May 7, 2015

# Making a 14-team World Cup work: a second look

Does a points system that takes into account the margin of victory involve too much math?

Recently, I proposed a format for a 14-team World Cup. The proposal was driven by two compulsions:

1. To ensure that literally every ball mattered.
2. To ensure that every team had a chance to give a fair account of themselves, and to make sure that one bad day did not result in a team being eliminated, while retaining the requirement that the eventual winner must successfully navigate knockout games.

The format achieved the first through the Performance Per Ball (PPB) system, which enables margin of victory to be measured. The format achieved the second goal with an expanded version of the Eliminator/Qualifier system used in the IPL. I've identified three broad points of criticism from readers:

1. The PPB incentives produce situations in which a winning team will receive fewer points than the losing team, or at least will allow teams that don't try to win to achieve better net PPBs than teams that do.
2. The PPB involves too much mathematics.
3. The Eliminator/Qualifier could result in the same match-up occurring multiple times in the Super Group.

PPB incentives:
The PPB system can perversely produce incentives for teams that preserve resources while risking defeat (for a team batting first) or ensuring it (for a team batting second). However, a situation in which a winning side scores a negative net PPB is mathematically impossible. The system is designed with the assumption that teams will always try to win. It is only when a win becomes impossible that they will make containment of the margin of defeat their primary focus.

Imagine a scenario in which a team has to ensure that its net PPB for a match is no worse than -0.500. Batting first, if the team makes 150 for 0 in its 50 overs, they would have to ensure that the chasing team used up at least 102 deliveries in reaching 151 for that chasing team to get a net PPB worse than -0.500. By contrast, if the team batting first reached, say, 300 for 5 and lost by one wicket off the last ball of the match, they would end up with a net PPB of -1.434.

Similarly a team that makes 150 for 0 in 50 overs in response to an opponent scoring 300 for 8 batting first would end up with a net PPB of -0.500. A team that tried to go for the runs and ended up 250 all out would end up with a net PPB of -2.204.

You can see why certain situations might encourage a team to protect its net PPB by preserving resources instead of risking resources to chase a win. Even though a team that tries to do this would probably be breaking a basic principle of sport (an example being the staged finish by Ferrari in Formula One at the 2002 Austrian Grand Prix, which suggests how controversial it is to lose on purpose in sport), it is worth preventing these situations.

Having tested and refined the PPB over the years, here are some of the results over 3502 ODIs that were won outright or ended in a tie.

1. The winning team in an ODI has never had a smaller PPB than the losing team.
2. Only eight winning teams (out of 1735) in ODI history have had a net PPB less than +1.00. The net PPB for a team is the difference between its PPB and that of its opponent on the day.
3. If we normalise the PPBs on a scale of 1, then the closest outright win was New Zealand's four-wicket win over Sri Lanka in Hambantota in November 2013. It was a rain-affected match in which Sri Lanka's first innings was terminated at 138 for 1 in 23 overs. New Zealand were set 198 to win in 23 overs. They got there after losing six wickets. They gained 58% of the normalised PPB.
4. Chasing teams rarely fail to win when they lose fewer wickets than the team batting first.

 Condition Wickets lost by team batting first Number of games Chasing team loses, having lost fewer wickets Any 111/1680 Chasing team loses, having lost the same number of wickets Any 227/1680 Chasing team loses, having lost more wickets Any 1342/1680 Chasing team loses, having lost up to 3 wickets (and fewer than team batting first)* 0,1,2,3 0/111 Chasing team loses, having lost fewer wickets 4, 5 4/111 Chasing team loses, having lost fewer wickets 6, 7 27/111 Chasing team loses, having lost fewer wickets 8,9,10 90/111 Chasing team loses, having lost the same number of wickets 10 172/227 Chasing team loses, having lost the same number of wickets 8, 9 35/227 Chasing team loses, having lost the same number of wickets 6, 7 18/227 Chasing team loses, having lost the same number of wickets 4,5 2/227 Chasing team loses, having lost the same number of wickets* 0,1,2, 3 0/227

*A team batting first has never finished its batting innings without losing a single wicket in an ODI, even in a match affected by rain.

In all but four ODIs in which the chasing team lost despite losing fewer wickets than the team batting first, at least six wickets fell in the first innings of the match. Of the 227 instances in which both sides lost the same number of wickets and the chasing team lost, in 172 cases both sides were bowled out.

If we disregard the first innings and consider only chasing teams, then the number of wickets lost by a team are an excellent indicator of its chances in the match. Chasing teams that lose five wickets or fewer win 97% of the time. Chasing teams that lose at least eight wickets lose 91% of the time.

All in all, the facts suggest that if a team is making a fair attempt to win an ODI, then the PPB system works very well. If a team isn't trying to win, then under the current rules, the ICC is supposed to step in and investigate. In the 1999 World Cup, when Australia chased slowly against West Indies to help West Indies' net run rate, it caused significant grumbling even though there was no question of Australia wanting anything other than a win.

I propose to make a simple modification to the PPB system. Any team that loses a match will be deemed to have been bowled out for the purpose of the PPB calculation. So a match that reads:

Batting first 280 for 0 in 50 overs
Batting second - 281 for 8 in 49.2 overs
will be considered as:
Batting first - 280 all out in 50 overs
Batting second - 281/8 in 49.2 overs.
The net PPB for the losing team will be -2.088 instead of -0.001.

Batting first - 300 for 8 in 50 overs
Batting second - 150 for 0 in 50 overs
will be considered as:
Batting first - 300 for 8 in 50 overs
Batting second - 150 for 10 in 50 overs.
The net PPB for the losing team will be -3.227 instead of -0.5

PPB involves too much mathematics
In its most common form, this objection is that the arithmetic is too complicated for people to follow. The existing arithmetic - 2 points for a win, 1 point for a tie or no-result, and 0 points for a loss, is much simpler.

The preference for this system is mainly due to some measure of moral comfort that a losing team gets no points, while a winning team gets all the points. The idea that a team should get points for losing understandably bothers a lot of people.

In fact, the 2-1-" system does not mean that a losing team gets no points. It only means that the losing team gets two points fewer than the winning team. Other properties of zero (division by zero for example) are irrelevant.

The 2-1-0 system contains exactly two propositions:

1. A win is worth two points more than a loss
2. A tie or no-result is worth one point more than a loss, and one point fewer than a win.

The following points systems are identical:
1. Two points for a win, one point for a tie or no-result, and 0 points for a loss.
2. Five points for a win, four points for a tie or no-result, and three points for a loss.
3. One hundred and one points for a win, 100 points for a tie or no-result, and 99 points for a loss.

Each would produce an identically ordered points table at the end of the league, maintaining the exact same distance between the teams. By distance, I mean the results required by a team to overcome a gap between itself and any team above it in the table.

More generally, any points system (Win: A, Tie/NR: B, Loss: C), such that A-B = x and B-C = y would be identical in cricket for any given numbers x and y as long as x and y are both greater than zero. The actual values of A, B and C are not significant.

X and y are basically net-PPB like values. Except, instead of actually measuring the margin of victory, it is predetermined to be +2 points per win.

The 2-1-0 points system, which looks simple, contains substantial assumptions. For one, it necessarily means that everything that happened in the game is irrelevant, and tells us nothing about the performance of the competing teams once the final result is known. Whether a team won by eight wickets with 18 overs to spare, or by one wicket with two balls to spare, is irrelevant to fairly measuring the performance of the teams in the match. Not only is 2-1-0 not simple, it is more arbitrary than the PPB system. The morality of the zero is an illusion.

The same match-ups could be repeated in the Super Group
This is possible. But I view it as a feature and not a bug. If a match-up is repeated, it suggests that among the top six teams, the two who are playing each other again are closer to each other in terms of quality than they are to any of the other four teams. This should not be a problem. Would watching New Zealand play South Africa twice, or India play Australia twice in the 2015 World Cup's final phase have been boring?

I hope I've addressed the major concerns raised to my original proposal. I thank readers for their comments. I welcome further comments as usual.

Kartikeya Date writes at A Cricketing View and tweets here