Originally posted on Fangraphs  |  Last updated 7/19/13

Chris Davis, with 37 home runs so far this season, has been generating a lot of buzz lately — both on the field and more recently with some comments he made during the All-Star break. When he was asked about the all-time home run record, Davis said: “In my opinion, 61 is the record, and I think most fans agree with me on that.” I have no idea if most fans agree with him, but it probably shouldn’t be  surprising that a guy within spitting distance of a 61 home run season would view that as the mark to beat — rather than 73 home runs, which is essentially out of range. So, just for fun, let’s figure out what Davis’ chances are of reaching Roger Maris. At Tom Tango’s website, there was a discussion that tried to put a number on Davis’ chances of reaching that mark. Tango performed a “quick back-of-envelope calculation” to do so, but today, I’ll be providing you with an interactive tool that might make it easy for you to perform a more sophisticated calculation for situations like this (and many other types of situations). Retracing my footsteps: Davis needs at least 24 home runs to reach or surpass 61. That’s the first entry that needs to be made, in the “number of successes” box. The next step is to enter the number of trials — in this case, plate appearances (PA).  Next to that box, you’ll enter your best guess as to the probability of the player getting that number of PAs. You can enter as many as 10 possibilities, or as few as one; just make sure the probabilities you enter add up to 100%. Repeat the same procedure for the “true rate estimate,” which for this exercise is home runs per plate appearance. For the assumptions I used, the calculator figures there’s only an 8.56% chance of Davis hitting at least 61 homers this season. But feel free to change the assumptions, either on this page or by downloading the spreadsheet. What is Davis’ True Home Run Rate? First of all, what is a “true rate?”  Well, for a fair flip of a fair coin, we intuitively know the true rate of heads is 50%. That doesn’t mean that if you flip a coin 100 times, it will come up heads 50 times; in fact, the binomial distribution that my calculator is based on says there’s only about an 8% chance of exactly 50 heads coming up over 100 flips. It also says there’s almost a 37% chance of the number of heads being at least five away from 50, after 100 flips. You can try that yourself in the calculator by entering “100″ as the number of trials, giving that a 100% probability, and setting “.5″ as the true rate (also at 100% probability), with “55″ as the number of successes (heads, in this instance). The answer box will say that there’s an 18.41% chance of getting at least 55 successes.  You can just double that number to get the chances that it will be at least five away from 50 in either direction. Davis is not a coin, unfortunately, which makes it a lot harder to intuitively pinpoint his true home run rate. If he were a coin, his true rate would probably be very close to zero, since coins are very bad at hitting home runs. Anyway, here are some of his particulars to consider: HR/PA 2013 to date .094 2012 .059 Steamer RoS .060 ZiPS RoS .062 Career .056 “RoS,” by the way, is the updated projection for the rest of the season for each projection system. Clearly, ZiPS and Steamer aren’t buying that he can  keep up this pace. For further context, the MLB leader in HR/PA last season was Josh Hamilton, at 0.068. Davis’ 0.059 was good enough for seventh in the majors. For my assumptions, I stuck pretty close to the ZiPS and Steamer RoS numbers that I believe to be the best guesses of his true ability — though I tried to err slightly on the side of, “He may have legitimately made a big improvement,” so the probability weighted average of my assumptions comes out to about .064. One factor you have to worry about is  pitchers may start pitching around Davis or intentionally walking him more often as his reputation grows, which will of course hurt his HR/PA. I haven’t done the research to project how that might affect him, but yeah, it matters. Projecting PAs Chris Davis has been regularly hitting in the fifth spot in the Orioles’ lineup. If that continues, he’ll have fewer plate appearance to work with than if he’d hit higher in the lineup. All else equal, getting fewer PAs would certainly hurt his chances at reaching the 61-homer milestone.  The Book says the five-spot in the American League gets 4.39 PA per game. That could use a bit of updating, though, since it was based on numbers from 1999 to 2002 seasons (basically the most offense-heavy era in modern baseball).  The 1999 to 2002 AL teams averaged .340 OBP; the 2013 Orioles have a .316 OBP. Clearly, there will be fewer PAs to go around when players aren’t getting on base. Some comparisons, which include the third lineup spot that Davis could hypothetically be moved up to: OBP PA per Game 3rd spot 5th Spot 2013 Orioles .316 4.39 4.16 2012 Orioles .311 4.45 4.25 1999-2002 AL .340 4.61 4.39 You may be wondering why the 2012 Orioles had more PAs despite a lower OBP than this year’s team. I think the most obvious explanation is that last year’s Orioles got into a ridiculous number of extra-inning games — 11.1% of their total games, compared to only 8.3% this year. Last year, the Orioles pitched 9.15 innings per game, compared to 8.91 this year. I looked at Baltimore’s double play and caught stealing numbers on offense to see if they also contributed, but it turns out they’ve actually improved substantially in the GIDP department this year: 1.58% of PAs this year vs. 2.47% last year. Anyway, the weighted average of my assumptions comes out to 253 remaining PAs for Davis this season, which means I expect him to average around 3.83 PAs for the team’s remaining 66 games. That’s the result of me unscientifically factoring in the chance that he’ll get some days off or get injured. Steamer and ZiPS are more pessimistic, figuring him for 199 and 241 PAs, respectively. Results As you see in the web app above, my assumptions predict an 8.56% chance of Davis reaching or surpassing that 61-homer mark this season. Here’s a more complete list of some of the other HR levels it expects for him: Davis’ Final 2013 HR Minimum Estimated Probability 51 67.5% 56 30.2% 60 11.4% 61 8.6% 62 6.4% 66 1.7% 71 .2% Thoughts I hope you’ll be able to get some use out of the web app here, since I think it has a lot of uses in baseball stats (and other things). Maybe I didn’t look hard enough, but the ability to account for uncertainty in your estimates seems like something other online binomial calculators you might come across online don’t have. If you’re wondering — yes, entering the whole distribution can make a big difference over simply using the weighted averages — using only the weighted averages of my assumptions would produce just a 3.43% chance of Davis hitting at least 61. Of course, there’s uncertainty within the uncertainty, especially with the assumptions I made in this exercise. These were just semi-educated guesses, without a ton of research put into them. As always, thoughts are welcome. I’ll be hanging around the comments section where I’ll attempt to answer questions.

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