most of track and field, all competitors start from the same line. In basket ball, teams alternate sides every quarter. So sport makes an eliminate to control variables that could affect outcome to the extent it can. The advantages conferred by the existing toss can be mitigated through mechanisms such as what I describe. You are right that this will not eliminate every source of randomness or favorability and you may also be right that my original statement may have been too strong. However, the argument "make equitable whats possible" is a stronger argument than "we cannot have complete equity so lets ignore whats possible". 4. Captains routinely complain that the toss affected the outcome or at least indicate that the toss mattered to the result. (I cant systematically augment this but I hope you agree.) Even if captains haven't called for a change, studies have shown how win probabilities are affected by the toss. Fans, are as big, if not bigger, stakeholders of the game. The next world cup is in India, where the final will likely be a day-night match and furthermore dew factor matters for win probability. I quote from the study below "In one-day matches, the advantage of winning the toss in a day and night match is 5.92%," I am hoping, you, like me, will not want to see this win probability advantage conferred to the side that wins the toss in the world cup final. It seems to me, therefore, that something is broken. Also please see link below. Arvind https://arxiv.org/abs/1605.08753
Paul
Roar Guru
"the toss-winner had a 2.8% advantage over a 40,000-game data set. This is a material advantage in elite sport. The toss therefore undermines the fundamental requirement of any sporting contest that is to have competing teams start on even footing on all known conditions except for skill." Many thanks for submitting your first article. I just have some questions/thoughts. 1) The passage above mentions a "material advantage". What "advantage" are you referring to? 2) How often did the captain winning the toss, win the game? In other words, the captain might have gained a "material advantage", but if the opposition won the game, does that advantage matter? 3) In the same passage, you talk about a fundamental requirement of sports that teams start on an equal footing in all areas but skill. You need to rethink this because this NEVER happens as there are so many variables that might favour one side or the other. Things like the temperature, humidity, the fact that one team is playing on another's home ground, that one team has had to travel, that in places like India, Australians would need to get used to the food and water ( and vice versa for the Indians of course), the size and shape of the grounds, the differing pitches that the home side plays on all the time and of course, the crowd. I'm sure there are other variables which mostly favour the home team, but these are all impossible to change so the teams start off on an equal footing. 4) Why do we need to make any change? I don't recall any international captain calling for a change in deciding who bats or bowls first? In other words, I'm trying to work out whether you're suggesting a fix for something that's not broken.
Arvind
Roar Rookie
Thanks Gavan. I agree with you that complexity should not be needlessly introduced. However, consider the following. 1. How would you deal with toss related advantages for elimination games in the world cup or in situations where each teams meets just once such as in the world cup league stages? 2. Even for test series, your proposal may only even out in the long run. The first test may have very significant favorable conditions, such as rain, that can be acted upon by judiciously choosing whether to bat first or to field first. The second test may not have the same material advantage for the toss (another e.g. first is a day night test and second isn't). So alternating coin toss wins may not adequately address the issue. The additional complexity introduced in the proposal attempts to provide a fair outcome for each individual contest.
Arvind
Roar Rookie
Thank you Marcus. I debated your suggestion myself before settling in favor of the fifth hypothetical as above. There are two considerations to my reasoning. ( A ) The fair value of two independent evaluations is likely to be closer to the average of the two evaluations than either of one of the evaluations is . This is why for e.g. the poll of polls, which averages across polls, is closer to the truth than any one poll. In that sense, the average of two teams evaluations for whats fair is probably closer to the real fair assessment of the value of the conditions. Put differently, two heads are better than one head (and a tail :) ) ( B ) Consider a situation where team A bids 31 runs to bat first and team B bids 1 run to field first. Settling at 0, and allowing A to bat first makes the settlement hugely in favor of A. The proposal is to have A bat first and award to B 15 runs ({31 - 1}/2). This seems fairer.
Gavan Iacono
Roar Rookie
Mad complexity. Coin toss 1st test. Rotate choice in subsequent tests. Consider a coin toss in final test of odd number of games series. Keep the coin and toss out the envelope.
Arvind
Roar Rookie
Thank you Presto. Your view is similar to that of other friends of mine. If you believe traditions of the gentleman's game must be left alone independent of whether it is good for the game or not, then theres no good argument to make any change to the game. Such a stance will obviate the inclusion of DRS, neutral umpiring, and the changes introduced to the traditions following Jardines introduction of leg theory. However, if you believe the tradition of the game includes a tradition of making changes towards fairness then there's potentially a debate to be had on what makes things fairer. Right now, the coin toss confers a statistically significant advantage to the team that calls correctly.
Arvind
Roar Rookie
Thank you Marcus for your input. I understand where your coming from and debated this myself before settling on the motivation for the fifth hypothetical as below. (A) The real fair value of a pitch is likely to be closer to the average of two independent fair evaluations than to either evaluation. (It's similar to an average of polls is likely to be closer to the truth than any one poll). By settling at the average we retain the above property. Put differently two heads are better than one head (and one tail. ????) (B) Consider a situation where team A wants to bat first and bids 19 runs. Team B wants to field first and bids 1 run. If we settle at 0 and let both teams get they want, it's very much settled hugely in favor of A. The proposal is to settle at (19-1)/2 or 9 runs for B who will field first. Thanks. Arvind