- Bats Left, Throws Right
- Height 6' 2", Weight 194 lb.
He debuted in the Extraliga at age 16, going 1 for 3 for Technika Brno in 2003. In 2004, he hit .130/.218/.159 and had a 0-5, 4.71 record. During 2005, he hit .167/.298/.187 and had a 0-5, 6.78 record. Mráz improved to .224/.379/.289 and 1-4, 3.28 in 2006; his 52 strikeouts were 8th in the circuit. In 2007, Daniel hit .275/.307/.314 and had a 5-2, 3.83 record. His 49 strikeouts were 9th-best in the Extraliga. Mráz batted .255/.340/.426 in 2008 and went 1-2 with a 2.00 ERA. He pitched for the Czech team in the 2008 World University Championship, going 0-1 with a 5.00 ERA.
He was 5-5 with a save and a 3.15 ERA in 2009 and hit .220. He was 8th in strikeouts (64, between Petr Minařík and Vojtěch Jelínek). In 2010, he was 5- 2with a 3.18 ERA and hit .346/.407/.474. He tied Jelínek and Martin Schneider for 5th in wins, was 5th in strikeouts and 9th in ERA (between Marian Gajdoš and Vojtěch Papež). He batted .364/.475/.455 in the postseason, going 2-1 with a 4.66 ERA and 28 K in 19 1/3 IP. He was 4th in the postseason in OBP and strikeouts.
Mráz was 3-4 with two saves and a 2.70 ERA, hit .394/.492/.519, stole 14 bases without being caught and scored 29 runs in 31 games in an excellent two-way campaign in 2011. He was 8th in average (between Alex Derhak and Tomáš Polanský), 4th in ERA (between Jan Blažek and Matěj Hušek), 9th in strikeouts (61, between Blažek and Jakub Černík), 3rd in saves, 4th in steals, tied for 8th in OBP with Polanský and tied for 7th in walks (21, even with Pavel Budský). In the postseason, he was 2-0 with a 5.79 ERA and hit .419/.526/.516. He led in runs (12, 3 over Derhak) and hits (13, tied with Derhak), was second to Derhak in average and OBP, was second to Polanský in walks (8 for 7), was third in total bases (16) and was second in wins (behind teammate Roger Deago). In the finale of the championship, he topped Minařík and Draci Brno, 6-5, to end a historic run of 16 straight titles by Draci Brno. Technika Brno had won the prior title in 1994 before Draci Brno started its run.
In 2012, Daniel again was an offensive sparkplug (.316/.430/.496) but struggled on the hill this time (2-2, 5.58). He tied for 8th in the loop in homers (5), tied Schneider for 4th in walks (25), led in runs (6 ahead of Martin Drong and Matthew Lawman) and tied Drong and Schneider for the most steals (22, caught only twice). He hit .450/.478/.1000 in the postseason and was 1-0 with a 8.03 ERA. He tied for second in home runs (3, one behind Jan Drábek), led in slugging and was 3rd in average. He hit .231/.333/.385 in the 2012 European Cup, going 0-1 with a 5.40 ERA, losing his lone decision to DOOR Neptunus.
He did not pitch in 2013, hitting .358/.483/.425 with 38 runs in 32 games and swiping 26 bases in 27 tries. The Technika Brno star tied Jan Utěšený for 8th in the league in hits (38), was 6th in OBP, 7th in walks (23), led in steals again (6 over Drong) and tied for third in runs. He was 5 for 15 with 5 walks in the playoffs. In 2014, he produced at a .348/.464/.598 with 41 runs in 35 games, 8 home runs and 16 steals in 17 tries. He tied for 8th in hits (46), 3rd in homers (behind former minor leaguers Jakub Sládek and Matěj Hejma), was 5th in total bases (79, between Petr Čech and Petr Zýma), ranked 7th in slugging, tied Přemek Chroust for 3rd in walks (27), was 8th in OBP, tied for 7th in RBI (29), tied Jakub Ondráček for 3rd in steals and tied Jakub Malik for third in runs. Pitching again after a year off, he was 2-2 with four saves and a 3.82 ERA, striking out 41 in 32 2/3 IP. He tied for second in saves, two behind Jan Tomek.
Making his Czech senior national team debut in the 2014 European Championship, he replaced Hejma in center late in a 17-2 romp over the Greek national team. He singled off Andy Orfanakos and came home on a hit by Drábek. He started on the mound against Spain, going 5 innings (8 H, 2 BB, 5 R, 4 ER, 4 K) before Jan Novák relieved; the Czechs lost, 9-2. He next pinch-ran for DH Drábek in a 14-3 mercy rule win over France, scoring on a hit by Michal Ondráček. He stayed in at DH and fanned against Yoann Vaugelade. Finally, he relieved Minařík versus Germany and turned in excellent work, retiring all 8 batters and fanning four in a 5-2 loss.
Mráz's batting line in 2015 was .392/.497/.669 with 44 runs and 36 RBI in 33 games in 2015, stealing 21 bases without being caught. He was 4-4 with 3 saves and a 3.79 ERA on the hill, fanning 65 in 61 2/3 IP. He was 6th in the league in OBP, 8th in average (between Jiří Marek and Daniel Vavruša), 9th in slugging, 6th in hits (51), tied Čech for 3rd in doubles (12), tied for 3rd in triples (3), 10th in home runs (6), 6th in total bases (87), tied Sládek for first in runs, 6th in RBI, 3rd in walks (behind Chroust and Jakub Ondráček), tied Boris Bokaj and Minařík for 7th in strikeouts, tied Nate O'Bryan for 3rd in saves and was second to Tomek in percentage of batters struck out (25%). In the postseason, he batted .394/.459/.485 with 8 runs and 8 games, going 1-1 with a save and a 3.00 ERA. He was second in hits (13, one behind Petr Síla), tied for 3rd in runs and tied Hejma for 6th in total bases (16).
In March 2016, he got a crucial start for the Czechs in the 2017 World Baseball Classic Qualifiers in the semifinals against Nicaragua. Facing a much stronger baseball power historically, he tossed shutout ball for the first four innings but allowed 2 runs (1 earned) in the 5th before Alex Sogard relieved with two outs. He had allowed 3 hits and 4 walks while fanning two, exiting with a 3-2 lead; the Czechs wound up falling in a tight extra inning game.