# What's more likely, Pedroia hitting 100 HRs or me winning the lottery?

Dustin Pedroia started off the season by hitting 2 homers in the first game and I was joking with a coworker that Pedroia was going to hit 100 HRs this season. Then we tried to compare it to the likelihood of me winning the Powerball. The odds of me winning the Powerball is ~ 1:175M (per wiki). Nobody has (yet) hit 100 HRs but it is conceivable. How would you try to compare the odds?

Non-comparable. Assuming the lottery isn’t fixed, everyone has the same chance of winning in every drawing.

With baseball, however, the pitchers can throw a batter unhittable junk. Note that in the 2000 season, Barry Bonds hit 49 home runs and was walked 117 times. The next season he hit 73 home runs but drew 177 walks. And in 2002 Bonds was walked 198 times.

The point is clear. The more home runs you hit, the fewer good pitches you will see, and your odds of hitting another home run will decline accordingly.

I was going to look at probability and confidence intervals and Monte Carlo statistics but…Pedroia has only hit 109 home runs in his entire career. And only 7 last year, so he seems to be slowing down even from the dizzying heights of his 2011 season (21).

But for fun, I will try to figure out the chances of him hitting 100 in a year. This may take a while.

Although an argument could be made that OPs chances of winning the lottery increase according to every ticket he buys. So by using your (perfectly valid) argument, the question is now “Will the chances of Pedroia seeing good pitches later in the season decrease at a proportional rate that OPs chances increase by buying tens of thousands of tickets”

Say if OP gets a new ticket/number combination for every good pitch Pedroia sees throughout the whole season, then what are the chances?

I conked out when I got to “in the trillions-to-one” for Pedroia hitting 100 HRs in a season. Someone else will have to take it up for me.

Did you buy a ticket? You can’t win if you don’t play.

Let’s crunch some numbers here. Pedroia’s been getting between 550 and 650 at bats per season – round it off to 600.

Assume for the sake of argument that he gets five pitches per AB, meaning he’ll see 3,000 pitches per season.

To get to 100 home runs he’d need one dinger for every 30 pitches. Oddly enough, the chances of winning any prize in the lottery are 1:32. Close enough that we’ll call them equal.

Now figure that once he gets to, let’s say, 65 home runs, the pitchers get fed up with him and start giving junk and only junk. He’s already seen 1,950 pitches. If the pitchers now walk him half the time he gets up there, he’ll now need to connect once every 15 pitches – double his previous rate.

So if the OP doubles his lottery ticket purchase, he should have better odds, right? Not necessarily. By buying 20 tickets, he’ll get to a nearly 50% chanceof winning something (not the jackpot, but something.) After that, however, the returns start to diminish.

Accordingly, Pedroia’s best chance to hit 100 home runs, is to hit all of them in the first half of the season, while the OP’s best return on his lottery investment is to buy about 20 tickets, but no more.

Trillions-to-one? Ouch. This is a former MVP you’re talking about! Ok, let’s up the odds: what are the chances that any player will hit 100 HRs this season?

I agree with a point that a couple of Dopers have already raised: if a player is on pace to hit 100 HRs nobody is going to pitch to him. The year Bonds juiced his way to 73 HRs he was walked so many times that almost half his hits were homers. Of course Bonds didn’t have Big Pappi hitting behind him. What’s interesting, though, is that according to his 2001 season splits there’s no evidence that pitchers threw him more junk as the season went along. He hit 16 HRs in Sept/Oct which is one short of his high/month. His BBs/month are pretty consistent. (One crazy stat is that in April, 11 out of 18 hits were HRs with 5 doubles. His singles/HR ratio was 2/11!)

This. Assuming the OP plays the lottery, it is far more likely that he will win than that Pedrioa will hit 100HRs.

However, since I don’t play the lottery, the odds that Pedrioa will hit hit 100 HRs is more likely than my winning the lottery by an … undefinable amount.

I don’t think Pedroia will hit 100 homers this year.

What team wouldn’t want a five-tool second baseman? Ryno (Cubs 2nd base) hit 282 homers (not in one season :b).

But no way he keeps that pace up after the All-star break. They’ll pitch around him. Pitch *at *him. He gets nada to hit if he reaches 40 homers.

Sure you can. I never buy a ticket, but if I see a discarded ticket I’ll pick it up and check it. Long shot; sure, but long shots sometimes come through.

I’ll allow it.

My guess is winning the lottery because Pedroia will always come up short.

Just to update the statistics, Pedroia has 5 home runs in 27 games. That puts him on pace to hit 30 home runs in 2015.

To get to 100 HR in the next 135 games, (continuing his average of 4.5 plate appearances per game) he’ll need to hit a home run once every 6.39 plate appearances. That’s slightly better than two homers for every three games.

Looking back at Barry Bonds’ 2001 record, it appears he was only able to pace at least two homers in three games a total of nine times throughout the season. To get to 100 Pedroia will need to do it 45 times over the rest of this season.

My advice, swing at first pitches.

David Ortiz (I think) once said that Pedroia was such a good fielder because Pedroia is so short it was impossible for a grounder to go through his legs.