Thursday, January 30, 2014

Net Run Rate in Cricket and Simpson's Paradox

Here's what happens when a football fan with an understanding of numbers and a passing interest in paradoxes turns his mind to cricket. (I'm sure something similar was possible when goal average was used as a tie-breaker in football, before goal difference became the preferred method.)

Imagine a typical eight-team cricket tournament, where the teams are divided into two groups of four, and the top two teams in each group progress to the semi-finals. Final placings in each group are decided by points gained (two points for a win, one point for a tie or no result) with the first tie-breaker being net run rate.

After two rounds of matches in one of the groups, these are the results.

North 250/4 off 50 overs defeated South 230/8 off 50 overs by twenty runs.
East 101/2 off 14 overs defeated West 100/10 off 22.3 overs by eight wickets.
East 205/7 off 44.3 overs defeated North 200/10 off 47.1 overs by three wickets.
South 160/10 off 31.2 overs defeated West 150/10 off 46.4 overs by ten runs.

Remembering that when a team is bowled out it counts as fifty overs batted, and that the decimal equivalent of 44.3 overs is 44.5, at this stage, the points table is as follows:

M W L P RS OB RRF RC OF RRA    NRR
East 2 2 0 4 306 58.5 5.231 300 100 3.000   2.231
South 2 1 1 2 390 100 3.900 400 100 4.000 -0.100
North 2 1 1 2 450 100 4.500 435 94.5 4.603 -0.103
West 2 0 2 0 250 100 2.500 261 64 4.078 -1.578

(M = Matches, W = Wins, L = Losses, P = Points, RS = Runs Scored, OB = Overs Batted, RRF = Run Rate For, RC = Runs Conceded, OF = Overs Fielded, RRA = Run Rate Against, NRR = Net Run Rate)

After two rounds, South and North are tied on points, but South are ranked narrowly ahead of North as the result of their better net run rate.

The third round of matches is then played, with the following results.

West 295/6 off 48 overs defeated North 294/4 off 50 overs by four wickets.
East 129/9 off 47 overs defeated South 125/10 off 21.3 overs by one wicket.

East now have three wins and therefore win the group.

West have joined North and South on one win, so net run rate will determine which of the three teams will finish second and progress to the semi-finals.

In this last round of games, West’s net run rate is 0.266, bringing their average net run rate over the three matches to -1.186. This will see West finish last in the group.

In the third round, South’s net run rate was -0.245, slightly better than North’s -0.266. South were already ahead of North on net run rate after two rounds, so one would expect that South would finish above North in the final standings.

But no! Amazingly, the overall net run rate for South is -0.165 while North’s is slightly better at -0.163. So even though South had a better net run rate than North after two matches, and achieved a better comparative net run rate in the third round, North finish with a better net run rate overall and progress to the semi-finals.

M W L P RS OB RRF RC OF RRA    NRR
East 3 3 0 6 435 105.5 4.123 425 150 2.833   1.290
North 3 1 2 2 744 150 4.960 730 142.5  5.123 -0.163
South 3 1 2 2 515 150 3.433 529 147 3.599 -0.165
West 3 1 2 2 545 148 3.682 555 114 4.868 -1.186

This is an example of Simpson’s Paradox and shows how adding and averaging numbers can be fraught with peril.

What if instead of combining the scores from the three matches and then doing the net run rate calculation, we calculated each team’s net run rate compared to their opponents for each individual match and then added these together to create the NRR?

North’s run rates compared to their three opponents were 0.400, -0.607 and -0.266 for a combined total of -0.473.
South’s run rates compared to their three opponents were -0.400, 0.200 and -0.245 for a combined total of -0.445.

M W L P RS OB RRF RC OF RRA    NRR
East 3 3 0 6 435 105.5 4.123 425 150 2.833 6.066
South 3 1 2 2 515 150 3.433 529 147 3.599 -0.445
North 3 1 2 2 744 150 4.960 730 142.5 5.123 -0.473
West 3 1 2 2 545 148 3.682 555 114 4.868 -5.149

So using this method, South would finish above North.


My personal feeling is that this is a fairer method of calculating net run rate and more accurately reflects the reality of what happened during the three matches. It certainly does a good job of depicting the thrashing East handed out to West in the first match.

It may also have some negatives I haven't thought of. Perhaps some statistical experts could provide their input.



Wednesday, January 15, 2014

Corruption throughout his Presidency, but Blatter thinks he's the man to steer FIFA, and who has the courage to stop him?

I recently came across an article on FIFA's own website, dated 29 January 2003, which if it weren't so sad, I would find quite funny. It is an interview with then recently-elected FIFA General Secretary, Dr Urs Linsi, and his answer to the first question is particularly ironic.

Partly it states: "In the first six months of 2002, FIFA attracted too much negative publicity, but this changed during and after the FIFA World Cup™ as we delivered a perfect tournament. In the last six months of the year, everything calmed down, both inside and outside FIFA, and we proved that FIFA is a healthy, clean and transparent organisation with nothing to hide."

Yes, you read that correctly.

FIFA proved it is a healthy, clean and transparent organisation with nothing to hide.

This was in 2003, remember, five years after Sepp Blatter was elected President, three years after the final illegal ISL payments were made to Joao Havelange, Ricardo Teixeira, Nicolas Leoz et al. (Sepp Blatter has now admitted he knew about a 1.5 million Swiss Franc payment to Havelange in 1997, although he feigned ignorance when asked about it by Andrew Jennings and did not divulge it to anyone) and a little over ten years before a slew of FIFA ExCo members were banned for various transgressions involving corruption and/or unethical behaviour.

Here's another quote from the Linsi interview: "There is huge public interest in FIFA, therefore we have to be as transparent as possible. We will try to communicate in a more open way concerning football matters so the world can believe us and be proud of their federation."

How did that work out? There is still a clamour for fairness, transparency and accountability, and it is only recently that Sepp Blatter has begun to even pretend to address this problem. Here we are, eleven years on, and the same old problems still exist. And everyone at FIFA knows and has always known that it is corrupt.

There is a telling comment by Tongan former FIFA ExCo member Ahongalu Fusimalohi in the transcript of his 2011 Court of Arbitration for Sport case against FIFA:

"351 Ahongalu Fusimalohi: It has to be strictly confidential.
352 Reporter: I just got the impression that to a certain extent the whole organization works like
that.
353 Ahongalu Fusimalohi: Yes. It just, I mean, the eleventh commandment of the CIA, just don’t
get caught, don’t get caught, that’s it."

Not surprisingly, the CAS found, amongst other findings:

"130. On the basis of the evidence before it, the Panel is of the view that the Appellant
realized that he was offered some significant money in exchange for an improper
and shady lobbying activity. In spite of this awareness, the Appellant set out the
conditions under which he would assist Franklin Jones. The attitude of the
Appellant throughout the whole Auckland Meeting clearly establishes that his
collaboration with the alleged lobbyists was linked to the personal profit he could
make.
131. In short, the Panel is comfortably satisfied that a gift or other advantage was
offered to the Appellant and that, accordingly, the first requirement of article 11
para. 1 FCE is met.
b) Incitement to breach duty or behave dishonestly for the benefit of a third
party"

I'll write more on this case soon in another blog post about the 2022 World Cup hosting bidding process.

So there we have it. Years and years of unbridled corruption and unethical behaviour, known by FIFA and Sepp Blatter, Illegal payments he knew about but did not divulge, and numerous ExCo members banned for illegal and unethical behaviour, and based on the comments of Fusimalohi above, these are the ones who were stupid enough to get caught.

And this man, Sepp Blatter, wants us to believe that he is the man to steer the FIFA ship through the stormy waters.

And in case you are tempted to think that Urs Linsi was speaking just for himself - he was, after all, fired from his job in 2007, shortly after Vice-President Julio Grondona had negotiated an expensive new contract for him - take note also that Linsi himself said in his interview: "Communications is now directly linked to the President, because FIFA should speak with one voice." It is hard to believe that Blatter would let this interview make it all the way to the FIFA website if it were not an accurate reflection of the organisation's views.

Blatter has been FIFA President for sixteen years, knowing full that the organisation was corrupt before he took on the role and has been corrupt ever since. He even manoeuvred to prevent his only opponent in the last election, Mohammed bin Hammam, from standing, by getting him banned.Yet the man still has the balls to tout his record on reform and has hinted that he might stand for election again.

And he might succeed too, because although he cannot be attired with the epithet 'Teflon', plenty of mud having stuck to him, he has survived due to the lack of courage of the people who can vote him out, namely the National Associations who are too scared to nominate another candidate. They know that should their nominee lose to Blatter,  the nominating association would be sure to feel Blatter's wrath in terms of reduced funding for GOAL Projects, cash grants, hosting opportunities, promotions, and the like.