Reference for Yoma 2:2
מַעֲשֶׂה שֶׁהָיוּ שְׁנֵיהֶם שָׁוִין וְרָצִין וְעוֹלִין בַּכֶּבֶשׁ, וְדָחַף אֶחָד מֵהֶן אֶת חֲבֵרוֹ, וְנָפַל וְנִשְׁבְּרָה רַגְלוֹ. וְכֵיוָן שֶׁרָאוּ בֵית דִּין שֶׁבָּאִין לִידֵי סַכָּנָה, הִתְקִינוּ שֶׁלֹּא יְהוּ תוֹרְמִין אֶת הַמִּזְבֵּחַ אֶלָּא בְפַיִס. אַרְבָּעָה פְיָסוֹת הָיוּ שָׁם, וְזֶה הַפַּיִס הָרִאשׁוֹן:
Two (priests) were once running neck to neck up the ramp, when one of them pushed his neighbor, who fell and broke his leg. When beth-din saw that there was risk in this, they instituted that the removal of the ashes be awarded only by lottery [as described above]. There were four lotteries there (in the Temple). [They would assemble for lotteries four times a day, and not conduct all at the same time, in order to raise a din four times, there being a large crowd in the azarah. And this is to the honor of the King, viz. (Psalms 55:15): "In the house of G d we went resoundingly!"] This is the first lottery.