Will Chipper hit .400?

Almost certainly not, no. But, let’s do some math and have fun.
The minimum number of plate appearances (at bats, walks, hit-by-pitches, bunts, sac flies, and defensive interference) to qualify for the batting title is 3.1 per game, or 502.
Let’s start by assuming that Chipper gets exactly 502 PAs. He’s walking/getting hit/sacrifice flying (Chipper don’t bunt) at about a 16% clip. His career average is a hair above 14.3%, but he’s only had a yearly average below that once in the last decade, and that was his injury plagued 2006 campaign. But whatever, no shenanigans here, we’ll call it 14.3%. That’ll knock it down to 502*0.857 for a total of 430 at bats.
With 430 at bats, Chipper would need exactly 430*.400 = 172 hits. At this point, he already has 79 hits 188 at bats, so really he just needs 93 hits in his next 242 at bats, a cool .384 average. Now comes the fun part. What are his chances of hitting that?
Well, that all depends on what you think his true average is. Using the cumulative distribution function for a binomial distribution (yes, I knew how to do this without looking anything up, I’m a nerd) we can plug in the expected probability of a discrete event (getting a hit) over a number of trials (total remaining at bats) and find the percentage of time the number is below a certain amount (number of hits needed).
Basically, plug this code into Excel and watch the answer pop up “=1-BINOMDIST(**hits**,**at bats**,**true average**,TRUE)” So, if we assume his true average is 400, since we need him to get 93 hits in 242 at bats the code is “=1-BINOMDIST(93,242,.400,TRUE)” and the result is: 66.62% of the time he hits .400.
But, of course, his true average isn’t .400. So what is it? Well, I guess that’s where this gets a little more fun. Is true average equal to his career average of .310? He’s been improving lately, so is it the .324 he hit two years ago or the .337 he hit last year? Maybe we can continue that improvement and assume .350? Maybe it’s .364 since, as ESPN points out, “over the past year, he has had only one month when he’s hit lower than .364.” As crazy as it sounds, it could even be .376, which is his total average over the past 12 months.
Not only will the true batting average change the result, but so too will the total number of plate appearances. It’s a lot easier to hit 93 times in 242 at bats than it is to hit 206 times in 514 at bats. If we assume 600 total plate appearances, that last set of numbers is what he would need to accomplish.
So, all that being said, here’s the chart I mapped out with Excel to look at Chipper’s chances. His “true” batting average is on the left, and his total plate appearances are on top.
| 502 | 525 | 550 | 575 | 600 | 625 | 650 | |
| .310 |
0.58% | 0.39% | 0.20% | 0.12% | 0.09% | 0.06% | 0.04% |
| .324 |
2.02% | 1.51% | 0.92% | 0.63% | 0.53% | 0.36% | 0.31% |
| .337 |
5.33% | 4.33% | 2.96% | 2.24% | 2.03% | 1.54% | 1.40% |
| .350 |
11.83% | 10.28% | 7.76% | 6.38% | 6.07% | 5.02% | 4.78% |
| .364 |
23.40% | 21.49% | 17.72% | 15.65% | 15.46% | 13.70% | 13.55% |
| .376 |
36.78% | 34.99% | 30.65% | 28.33% | 28.56% | 26.49% | 26.72% |
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