Instant Replay and the 1985 World Series
Imagine it's the seventh game of the World Series with two outs in the bottom of the ninth inning. There's a runner on first base with the home team trailing by one run. The game is being played at Minute Maid Park in Houston with all its outfield nuances.
The Houston batter drives the ball toward the wall in deep left-center field. If it hits to the left of the line drawn on the outfield wall, it's a two-run home run, walk-off victory and World Championship for the Astros. If not, it's a possible tie game. The ball rockets off the wall near the line. To the umpire, it appears to hit right of the line, so the ball is ruled in play - a ruling that might become the biggest umpiring mistake in baseball history. The outfielder fields the ball quickly off the wall and fires it to the cut-off man. The relay throw comes to the catcher as the base runner heads home with the potential tying run. It's a close play, but the runner is clearly out for the final out of the game! In an instant, the visiting American League team has just won the World Series! Or did they?
Was it to the left or the right of the line? During the lengthy conference, TV replays in slow motion show that the ball did indeed land inches left of the line for what should have been ruled a home run! The Astros should be celebrating their championship! Now the crowd is screaming at the umps to reverse the call. The TV coverage shows it again, and again, and again from every possible angle with the same result. The crowd gets more and more hostile. Finally, the head umpire emerges from the huddle with clenched fist in the air, indicating the runner is out at home plate and the call stands. All hell breaks loose...
One can only imagine the bedlam this scenario could create. The outcome of the World Series would be completely decided by a blown call. Increasingly, it seems officiating is coming into question in major American sporting events. The Super Bowl saw a series of non-reviewable calls go the way of the Steelers that helped them win the NFL title. Likewise, the MLB playoffs and World Series saw a number of controversial calls, most notably the A.J. Pierzynski dash to first. Less controversial was a home run in Game 3 of the World Series, similar to the one described above, in which a ball scorched by Jason Lane actually hit to the right of the line but was ruled a home run for the Astros. Luckily for the umpires, the White Sox eventually won that game, and their blown call didn't affect the outcome. These situations always take me back to the 1985 World Series between the Cardinals and the Royals, and the "safe" call at first by umpire Don Denkinger. It is arguably the most crucial blown call in the history of baseball. More than twenty years later, Cardinals fans still claim their team would have won the Series if Denkinger made the correct call. Royals fans claim it was destiny regardless of the blown call. Clearly it didn't affect the outcome 100% like the scenario above, but it was certainly significant. I recently set out to try and quantify the impact of the blown call. You might be surprised at my conclusion.
The probability of the Cardinals winning Game 6 following Denkinger's blown call (assuming a 50% chance of winning an extra inning game) is then: X0 + 0.5*X1 = .5750 + 0.5*.1833 = .6667. And the probability of the Royals winning Game 6 is therefore 1 - .6667 = .3333.
The probability of the Cardinals winning Game 6 if Denkinger had made the correct call is: Y0 + 0.5*Y1 = .8420 + 0.5*.0915 = .8878. So the probability of the Royals winning Game 6 is 1 - .8878 = .1122.
Denkinger's call therefore effectively tripled the Royals chances of winning the game from .11 to .33.
Of course, this is assuming Todd Worrell and the Cards' defense gave up runs at the league average for the 1985 season, and that the Royals scored runs at the league average. This was actually not the case. The Royals' offense was less than ordinary, scoring 4.24 runs per game versus the major league average of 4.33 runs per game - roughly 2% below average. Meanwhile, the Cards' defense was best in the majors in 1985 thanks to Gold Glove winners like Ozzie Smith, Andy Van Slyke, Willie McGee, Terry Pendleton and Joaquin Andujar. Combined with their exceptional pitching, the 1985 Cardinals allowed 3.53 runs per game, 2nd best in the majors and 18% better than the league average. Assuming a stingier Cardinals run prevention pattern against the Royals by 20%, the probability of a comeback in Game 6 following a correct call would be .0898 instead of .1122.
I would also contend that the blown call created doubt in the Cardinals minds and uplifted the Royals hopes, resulting in more advantageous odds for the Royals. This hopefulness combined with momentum and home field advantage for the Royals would result in greater than a 50% chance of winning an extra inning game, and a greater than 50% chance of winning Game 7. Let's say both odds are .60 instead of .50. And let's say that the blown call reduced the Cardinals to mere mortals, at the league average in preventing runs. These are reasonable assumptions considering the Cards unraveled in Game 6 after the blown call, and continued that trend in Game 7, losing by a score of 11-0. And since the objective is not merely to win Game 6, but to win the World Series, let's redo the analysis to see the total impact of the call. The chance of the Royals winning both Game 6 and Game 7 if the correct call were made is:
P(winning Game 6)*P(winning Game 7) = .0898*0.5 = .0449
In comparison, the probability of the Royals winning both Game 6 and Game 7 following the blown call is: (1 - (X0 + 0.6*X1))*0.6 = (1 - (.5750 + 0.6*.1833))*0.6 = .1890.
This revised analysis indicates that Don Denkinger's call made a significant difference in the outcome of the 1985 World Series, allowing the Royals to improve their chances more than 4-fold, from a mere 4% chance of winning it all to a more encouraging 19%. In reality, the call at first base opened the door from a crack to ajar, and to their credit, the Royals were able to take advantage of their good fortune. Regardless, the odds are 4 to 1 that the blown call changed the outcome of the World Series. If instant replay were used to make the correct call, the chances are greater than 80% that the Cardinals would have won the World Series instead of the Royals.
Ross Roley is a lifelong baseball fan, a baseball analysis hobbyist, and former Professor of Mathematics at the U.S. Air Force Academy.