July 17, 2005
Damon at 28
Johnny Damon extended his hit streak to 28 games yesterday, putting him halfway to DiMaggio's magic number of 56. This is when hit streak get interesting to me; all you have to do at this point is repeat what you just did! :-) Notice Damon has played 29 games during the streak, but he did not bat on 6/22 so the game does not count against the streak.
One thing that helps Damon is the number of plate appearances he's getting. During the streak, he averages 4.8 PA per game. The more you come to the plate in a game, the more likely you are to get a hit.
When I work on hitting streaks, I like to use a statistic I call hit average, hits divided by plate appearance. It's the probability that you'll get a hit once you step to the plate. Wade Boggs and Tony Gwynn had very similar batting averages, but Gwynn had a higher hit average than Boggs because he walked a lot less. This season, Damon has 124 hits in 391 plate appearances for a hit average of .317. That means, if Damon gets one plate appearance in a game, his chance of extending his hit streak is .317.
Chance of Johnny Damon Extending His Hit Streak
| Number of PA | Probability of Extending Streak |
| 1 | .317 |
| 2 | .534 |
| 3 | .681 |
| 4 | .782 |
| 5 | .851 |
| 6 | .898 |
For the season, Damon is averaging 4.8 PA per game. That means, in a 5 game stretch, we would expect Johnny to have four games with five plate appearances and 1 game with four plate appearances. So the probability of hitting in five straight could be approximated as .851^4 * .782 or .41. For 28 games, I'll be a little conservative and use .851^22 * .782^6 (^ means raised to the power). That means the probability of Damon hitting in another 28 straight games is .00657 or about 1 chance in 152.
Remember, the chance of the streak continuing has nothing to do with what's gone on before. At the start of the streak, Damon had a .000043 chance of going 56 games. But every game he extends the chain makes the rest of the streak more likely.
The next milestone is DiMaggio's Boston record; Dom DiMaggio that is. The Little Professor hit in 34 straight for the Red Sox in 1949. Boggs couldn't top that; we'll see if Damon can.
Posted by David Pinto at
08:17 AM
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What was Nomar's Hit Average back during his 30 game hit streak? Was it better or worse than Damon's current one?
"the chance of the streak continuing has nothing to do with what's gone on before" ...
this assumes that plate appearances, day to day, are a set of independent events. from anecdotal evidence, ie baseball players claiming "i'm seeing the ball really well right now" or "i'm pressing" or "i need to shorten my swing", i doubt that assumption is strictly true.
You also have to wonder if the media attention and pressure on the streak have anything to do with a streak continuing.
You are assuming that Damon's "hit average" is independent of the number of PA's he gets. That is not necessarily true. Suppose he gets only 3 PA's in a game. There are 3 possible explanations. The game may have been shortened by weather or something else. Or Johnny may have left the game early due to injury or for some other reason. In these situations, independence is a reasonable assumption. But if he played a normal 9 inning game, then the only explanation for his getting only 3 PA's is that the opposing pitcher threw a perfect game, in which case his hit rate for that game had to be 0! (OK, there are a couple ways he could have gotten a hit even though only 27 batters came to the plate: he could have been doubled up or thrown out on the bases. So his potential hit average isn't quite 0, but it is very close.)
The opposite is true if he gets 6 or more PA's. If it's an extra inning game, independence may be a reasonable assumption. But if it is a regulation game, that means the Red Sox had at least 19 baserunners. What are the odds of that happening without their leadoff hitter getting any hits?
With the Day by Day Database it should be easy to compute Johnny's hit average by Number of PA's.
Don't ask me about statistical independence in hitting streaks. But Damon just extended the streak to 29 games with a double in the eighth. Gave the Fenway faithful something to cheer about despite a 5-1 Yankee lead.
the media will start going crazy after he passes 30 - you'll see...
I ran the numbers while I watched the game tonight.
In 24 games where he got 4 PA's or less, Damon has 24 hits in 88 PA's, a .272 "hit average". He averaged exactly one hit per game here.
In 53 games with exactly 5 PA's (including tonight) he's 79-for-265, a .298 hit average. He averaged 1.5 hits in these games.
Note that both of these averages are considerably below the .317 you used in your calculation.
Here's the kicker. In 7 games where he came up 6 or 7 times he's a remarkable 22-for-43, A .511 HIT AVERAGE!. In long games, he is averaging better than 3 hits per game.
It's also instructive to look at his hit frequency pattern broken down by PA's.
H 4-/ 5 / 6+
0 8 / 5 / 0
1 10/23/ 0
2 4/19/ 2
3 2/ 8 / 2
4 0/ 0 / 3
T 24/53/ 7
In other words, when he has 4 PA's or less he fails to get a hit 1/3 of the time. It's hard to put much of a streak together that way. OTOH, he gets 5 PA's more than twice as often. And in those games he gets at least one hit better than 90% of the time! And in games where he comes up more than 5 times, he's a virtual lock to get a hit, and a good bet to get two or more.