## Luck

I thought I'd simulate a double-round-robin tournament with eight teams, to model the IPL. So Teams A to H each play 14 games. Here is the final ladder, ordered by number of wins:

C: 10
F: 10
B: 9
G: 7
H: 7
D: 6
A: 4
E: 3

Team E'll be looking for a new coach — only three wins out of fourteen.... Anyway, as the title of this post will suggest, the result of each match was decided by a (virtual) coin toss. The point here is that if all teams are perfectly evenly matched and results come down to the luck of the day, you'll still end up with teams at the top of the ladder having much better records, over 14 matches, than the teams at the bottom.

Now of course there is skill involved in cricket, and some teams in the IPL are better than others. But can we tell which team is the best just from the results? Probably not from just one season (unless they put in a really dominant performance — lots of wins, by big margins). And more importantly, it'll be impossible to say how good each team actually is. To explain this point, I'm going to borrow the notation from American sports (since that's how I think of it in my head — much of what I write here can be found somewhere in the archives of this blog and this blog). A .500 team ("five hundred") is a team that wins 50% of its matches. A 0.600 team wins 60%, and so on.

To work out if a team is really a .600 team (say), you'd need an infinite number of matches to prove it. Of course, we could get by with a large number — just how large depends on how much luck is involved in each game. The problem with T20 is that we don't know how much luck there is. So we're going to be fumbling around in the dark somewhat — once we've had a few seasons (to get enough data), we'll be able to look at the win-loss records of the teams and see if the how much greater the variance is than that expected by chance.

I worked out some numbers for ODI's and Tests here; T20 will have more luck involved than fifty-over cricket, but the IPL complicates things as the foreigners are dominant, and there's only four of them per side. If the long-term variance in win percentage is the same in the IPL as it is for ODI's (a big if), then you'll need each team to play about 17 or more games before the skill will demonstrably be playing a part in the results.

One season of IPL isn't going to be enough. In the coin-toss example above, every team was a .500 team. Only G and H ended with .500 records. Teams above them were lucky, teams below (especially E) were unlucky.

If we look at the IPL table today, Rajasthan are at .833. Are they genuinely an .833 team? They could be. Or they could be a .900 team that happened to lose one of their first six matches, or a .500 team that's had a bit of luck.

Let's not forget, Zimbabwe beat Australia not long ago in a T20 game. We should expect bad teams to win matches. And sometimes, mediocre teams will string together a few wins on the trot. Conversely, good teams will lose some. Does anyone really believe that Deccan (Gilchrist, Afridi, et al.) is a .167 team?

One way of seeing how much skill is involved will be to compare the first half of the tournament with the second, and see what correlation there is. Unfortunately, the coming and going of lots of big stars will make this really muddy, but I'll still do it at the end of the tournament.

So my message is, don't read too much into individual results. Don't say that the team on top of the ladder is the best simply because they're coming first — they might be the best team, but they might just be lucky. Go and read this excellent piece by Lawrence Booth at Cricinfo.

Have to say I agree with your post and have thought of similar things (and tried out the coin toss example on my own) several times.

However, I have found, by logic and testing, that the "luck" factor is much lower in cricket than it is in other games, most notably football.

For example, how often can we expect a team like Bolton or Reading to beat a team like Liverpool or Arsenal? Man United lost to teams like Stoke, Bolton, Southend, Portsmouth, West Ham recently. Chelsea lost to Cardiff (was it?)

The point is, we can expect such results in football every now and then. But can we expect such results in cricket very often? When Australia or India plays Namibia or Scotland (or even Kenya or Ireland), do we really "expect" an upset?

Arjwiz, in general I agree that there's less luck involved in cricket than in some (most?) other sports. But there are a few factors at play, one of which I perhaps should have mentioned in my post. That is the talent distribution. The gap between Australia and Namibia is so huge that you only need one game to work it out, cricket being the way it is. It's hard to say exactly what the football equivalent is (Man U v a third division side?), but yes, the weak team can play a 10-1 and scrape out a draw or something. You'd need a few games to work out which is the stronger team, even if the two sides are mismatched.

But if you have a relatively narrow talent distribution, then it changes. Amongst the top eight cricket nations, the worst recently has been the Windies, and they still win about a third of their ODI's. The luck factor in Test cricket is even smaller, of course - only for teams close to each other in strength do you really need more than a three-Test series to tell them apart.

The IPL should have a talent distribution that looks more like Australia-to-Windies rather than Australia-to-Namibia (if the bidding had been uniformly good, it would be even narrower than that). And T20 being the way it is, the results should be even more evened out.

luck do play part in sport...

i also agree that t20 narrows the gap of skill to the level that even zim can beat oz...

but can they do it consistently is the question...? no...

so the team who is wining 'consistently' with different teams...seizing the initiative at crucial moments cant be just lucky everytime...

In agree DB to a large extent. But you would have to agree that at the end of the day the teams that have played better cricket have won. As Nesta has pointed out in his latest post the batsman with the better technique / hand-eye coordination have done better than others. Same for bowlers who have varied their line and length.

Luck is definitely involved but we can still say that Rajhastan have looked like the best team because they have played better and smarter cricket than others.

While Bangalore and Mumbai have played poor cricket.

Q, I think you're confusing the teams that play "better cricket on the day" with the "best cricket teams". The team that plays the best cricket on the day will usually win. Teams that win usually look good, and teams that lose usually look bad.

If the teams are evenly matched, then the team that plays best on the day looks a pretty random thing.

Hmm.. I would say Rajhastan are the best team in the IPL because they have played better and smarter cricket than the others.

There is a difference between a team looking strong on paper and actually perorming well in their roles.

Holds true for tests, ODIs, and T20.

I hope I haven't confused it further..

I agree that the best team on paper is not always the best team. When I refer to the best team, I'm talking about the team that would win the most matches in a suitably long tournament (that might be fifty or a hundred games each).

But by now whats happened in the IPL would tell you who would win more games than others?

Did Warne get lucky against Symonds with those 17 runs or did he bat outstandingly? or did Symonds bowl poorly?

But by now whats happened in the IPL would tell you who would win more games than others?
To some extent yes, but not a lot. I'm far from confident that Rajasthan are the best team in the IPL and that Deccan are the worst. They might be, and if all you had to go on were the results so far, then you'd say that, of all teams, it's most likely that Rajasthan are the best and Deccan the worst. The difference between first and fourth (and fifth and eighth) is only one win in six matches.

The luck involved in cricket results is spread out randomly in games. An LBW decision here, a lucky slog there, a scrambled seam luckily biting on the pitch, etc. Or a bowler just having a rare good day and bowling an excellent length. All sorts of little events can turn matches.

Well I agree with the luck factors involved here and there but after 7 games each, I can say Rajhastan are the best team in it. So far they have played the best cricket out of the lot.

It may change over the 2nd half but till now, they do look like the best.