The newspapers here are full of news that the Pittsburgh Pirates (Major League Baseball) have broken a twenty-year reign of mediocrity by guaranteeing a non-losing season. Since they have won 81 games in a 162 game season, that seems self-evident.
But those of us in operations research know enough to check out the details before leaping to a conclusion. Consider the following situation:
1) The Pirates proceed to lose all their remaining games to end up at 81-81.
2) St. Louis and Cincinnati pass the Pirates, to win the division and the first wild-card.
3) Arizona ends up at 81-81 also, with all other teams (except division winners) with a worse record.
The Pirates would then play Arizona a one-game tie-breaker to determine who the second wild-card team is. Suppose (horrors!) they lose again. Where does the game count? It turns out that tie-breaking games count in the regular season records, as Wikipedia confirms. So Pittsburgh would end up 81-82, for another losing season. Note that it has to be a one-game tie-breaker: subsequent playoff games are not included in regular season records.
I don’t think anyone is losing sleep over this possibility. But a correct computer system for determining clinching of non-losing seasons would have to take this into account. Having worked on such a system for another professional sports league, I can assure you that all the difficulty is in these near (but not quite) impossible events. 99% of the code handles cases that have never occurred, and are unlikely to occur in our lifetimes.
Note that if Pittsburgh wins one more game, then they are guaranteed a winning season: a tie-breaker can’t turn their record into a losing (or .500) season.
Update 9/9: With the win tonight, the Pirates guarantee a winning season. Now the streak is truly broken! Go Bucs!
Please don’t mathematically analyze Cubs’ records in current or past seasons – that will be even more depressing than the Pirates’ history 😉
I like the idea that 99% of computer code handles exceptions. I’d love processes so thorough that they handle exceptions as good as a bug-free (or at least a less buggy) computer program.
And I’m still a Cubs fan, even if the analysis isn’t pretty.
so um when they win their next game all of this “work” you did becomes completely irrelevant. nice. cool blog post bro.
You can see my post in two ways: you can see it as specific to the Pirates, in which case the time-value of the post is indeed quite short. Or you can see it as a more general comment on the difficulty in determining things like clinching, elimination or guaranteeing a particular result in complicated systems. I prefer the latter interpretation: it lasts longer!