10 Responses to “Lucky Streaks”

1. SJBlonger Says:
   February 9th, 2010 at 11:38 pm

   The inevitable result of some of these "degenerate" streaks, for example Gonzalez's, is that the player's batting average actually declined over the course of the streak.

2. cubbies Says:
   February 10th, 2010 at 1:17 am

   i cant do the math, but there has to be some way to calculate the probability of someone haveing a 20 or 30 or whatever game hitting streak wih a certain average.
   just in case the last sentence didnt make sense: what are the odds of someone with a .350 average over a span of 30 games to have a 30 game hit streak during that time? and how about a .350 hitter for the season? what are the odds that sometime during the year,he will have a 30 game hit streak?

   any ideas?

3. JAD Says:
   February 10th, 2010 at 9:53 am

   Tommy Agee was benched a couple of games about halfway through his 1970 20-game hitting streak for "not hitting."

4. Whiz Says:
   February 10th, 2010 at 4:28 pm

   Cubbies: Of course that depends on the team you're on, since a higher offense team will give you more PA. And walks hurt your chances since H/PA is less than AVG = H/AB.

   But assuming a constant 4 AB per game, your chance of going hitless in a game is (1-AVG)^4, so your chance of getting at least one hit in a game is p = 1-(1-AVG)^4. Then your chance of an n-game hitting streak in a given n games is p^n. For AVG=.350, you have about a 2% chance for n=20 and a 0.27% chance for n=30.

   There are 133 possible 30 game streaks in a 162-game season, but you can't just multiply the probablity p by 133 because of correlations. The proper formula for the probability of at least one streak of at least n-games long in an N-game season is complicated (it can be done recursively), but an approximate formula is p^n [(N-n)*(1-p)+1], where p is the probability of getting at least one hit in game. For n=30, N=162 and AVG=.350, I get about a 6.7% chance of a 30-game hitting streak in a season. For a 20-game streak I get about a 52% chance (the exact number is more like 42%). BTW, for a 56-game streak, a .350 hitter would have about a .033%, or about 1 in 3000, chance -- for a .400 hitter, it would be .62%, or about 1 in 160. There is a website that has a hitting streak calculator, http://www.bumblebeagle.org/horsehide/hitstreaks.html I used it for the exact results.

   Of course, not all games have 4 AB -- if you only get 2 or 3 official AB in a game it will hurt your chances. Also, facing a tough pitcher will reduce your chance in one game of continuing the streak, which will lower your chances also.

5. bdunc8 Says:
   February 10th, 2010 at 4:38 pm

   Dear Cubbies,
   Let's assume this player is a .350 hitter, plays all 162 games, and gets 4 at bats per game.

   P(getting a hit in any given at bat) = .350
   P(not getting a hit in any given at bat) = 1-.350 = .650
   P(getting no hits in a game) = (.650)^4 = .179
   P(getting at least one hit in a game) = 1-.179 = .821
   P(getting at least one hit in 30 games in a row) = (.821)^30 = .003

   This player could have a 30 game hit streak from games 1-30, 2-31, ... , 133-162. So, there are 133 different 30 game stretches in a season.

   P(having a 30 game hit streak in a season) = (.003)*(133) = .365

   So, this player has a 36.5% chance.

   Love,
   bdunc8

6. bdunc8 Says:
   February 10th, 2010 at 4:48 pm

   Oops...Whiz, can you explain a little more why you can't simply multiply (.003)*(133)?

7. Whiz Says:
   February 10th, 2010 at 5:37 pm

   Basically, because games 1-30, 2-31, etc., are overlapping and are not independent events.

   You can convince yourself that multiplying by the number of possible streaks a season is not correct by the following example.

   Assume your chance of getting a hit is .500 in a game. The prob. of a 2-game streak in a given set of 2 games is, naturally, .25. There are 2 such 2-game streaks possible (1-2 and 2-3), so simple multiplication gives a 50% chance of a 2-game streak. But if you consider the eight possible results for the 3 games (xxx, xx-, -xx, -x-, x-x, x--, --x, ---, where x is a game with a hit and - is one without), you see there are only 3 streaks of at least two games out of 8 possible outcomes, or a 37.5% chance.

   BTW, the approximate formula I gave slightly overestimates the probability for a season because it double counts seasons where there might be more than one such streak in a season, but for rare events (long streaks) the deviation from the correct answer is small.

8. bdunc8 Says:
   February 10th, 2010 at 6:01 pm

   Got it. Thanks.

9. eorns Says:
   February 10th, 2010 at 8:45 pm

   I noticed that John Kruk had a 19-game streak despite only 63 AB in those games (3.3/G). Tough to do also because it included a pinch hitting appearance early in the streak. Do we know the longest streak that included a batter as a PH?

10. Friday Links (12 Feb 10) – Ducksnorts Says:
    February 12th, 2010 at 9:11 am

    [...] Lucky Streaks (Baseball-Reference). Raphy highlights some fun hitting streaks. Several Padres are represented, including Tony Gwynn (duh), Bobby Brown, and Jeff Gardner. Hmmm, which of these names is not like the other? [...]