They have only lost once in 12 games in any form of cricket in 2017.
As well as reaching the One-Day Cup semi-finals, four straight Championship wins adds up to their best start since the title-winning year of 1964.
"Twelve months ago we were playing pretty similar cricket and hadn't won a game," 26-year-old Leach said.
"This time, we've managed to kill teams off when we've put ourselves in a position to win. Four from four shows that."
Director of cricket Steve Rhodes made the big decision last September to change his captain, replacing Daryl Mitchell with Leach.
"We're trying to enjoy our successes. Equally we're making sure we keep putting in the hard yards to win games," Rhodes told BBC Hereford & Worcester.
"Apart from one bad day at Old Trafford, it has been an amazing effort.
"The bowlers are sharing the wickets around, the batsmen are dovetailing and sharing the runs and we've been excellent in the field."
Going back to the final two County Championship games of last season under Mitchell's captaincy, Worcestershire have won six on the trot - the county's best run since seven straight Championship victories in July and August 1961.
That six-game winning run started last September at Hove when, inspired by the new arrival of West Indian fast bowler Miguel Cummins, who took 12 wickets in the match, Worcestershire beat Sussex by 11 runs.
Now they must go to Hove again on Friday for another meeting with a Sussex side who have already this season used five foreign-born players in Championship Division Two, Jofra Archer (Barbados) and Steve Magoffin (Australia), as well as their three South Africans, Stiaan Van Zyl, Vernon Philander and David Wiese.
"They're an interesting side with quite an international flavour to them as they're got quite a few overseas players," said Rhodes, who has never been an advocate of signing Kolpak players.
"We're a small club and we like to play our young academy players. We don't venture off too much with the non-English players."
Worcestershire have used just one overseas player in Championship matches this season, all-rounder John Hastings.
He played in the first two games before being replaced by fellow Australian Nathan Lyon after Hastings was called up for the Champions Trophy.
In only his second first-class appearances in two months, since Australia lost their series 2-1 to India in March, Lyon bowled 29 overs in the second innings at Northampton to take 3-94 - and Rhodes hopes the 29-year-old spinner has bowled himself into some form.
"It was really important to get overs under his belt and blow any cobwebs away," said Rhodes.
"Young Josh Tongue also showed he's got some good pace at Northampton and the way our batsmen are sharing the runs around, it wouldn't surprise me if Tom Fell now gets a good score down at Hove.
"We're going to find it quite tough. In their own backyard, they're not a side that will roll over. We've got to get into a winning position and try to ram it home."
BBC Hereford & Worcester's Dave Bradley
"Worcestershire have had an amazing start, having won their first four County Championship matches of the season for the first time since 1964, when they went on to win the first of their five county titles.
"They also lost only once in eight qualifying games in the One-Day Cup to top the North Group, bypass the quarter-finals and earn a semi-final at New Road for the first time in 13 years.
"All this has been done with basically a home-grown squad. Worcestershire's success is down to hard work and a great team spirit. 10 of the County Championship team have come through the Academy and Second XI structure - and are English.
"Some of these lads have been playing together for a few seasons now. Steve Rhodes and the coaching team at the club have worked hard to develop what they called 'the Worcester way'.
"They have also been very selective about the character of the overseas players they have bought in, Australians John Hastings and Nathan Lyon this season being great examples."
Worcestershire captain Joe Leach says his side's superb winning start to the season is simply down to having found the knack of finishing teams off.