Tie-breaker

In this week's column in our Insights newsletter, I wonder a bit about whether T20 matches really need tie-breakers. 

I’m not convinced there’s anything wrong with a tie. Why are we always trying to break them?

We left Friday’s T20 match between the Black Caps and India after the 16th over. New Zealand needed only 26 runs from 24 balls with plenty of wickets in hand. The WASP had New Zealand almost certain to win. It was well past 11 pm, and our 9-year-old was dozing off.

I read CricInfo’s commentary aloud to my rather more awake son and his friend as we walked to the car. Back at the stadium, the roars we heard from a crowd heavy with India’s supporters during the final over probably meant wickets rather than boundaries, as CricInfo eventually confirmed.

So they were off to another Super Over that would take the game to a too-familiar outcome, well past midnight. And we were off to get the kids to bed.

The drive home had me wondering about tiebreakers.

If both teams end a match with an identical score, is there any fair way of determining which side deserved to win?

Deciding a match on the number of boundaries tends to reward the flashier team over a patient one grinding forward on ones and twos. Is the former really better than the latter?

Equally, handing a win to the team with more wickets in hand says that it’s worse to run out of wickets than to run out of overs in a limited-overs game. Both are surely valuable, so why set the one above the other?

But going to a Super Over is plainly a mistake – not simply because of any recent and repeated unpleasantness. You might think that, because an extra over in a twenty-over game gives us 5% more information about which team is really the better one, it is a fair way of resolving a tie. But this format privileges the team with top-heavy talent over the side with talent spread across its order.

Ties are more likely to happen when both teams have comparable skill, so it is no surprise that picking a winner between them involves some arbitrariness. Worse, every method of choosing can skew the pitch.

Yet nothing in cricket demands every match have a winner or loser. We could just accept that both teams were equally decent on the night.

At least that's better than being forced to consider New Zealand’s performance in the Super Overs. 

I tend to run cricket stuff past Scott Brooker to make sure I'm not beclowning myself too badly as a relatively recent convert to the game. 

Scott had an excellent suggestion for a way of avoiding ties, should one wish to avoid ties. 

At the start of the second innings, flip a coin. The coin flip determines whether the chasing team needs to meet the defending team's score to win, or exceed that score. Both teams then have the full inning to chase or defend a known target. No chance of a tie. And nothing that skews play. I rather like it. If you don't want to allow ties.

And this idea also has merit:

Maybe the side that wins the toss should always has to have one more run than the opponent to win. The side that loses must only be equal to the opposition to win, thereby balancing the winner’s advantage in being able to decide whether to bat first or not.

— Russell Hutchinson (@russellhutchins) February 6, 2020

Is 400 the new 300 in ODIs?

The current ODI series between England and NZ has been quite extraordinary. England has scored more than 300 in every game, but has lost twice. Yesterday morning, New Zealand’s total of 349 was not only chased down by England, it was chased down with ease, with England losing only three wickets and having 6 overs to spare. 

My sense from my Twitter feed is that the conventional wisdom is as follows:

1. The rule changes dating from October 2012 (that saw two new balls in each innings and a reduction in the number of fielders allowed outside the circle in non-powerplays) allowed for larger scores, as the outfield gaps and still-hard balls allow batsmen to score at will in the final overs.
2. These rule changes coincided with new batting skills honed in 20-20 competitions like the IPL.
3.  New Zealand has been leading the way in showcasing an aggressive approach to cricket; England  prior to now has continued to play with an outdated conservative style, but has now belatedly accepted the new approach, in which “400 is the new 300”.

There is probably much right with this version of events, but I’m not fully convinced. Here are some raw numbers. Since the October 2012 rule changes prior to the current series between England and New Zealand, there were 177 ODI games played involving two teams from the top 8 (defined as the test-playing nations excluding Zimbabwe and Bangladesh), excluding games with a Duckworth-Lewis-Stern reduction in overs. Of those, 56 (or 31%) saw the team batting first score 300 or more. This is certainly a higher rate than we would have seen in past eras, but not as high as conventional wisdom seems to be suggesting. Moreover, getting to 300 still made the team batting first the overwhelming favourite. Of those 56 games with a first-innings score in excess of 300, the team batting first won 48 (86%). More pertinently, of the 18 games where the first innings score only just got to 300 (defined as a score between 300 and 310), the team batting first won 14, which is still a %77 success rate. If 400 is the new 300, it really should be easier to chase down 300 than these data suggest.

I wrote last year about how, once you adjust for mismatches between teams and where the game has been played, there wasn’t much evidence in the data for a general trend towards increasing first-innings scores. Taking all games from the start of the English 2002 season through to the end of the World Cup, controlling for team ability, home-field advantage, and the ground being used, first innings scores since Oct 2012 are only 12 runs higher on average than in the 10 years before Oct 2012. (For data geeks, I describe the exact model at the bottom.)

The following graph illustrates the lack of a trend. The small red dots are the difference between the first-innings score and a prediction based on the team batting, the team bowling, which team (if any) was playing at home, the ground at which the game was played, and allowing for a 12-run premium for the current rules. The solid red dots are a 25-game smoothed moving average, to take out some of the random variation and make any trends clearer. Although there appears to be a bit of an upward trend over the period since October 2012, scores by the end of this period were still only 28 runs higher than in the 2002-2012 period, suggesting that 328 is the new 300!

But now look at the four blue dots. These are the out-of-sample prediction errors for the first four ODIs between England and NZ in the current series. These predictions take into account England’s and New Zealand’s recent (since Oct 2012) batting and bowling form, England’s home-field advantage, and how high scores typically are at those four grounds. The prediction, actual score, and prediction error are as follows:

Ground	Predicted Score	Actual Score	Prediction Error
Edgbaston	235	408	173
The Oval	256	398	142
The Rose Bowl	269	302	33
Trent Bridge	232	349	117
Chester-le-Street	225 (Eng) 228 (NZ)	?	?

The point here is that rather than there having been a world-wide trend in the past few years that England have only now come to grips with; the current series has been extraordinary in every respect even in comparison to recent history. So what is going on? I can think of four hypotheses:

1. I have made a massive coding error in my database.
2. There has been a structural break in conditions: The four English groundsmen have produced very different pitches than in the past, ones much more favourable to high scores.
3. There has been a structural break in team quality: Both NZ and England have better batting and/or worse bowling in this series than they had in the recent past.
4. These four games have been black-swan events; and things will return to normal soon.
5. There has been a strategic mindset shift in both New Zealand and England.

When things look extraordinary, coding errors are always a good bet, and I wouldn’t rule this out, but the raw predictions don’t look too far out from my own intuition, so I  don’t think this is the problem here.

I can’t comment on whether conditions were very different from usual in the four games so far, but I haven’t seen any commentary from England suggesting that the groundsmen have been producing untypical pitches, so I suspect hypothesis 2 is not the right one.

There is probably some truth to hypothesis 3. I don’t think the batting is too much different, but the bowling is quite possibly weaker. New Zealand have lost Vettori, Anderson and Milne from their World Cup bowling line-up, and have had Southee and Boult together for only one of the four matches. England have rested Anderson and Broad. Even so, I would put my money on the final two hypotheses explaining most of the data. 

The idea that teams are not aggressive enough when batting is something Scott Brooker and I have been saying for a long time. Back when he was writing his thesis, Scott experimented with what an average team would be able to achieve if they applied the optimal level of aggression. Based on the strike rates and dismissal rates that we can observe batsmen having in different game situations (e.g. conservative batting in the middle overs versus aggression in the death overs), he constructed a set of frontiers describing the trade-off between risk and return for typical batsmen in positions #1-#11, and then simulated optimal behaviour. He found that scores could be roughly 30 runs higher if batting teams were more aggressive, but that there would be more variance in scores and a higher probability of not batting out the overs. This was based on data from before 2007. It is likely that under the new rules, the value of extra aggression is even higher. 

What I think we are seeing in the current series is two teams who keep pushing the boundaries of this approach, forcing the other team to react in kind, and so all kinds of previously unrealised potential that has existed for a while is now being revealed. Contrary to the conventional wisdom, I don’t think this has been New Zealand’s approach before now. Rather, I think they have emphasised retaining wickets during the middle overs in preparation for an all-out assault in the final 10. New Zealand’s famous aggression in the World Cup was mostly seen in its approach to bowling, putting an emphasis on wicket taking rather than containment.

If I am right, that there has been a mind-set change for both teams in the current series, I am mindful that Scott’s conclusion was that the additional 30 runs on average would come alongside a big increase in variance. This brings me back to the black-swan hypothesis. We have seen scores more than 100 runs in excess of what recent form would have predicted on average. It is likely that in each game, there was a degree of luck. Batsmen got away with taking risks on these occasions, but we could just as easily have seen scores that were quite low. Even allowing for the fact that dropped catches are more likely when batsmen are hitting the ball hard, the catching in the current series does seem to have been below par. Realistically, 370 might be the new 300, but equally 180 the new 200.

Method:

My prediction model was based on a database of all non-rain-affected ODIs involving the top-8 countries since May 2002, using only games played on grounds where there were at least 10 matches played (but also including Chester le Street, as that is the venue for the final ODI between England and NZ).

The model was an OLS regression of first innings score on a dummy variables for the batting-team country, dummy variables for the bowling-team country, a dummy variable for each of the 53 grounds, a dummy variable for when the batting team was playing at home, and for when the bowling team was playing at home. Finally, I added a dummy variable for matches played since Oct 2012, and more dummy variables for this recent-era interacted with the batting and bowling team dummies. 

These interaction teams mean that only post-Oct-2012 data is used to determine the effect of team ability on scores; the only reason for pooling the data with the pre-Oct-2012 era is to provide enough data to estimate ground effects. Essentially, the model is assuming that the relative impact on scores of being at a particular ground and the relative impact of home-field advantage has not changed from before the Oct 2012 to after.

In the 25-game  moving average shown in the chart above, the data is broken around the structural break of Oct 2012, so that the smoothed line before the break is not influenced by games played after the break and vice versa. 

Are the All Black Selectors biased against Canterbury?

This is a guest post by Scott Brooker.

Does the Canterbury rugby team's recent run of success suggest that the All Black selectors are biased against Canterbury players? I don't know. But it's certainly an interesting question. As a result of their away victory in the final against Wellington last Saturday night, Canterbury has now won six national rugby premierships in a row. The NZRU keeps changing the competition format on a regular basis, but at a minimum there have been seven teams who are in the top division and therefore eligible to win the premiership each year. These teams are generally strong, and one weak team at least has the potential to get relegated to the lower division in any given year. To win six championships in a row is an exceptional achievement. It's easy to conclude that Canterbury is simply a very strong team, but there are at least a couple of factors that should naturally assist with spreading the talent pool more evenly and therefore contribute to making it difficult for the same team to win year after year:

• The ITM cup is run at the same time as the best players in the country should be in the All Black environment. This can take as many as 30 players out of the ITM cup at any one time. The number of players who would be considered All Blacks who are playing in the ITM cup is few and decreasing every year. Very good players should be selected for the All Blacks, which should disproportionately hurt the chances of winning of the provinces with the better talent base.

• It could be argued that the above only affects the very top players, but there is another factor that affects the rest of the player base. It is reasonably common for players to shift to different teams from season to season. A common reason is to get more opportunity. If there are too many good players that play your position in your current team, you think about moving to a team that is weaker in that position, thereby weakening your former team and strengthening your new team. This generally occurs between seasons.

Neither of these factors would perfectly balance out the competition. But they would assist with increasing the probability of a different winner each year, and making six wins in a row very unlikely.

So what are the candidate explanations for Canterbury's consistent success? I can think of a few:

1. Pure luck. Although winning the title by luck alone six years in a row must be extremely unlikely.
2. As inferred in the title, perhaps All Black selectors are for some reason more reluctant to pick Canterbury players than players of similar ability from other provinces, which would  diminish the effect of the first bullet point above. They might require a longer period of good performance to be picked, or they may be ignored entirely. I'm not really suggesting that the All Black selectors sit there with their clipboards and put big red lines through player names simply because they play for Canterbury, but it is possible that Canterbury selects players with particular attributes (eg. Goal kicking ability, percentage of missed tackles etc) that contribute to success which are undervalued by the All Black selectors.
3. Canterbury is a fantastic place to live, which encourages players to stay here regardless of their selection opportunities. The counterpoint to this one would be that Canterbury has probably never been a more difficult place to live than it is currently.
4. Canterbury is no better than other teams in terms of individual player ability, but has a team culture that leads to a more cohesive style of play and helps the team to win more often. A counterpoint to this would be that with player movements between provinces, other teams have an opportunity to learn and improve their own team cultures.
5. Canterbury is no better than other teams in terms of individual player ability OR team culture, but has uncovered a secret formula for how to play in play-off matches. If we assume that the team that finishes top in round-robin play is likely to be the best team, then Canterbury has been the best team in only three of their six successes. In the other three successes, they played the top qualifier in the final and had to play the final away from home.
6. Referee bias in favour of Canterbury (unlikely as their performance is assessed).

What other possibilities are there to explain this run of success? With a well-designed framework, some of these are probably testable using variables including player movement rates, All Black selection rates and how long a player lasts in the All Blacks after initial selection. Any other ideas on how to distinguish these hypotheses in the data are welcome.

What If Lecture on Cricket

Last year, Eric presented a talk on alcohol in the University's What If Wednesday series. This coming Wednesday it will be my turn, talking about economics and cricket. The title is "What if...Economics could help cricket teams win matches?" I have blogged a bit about my work with students on various aspects of cricket in the past (click on the tag "cricket" to see all those posts).

On Wednesday, I am going to focus on how an economics-derived approach to the analysis of cricket can yield interesting analyses of on-field strategy. Specifically, I will be talking about an aspect of the work from Scott Brooker's doctoral thesis that I haven't blogged on previously--how we can estimate batter "production possibility frontiers" showing the tradeoff between risk and return for specific batsmen, and from that to suggest one explanation for why New Zealand has traditionally punched above its weight in ODI cricket.

The announcement and link to register for the lecture are here. I understand that the registration process can be a bit cumbersome as it seems like you are registering for a course, but it is free to attend and registering enables the University to ascertain likely numbers. (And to be honest, I haven't registered for the ones that I have attended.)

I hope to see as many loyal readers of Offsetting there as possible, conditional, of course, on your caring about cricket.

Move over Duckworth Lewis

Dr. Scott Brooker's scoring method for rain-affected cricket games, and his graduation, made the weekend Press.

Self-confessed cricket nut Scott Brooker has created an adversary to the complex cricket-target formula used when rain disrupts play.

Brooker yesterday graduated from Canterbury University with his PhD on "An economic analysis of ability, strategy and fairness in one-day international cricket".

It marked the culmination of four years' work that began with "a phone call out of the blue" from the university's economics department asking him to investigate alternatives to the controversial Duckworth-Lewis method.

...
"What the Duckworth-Lewis method does is calculate what the target score should be based on the time that is left to play," Brooker said. "I show the Duckworth-Lewis method is better than the other systems used for international cricket before, but it is still not perfect and it can still be improved."

Brooker said his system used a different criterion of fairness to adjust the target score, based on the probability of winning before rain disrupted play.

"If you have a 60 per cent chance of winning when it rained, the readjusted target score should still be that you have a 60 per cent chance of winning the game," he said.

Scott wrote under Seamus Hogan. So I hope someday to be as confused by sports reporting on the Brooker-Hogan method as I am by the Duckworth-Lewis method.