Jenks v. Webb: Which Feat is more Impressive?
On August 20th, Bobby Jenks' streak of 41 consecutive batters retired came to an end. Jenks streak tied Jim Barr for the Major League record. Currently, Arizona's Brandon Webb has pitched 42 consecutive scoreless innings. Both are tremendous accomplishments, but which is more impressive? To answer that question we'll look at the probability of each feat using the binomial distribution. For those that aren't as statistically inclined, the binomial distribution allows us to calculate the probability of getting a given number of successes over a specific number of trials with a probability of success of each trial. Confused? Think of flipping a coin. If we designate flipping heads as a success we could calculate the probability of getting X number of heads in Y number of flips without actually multiple sets of flips. On to the comparison!
First will look at Jenks:
Jenks' streak came against Cleveland, Boston, Detroit, Toronto, New York (A), and Seattle. To determine Jenks' probability to retire 41 consecutive batters, I used the teams' on-base percentage as a proxy for their ability of avoiding an out (thus getting on base). Using a weighted average to adjust for varying amounts of batters faced, the OBP of Jenks' opponents is .344. Setting that as the probability of success, I calculated the probability of running 41 trials (ABs) and getting zero successes (no baserunners). The result? 0.0000000302 (3.02ee-8).
Now let's look at Webb:
Webb's current streak has come against the bats of Baltimore, New York (N), Washington, Houston, San Deigo, Los Angeles, Colorado, and San Francisco. Again, we need the probability of success (in this case the probability that a team will score) and the event (an inning). To approximate this I averaged the teams runs scored per game. After some grueling spreadsheet calculations, I got 4.5. Taking that number and dividing by 9 I get a proxy for th probability of scoring a run in an inning. The probability of zero successes in 42 trials? 0.000000000000233 (2.33e-13).
The chances of both feats are essentially statistically impossible. Webb's is more so (about 100,000x) less likely.
First will look at Jenks:
Jenks' streak came against Cleveland, Boston, Detroit, Toronto, New York (A), and Seattle. To determine Jenks' probability to retire 41 consecutive batters, I used the teams' on-base percentage as a proxy for their ability of avoiding an out (thus getting on base). Using a weighted average to adjust for varying amounts of batters faced, the OBP of Jenks' opponents is .344. Setting that as the probability of success, I calculated the probability of running 41 trials (ABs) and getting zero successes (no baserunners). The result? 0.0000000302 (3.02ee-8).
Now let's look at Webb:
Webb's current streak has come against the bats of Baltimore, New York (N), Washington, Houston, San Deigo, Los Angeles, Colorado, and San Francisco. Again, we need the probability of success (in this case the probability that a team will score) and the event (an inning). To approximate this I averaged the teams runs scored per game. After some grueling spreadsheet calculations, I got 4.5. Taking that number and dividing by 9 I get a proxy for th probability of scoring a run in an inning. The probability of zero successes in 42 trials? 0.000000000000233 (2.33e-13).
The chances of both feats are essentially statistically impossible. Webb's is more so (about 100,000x) less likely.
posted by Epiphanic at
5:12 PM
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