# Jaro–Winkler distance

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In computer science and statistics, the **Jaro–Winkler distance** (Winkler, 1990) is a measure of similarity between two strings. It is a variant of the **Jaro distance** metric (Jaro, 1989, 1995), a type of string edit distance, and was developed in the area of record linkage (duplicate detection) (Winkler, 1990). The higher the Jaro–Winkler distance for two strings is, the more similar the strings are. The Jaro–Winkler distance metric is designed and best suited for short strings such as person names. The score is normalized such that 0 equates to no similarity and 1 is an exact match.

## Definition

The Jaro distance of two given strings and is

where:

Two characters from and respectively, are considered *matching* only if they are the same and not farther than .

Each character of is compared with all its matching
characters in . The number of matching (but different sequence order) characters
divided by 2 defines the number of *transpositions*.
For example, in comparing CRATE with TRACE, only 'R' 'A' 'E' are the matching characters, i.e. m=3. Although 'C', 'T' appear in both strings, they are farther than 1, i.e., floor(5/2)-1=1. Therefore, t=0 . In DwAyNE versus DuANE the matching letters are already in the same order D-A-N-E, so no transpositions are needed.

Jaro–Winkler distance uses a prefix scale which gives more favourable ratings to strings that match from the beginning for a set prefix length . Given two strings and , their Jaro–Winkler distance is:

where:

- is the Jaro distance for strings and
- is the length of common prefix at the start of the string up to a maximum of 4 characters
- is a constant scaling factor for how much the score is adjusted upwards for having common prefixes. should not exceed 0.25, otherwise the distance can become larger than 1. The standard value for this constant in Winkler's work is

Although often referred to as a *distance metric*, the Jaro–Winkler distance is actually not a metric in the mathematical sense of that term because it does not obey the triangle inequality [1].

In some implementations of Jaro-Winkler, the prefix bonus is only added when the compared strings have a Jaro distance above a set "boost threshold" . The boost threshold in Winkler's implementation was 0.7.

## Example

*Note that Winkler's "reference" C code differs in at least two ways from published accounts of the Jaro–Winkler metric. First is his use of a typo table (adjwt) and also some optional additional tolerance for long strings.*

Given the strings *MARTHA* and *MARHTA* we find:

We find a Jaro score of:

To find the Jaro–Winkler score using the standard weight , we continue to find:

Thus:

Given the strings *DWAYNE* and *DUANE* we find:

We find a Jaro score of:

To find the Jaro–Winkler score using the standard weight , we continue to find:

Thus:

Given the strings *DIXON* and *DICKSONX* we find:

D | I | X | O | N | |

D | 1 | 0 | 0 | 0 | 0 |

I | 0 | 1 | 0 | 0 | 0 |

C | 0 | 0 | 0 | 0 | 0 |

K | 0 | 0 | 0 | 0 | 0 |

S | 0 | 0 | 0 | 0 | 0 |

O | 0 | 0 | 0 | 1 | 0 |

N | 0 | 0 | 0 | 0 | 1 |

X | 0 | 0 | 0 | 0 | 0 |

We find a Jaro score of:

To find the Jaro–Winkler score using the standard weight , we continue to find:

Thus:

## See also

## References

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