Blogtrek

Borderline Plays

The post-season baseball play is starting to become interesting. The Chicago Cubs have not won a World Series since 1945, and the Boston Red Sox have not won any since 1922. Further, I was near Chicago, studying for my doctorate in mathematics, in 1969 when the Cubs led most of the way, only to falter to the Mets near the end of the season. So I started looking at the games. To me the most interesting plays are the borderline plays.

These are plays that are close to the borderline to being other plays. An example of what I mean is a batted ball that bounces just along the left foul line and stays fair. This could be a single. Just a little bit, an epsilon (mathematicians use this Greek letter to denote a small quantity) to the left and it's a foul ball. A single and a foul ball have vastly different effects on the game. So this is a borderline play. In this case the border is physical: the foul line. On the other hand, a long fly to center is caught by the center fielder. If it veers in any direction about a foot way from this, the center fielder would still catch it. So this play is "in the middle", and is not a borderline play.

There have been several borderline plays in the pennant playoffs. One Yankee hit a long fly ball that was caught at the fence by one of the outfielders for an out. A little epsilon higher, and this Yankee would have had a home run. In another case, with bases loaded and one out, a grounder was hit to the shortstop, who threw to second baseman, who threw to first. The throw to second resulted in an out, but the throw to first was just a microsecond too late. A run scored, nearly tying the game.

The biggest one happened though on the night of 2003 October 14. The first batter flied out, and the second (Pierre) doubled. Castillo hit a foul ball right on the boundary of the stands. Into the stands, and it's a foul ball, a strike. Within the ballpark, if fielder Alou could catch it, it's an out. Alou just barely made the catch, only to have a fan strike the ball and deflect it away. The result was an eight-run Marlin outburst. Here is the play by play:

Flyout 000 (0) 1
Double Juan Pierre 010 (0) 1
controversial foul ball deflected by fan
Castillo walk 110 (0) 1
Wild pitch advances Pierre 101 (0) 1
Rodriguez singled in run 110 (1) 1
Cabrera grounder errored by Gonzalez 111 (1) 1
Derrek Lee double scores two 011 (3) 1
Lowell walk intentional 111(3) 1
Conine sacrifice fly 011 (4) 2
Hollinsworth intentional walk 111 (4) 2
Double Mordecai scores all the runners 010 (7) 2
Pierre single scores Mordecai 100 (8) 2
Castillo popped out 100 (8)

My notation 010 (1) 2, for example, means no runner on first, a runner on second, no runner on third, one run scored in the inning, and two out. Now what would have happened had Alou caught Castillo's ball?

Flyout 000 (0) 1
Double Juan Pierre 010 (0) 1
Castillo fouls out to Alou 010(0)2
Wild pitch advances Pierre 001 (0) 2
Rodriguez singled in run 100 (1) 2
Cabrera grounder errored by Gonzalez 110 (1) 2
Derrek Lee double scores one 110 (2) 2
Lowell walk intentional 111(2) 2
Conine flyout ends inning 111 (2) 3

Now the Marlins score only two runs, and quite likely the Cubs would have won the game. But is that so? How do we know the Marlins would then be scoreless in the ninth and the Cubs in the eighth? Here the butterfly effect occurs. If there are a lot of borderlines, the system becomes unstable and unpredictable. The stepping on a butterfly in Brazil can cause a tornado in Texas. For that matter, would Lowell have been walked if the fan had not interfered? With runners on first and second, two out, there is a play at any plate. What advantage is there in getting one at home, too? If Lowell had been pitched to, then maybe he would have hit and scored runners, and the Marlins would have won anyway.

So if you tiptoe over the borderline, the whole universe goes awry and may not seem what you think. In particular, it is not necessarily true that the fan's interference with the ball lost the Series for the Cubs.